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;; Old version of python array optimization that does not include CSE with let statements
;; serves as a benchmark for adding large expressions to egglog
(ruleset array_api_ruleset)
(sort Int)
(constructor cast_Callable__Int__Int___Int___lambda_i_____i_ (Int Int) Int)
(rewrite (cast_Callable__Int__Int___Int___lambda_i_____i_ __var__i __var___) __var__i :ruleset array_api_ruleset)
(sort TupleInt)
(constructor TupleInt_single (Int) TupleInt)
(sort UnstableFn_Int_Int (UnstableFn (Int) Int))
(constructor TupleInt___init__ (Int UnstableFn_Int_Int) TupleInt)
(constructor Int___init__ (i64) Int)
(rewrite (TupleInt_single __var__i) (TupleInt___init__ (Int___init__ 1) (unstable-fn "cast_Callable__Int__Int___Int___lambda_i_____i_" __var__i)) :ruleset array_api_ruleset)
(constructor cast_Callable__Int___Int___lambda_i__i_ (Int) Int)
(rewrite (cast_Callable__Int___Int___lambda_i__i_ __var__i) __var__i :ruleset array_api_ruleset)
(constructor TupleInt_range (Int) TupleInt)
(rewrite (TupleInt_range __var__stop) (TupleInt___init__ __var__stop (unstable-fn "cast_Callable__Int___Int___lambda_i__i_")) :ruleset array_api_ruleset)
(sort Vec_Int (Vec Int))
(constructor TupleInt_from_vec (Vec_Int) TupleInt)
(constructor index_vec_int (Vec_Int Int) Int)
(rewrite (TupleInt_from_vec __var__vec) (TupleInt___init__ (Int___init__ (vec-length __var__vec)) (unstable-fn "index_vec_int" __var__vec)) :ruleset array_api_ruleset)
(constructor cast_Callable__TupleInt__TupleInt__Int___Int___lambda_other__self__i__Int_if__i_<_self_length____self_i___other_i_-_self_length_____ (TupleInt TupleInt Int) Int)
(sort Boolean)
(constructor Int_if_ (Boolean Int Int) Int)
(constructor Int___lt__ (Int Int) Boolean)
(constructor TupleInt_length (TupleInt) Int)
(constructor TupleInt___getitem__ (TupleInt Int) Int)
(constructor Int___sub__ (Int Int) Int)
(rewrite (cast_Callable__TupleInt__TupleInt__Int___Int___lambda_other__self__i__Int_if__i_<_self_length____self_i___other_i_-_self_length_____ __var__other __var__self __var__i) (Int_if_ (Int___lt__ __var__i (TupleInt_length __var__self)) (TupleInt___getitem__ __var__self __var__i) (TupleInt___getitem__ __var__other (Int___sub__ __var__i (TupleInt_length __var__self)))) :ruleset array_api_ruleset)
(constructor TupleInt___add__ (TupleInt TupleInt) TupleInt)
(constructor Int___add__ (Int Int) Int)
(rewrite (TupleInt___add__ __var__self __var__other) (TupleInt___init__ (Int___add__ (TupleInt_length __var__self) (TupleInt_length __var__other)) (unstable-fn "cast_Callable__TupleInt__TupleInt__Int___Int___lambda_other__self__i__Int_if__i_<_self_length____self_i___other_i_-_self_length_____" __var__other __var__self)) :ruleset array_api_ruleset)
(constructor cast_Callable__Int__Boolean__Int___Boolean___lambda_i__acc__j__acc_|__i_==_j__ (Int Boolean Int) Boolean)
(constructor Boolean___or__ (Boolean Boolean) Boolean)
(constructor Int___eq__ (Int Int) Boolean)
(rewrite (cast_Callable__Int__Boolean__Int___Boolean___lambda_i__acc__j__acc_|__i_==_j__ __var__i __var__acc __var__j) (Boolean___or__ __var__acc (Int___eq__ __var__i __var__j)) :ruleset array_api_ruleset)
(constructor TupleInt_contains (TupleInt Int) Boolean)
(sort UnstableFn_Boolean_Boolean_Int (UnstableFn (Boolean Int) Boolean))
(constructor TupleInt_fold_boolean (TupleInt Boolean UnstableFn_Boolean_Boolean_Int) Boolean)
(constructor FALSE () Boolean)
(rewrite (TupleInt_contains __var__self __var__i) (TupleInt_fold_boolean __var__self (FALSE) (unstable-fn "cast_Callable__Int__Boolean__Int___Boolean___lambda_i__acc__j__acc_|__i_==_j__" __var__i)) :ruleset array_api_ruleset)
(sort NDArray)
(constructor NDArray_size (NDArray) Int)
(sort UnstableFn_Int_Int_Int (UnstableFn (Int Int) Int))
(constructor TupleInt_fold (TupleInt Int UnstableFn_Int_Int_Int) Int)
(constructor NDArray_shape (NDArray) TupleInt)
(constructor Int___mul__ (Int Int) Int)
(rewrite (NDArray_size __var__x) (TupleInt_fold (NDArray_shape __var__x) (Int___init__ 1) (unstable-fn "Int___mul__")) :ruleset array_api_ruleset)
(constructor unique_values (NDArray) NDArray)
(sort TupleValue)
(constructor NDArray_vector (TupleValue) NDArray)
(sort Value)
(constructor possible_values (Value) TupleValue)
(constructor NDArray_index (NDArray TupleInt) Value)
(constructor ALL_INDICES () TupleInt)
(rewrite (unique_values __var__a) (NDArray_vector (possible_values (NDArray_index __var__a (ALL_INDICES)))) :ruleset array_api_ruleset)
(constructor Value_isfinite (Value) Boolean)
(constructor Value_int (Int) Value)
(constructor TRUE () Boolean)
(rewrite (Value_isfinite (Value_int __var__i)) (TRUE) :ruleset array_api_ruleset)
(constructor Value_bool (Boolean) Value)
(rewrite (Value_isfinite (Value_bool __var__b)) (TRUE) :ruleset array_api_ruleset)
(sort Float)
(constructor Value_float (Float) Value)
(constructor Float___init__ (f64) Float :cost 3)
(rewrite (Value_isfinite (Value_float (Float___init__ __var__f))) (TRUE) :when ((!= __var__f NaN)) :ruleset array_api_ruleset)
(constructor isfinite (NDArray) NDArray)
(sort OptionalIntOrTuple)
(constructor sum (NDArray OptionalIntOrTuple) NDArray)
(constructor OptionalIntOrTuple_none () OptionalIntOrTuple)
(constructor NDArray_scalar (Value) NDArray)
(rewrite (isfinite (sum __var__arr (OptionalIntOrTuple_none))) (NDArray_scalar (Value_bool (Value_isfinite (NDArray_index __var__arr (ALL_INDICES))))) :ruleset array_api_ruleset)
(constructor assume_value_one_of (NDArray TupleValue) NDArray)
(rewrite (NDArray_shape (assume_value_one_of __var__x __var__vs)) (NDArray_shape __var__x) :ruleset array_api_ruleset)
(sort DType)
(constructor NDArray_dtype (NDArray) DType)
(rewrite (NDArray_dtype (assume_value_one_of __var__x __var__vs)) (NDArray_dtype __var__x) :ruleset array_api_ruleset)
(rule ((= __var__v (NDArray_index (assume_value_one_of __var__x __var__vs) __var__idx)))
((union __var__v (NDArray_index __var__x __var__idx))
(union (possible_values __var__v) __var__vs))
:ruleset array_api_ruleset )
(constructor assume_isfinite (NDArray) NDArray)
(rewrite (NDArray_shape (assume_isfinite __var__x)) (NDArray_shape __var__x) :ruleset array_api_ruleset)
(rewrite (NDArray_dtype (assume_isfinite __var__x)) (NDArray_dtype __var__x) :ruleset array_api_ruleset)
(rewrite (NDArray_index (assume_isfinite __var__x) __var__ti) (NDArray_index __var__x __var__ti) :ruleset array_api_ruleset)
(rewrite (Value_isfinite (NDArray_index (assume_isfinite __var__x) __var__ti)) (TRUE) :ruleset array_api_ruleset)
(constructor assume_shape (NDArray TupleInt) NDArray)
(rewrite (NDArray_shape (assume_shape __var__x __var__shape)) __var__shape :ruleset array_api_ruleset)
(rewrite (NDArray_dtype (assume_shape __var__x __var__shape)) (NDArray_dtype __var__x) :ruleset array_api_ruleset)
(rewrite (NDArray_index (assume_shape __var__x __var__shape) __var__idx) (NDArray_index __var__x __var__idx) :ruleset array_api_ruleset)
(constructor assume_dtype (NDArray DType) NDArray)
(rewrite (NDArray_dtype (assume_dtype __var__x __var__dtype)) __var__dtype :ruleset array_api_ruleset)
(rewrite (NDArray_shape (assume_dtype __var__x __var__dtype)) (NDArray_shape __var__x) :ruleset array_api_ruleset)
(rewrite (NDArray_index (assume_dtype __var__x __var__dtype) __var__idx) (NDArray_index __var__x __var__idx) :ruleset array_api_ruleset)
(sort IndexKey)
(constructor NDArray___getitem__ (NDArray IndexKey) NDArray)
(constructor IndexKey_int (Int) IndexKey)
(rewrite (NDArray___getitem__ __var__x (IndexKey_int __var__i)) (NDArray_scalar (NDArray_index __var__x (TupleInt_single __var__i))) :ruleset array_api_ruleset)
(sort OptionalBool)
(constructor reshape (NDArray TupleInt OptionalBool) NDArray)
(rule ((= __a (reshape __var__x __var__shape __var__copy)))
((NDArray_shape __var__x)
(TupleInt_length (NDArray_shape __var__x)))
:ruleset array_api_ruleset )
(rule ((reshape __var__x __var__shape __var__copy))
((TupleInt_length __var__shape)
(TupleInt___getitem__ __var__shape (Int___init__ 0)))
:ruleset array_api_ruleset )
(rewrite (reshape __var__x __var__shape __var__copy) __var__x :when ((= (TupleInt_length (NDArray_shape __var__x)) (Int___init__ 1)) (= (TupleInt_length __var__shape) (Int___init__ 1)) (= (TupleInt___getitem__ __var__shape (Int___init__ 0)) (Int___init__ -1))) :ruleset array_api_ruleset)
(constructor TupleValue_length (TupleValue) Int)
(rewrite (NDArray_shape (NDArray_vector __var__vs)) (TupleInt_single (TupleValue_length __var__vs)) :ruleset array_api_ruleset)
(constructor Value_dtype (Value) DType)
(constructor TupleValue___getitem__ (TupleValue Int) Value)
(rewrite (NDArray_dtype (NDArray_vector __var__vs)) (Value_dtype (TupleValue___getitem__ __var__vs (Int___init__ 0))) :ruleset array_api_ruleset)
(rewrite (NDArray_index (NDArray_vector __var__vs) __var__ti) (TupleValue___getitem__ __var__vs (TupleInt___getitem__ __var__ti (Int___init__ 0))) :ruleset array_api_ruleset)
(constructor TupleInt_EMPTY () TupleInt)
(rewrite (NDArray_shape (NDArray_scalar __var__v)) (TupleInt_EMPTY) :ruleset array_api_ruleset)
(rewrite (NDArray_dtype (NDArray_scalar __var__v)) (Value_dtype __var__v) :ruleset array_api_ruleset)
(rewrite (NDArray_index (NDArray_scalar __var__v) (TupleInt_EMPTY)) __var__v :ruleset array_api_ruleset)
(constructor any (NDArray) NDArray)
(constructor TupleValue_includes (TupleValue Value) Boolean)
(constructor Value_to_truthy_value (Value) Value)
(rewrite (any __var__x) (NDArray_scalar (Value_bool (TupleValue_includes (possible_values (Value_to_truthy_value (NDArray_index __var__x (ALL_INDICES)))) (Value_bool (TRUE))))) :ruleset array_api_ruleset)
(constructor NDArray___lt__ (NDArray NDArray) NDArray)
(constructor Value___lt__ (Value Value) Value)
(constructor broadcast_index (TupleInt TupleInt TupleInt) TupleInt)
(constructor broadcast_shapes (TupleInt TupleInt) TupleInt)
(rewrite (NDArray_index (NDArray___lt__ __var__x __var__y) __var__idx) (Value___lt__ (NDArray_index __var__x (broadcast_index (NDArray_shape __var__x) (broadcast_shapes (NDArray_shape __var__x) (NDArray_shape __var__y)) __var__idx)) (NDArray_index __var__y (broadcast_index (NDArray_shape __var__y) (broadcast_shapes (NDArray_shape __var__x) (NDArray_shape __var__y)) __var__idx))) :ruleset array_api_ruleset)
(constructor NDArray___truediv__ (NDArray NDArray) NDArray)
(constructor Value___truediv__ (Value Value) Value)
(rewrite (NDArray_index (NDArray___truediv__ __var__x __var__y) __var__idx) (Value___truediv__ (NDArray_index __var__x (broadcast_index (NDArray_shape __var__x) (broadcast_shapes (NDArray_shape __var__x) (NDArray_shape __var__y)) __var__idx)) (NDArray_index __var__y (broadcast_index (NDArray_shape __var__y) (broadcast_shapes (NDArray_shape __var__x) (NDArray_shape __var__y)) __var__idx))) :ruleset array_api_ruleset)
(rewrite (NDArray_index (NDArray_scalar __var__v) __var__idx) __var__v :ruleset array_api_ruleset)
(constructor astype (NDArray DType) NDArray)
(constructor Value_astype (Value DType) Value)
(rewrite (NDArray_index (astype __var__x __var__dtype) __var__idx) (Value_astype (NDArray_index __var__x __var__idx) __var__dtype) :ruleset array_api_ruleset)
(relation greater_zero (Value))
(sort TupleNDArray)
(constructor TupleNDArray___getitem__ (TupleNDArray Int) NDArray)
(constructor unique_counts (NDArray) TupleNDArray)
(rule ((= __var__v (NDArray_index (TupleNDArray___getitem__ (unique_counts __var__x) (Int___init__ 1)) __var__idx)))
((greater_zero __var__v))
:ruleset array_api_ruleset )
(rule ((greater_zero __var__v)
(= __var__v1 (Value_astype __var__v __var__dtype)))
((greater_zero __var__v1))
:ruleset array_api_ruleset )
(rule ((= __var__v (Value_float (Float___init__ __var__f)))
(> __var__f 0.0))
((greater_zero __var__v))
:ruleset array_api_ruleset )
(rule ((= __var__v (Value_int (Int___init__ __var__i)))
(> __var__i 0))
((greater_zero __var__v))
:ruleset array_api_ruleset )
(rule ((greater_zero __var__v)
(greater_zero __var__v1)
(= __var__v2 (Value___truediv__ __var__v __var__v1)))
((greater_zero __var__v2))
:ruleset array_api_ruleset )
(rule ((greater_zero __var__v)
(= __var__v1 (Value___lt__ __var__v (Value_int (Int___init__ 0)))))
((union __var__v1 (Value_bool (FALSE))))
:ruleset array_api_ruleset )
(constructor TupleValue___init__ (Value) TupleValue)
(rewrite (possible_values (Value_bool __var__b)) (TupleValue___init__ (Value_bool __var__b)) :ruleset array_api_ruleset)
(rule ((= __var__v1 (Value_astype __var__v __var__dtype))
(greater_zero __var__v))
((greater_zero __var__v1))
:ruleset array_api_ruleset )
(constructor TupleNDArray_length (TupleNDArray) Int)
(constructor svd (NDArray Boolean) TupleNDArray)
(rewrite (TupleNDArray_length (svd __var__x __var__full_matrices)) (Int___init__ 3) :ruleset array_api_ruleset)
(constructor unique_inverse (NDArray) TupleNDArray)
(rewrite (TupleNDArray_length (unique_inverse __var__x)) (Int___init__ 2) :ruleset array_api_ruleset)
(rewrite (TupleNDArray___getitem__ (unique_inverse __var__x) (Int___init__ 0)) (unique_values __var__x) :ruleset array_api_ruleset)
(constructor ndarray-abs (NDArray) NDArray)
(constructor Float_abs (Float) Float)
(rewrite (ndarray-abs (NDArray_scalar (Value_float __var__f))) (NDArray_scalar (Value_float (Float_abs __var__f))) :ruleset array_api_ruleset)
(rewrite (TupleNDArray_length (unique_counts __var__x)) (Int___init__ 2) :ruleset array_api_ruleset)
(rewrite (sum (TupleNDArray___getitem__ (unique_counts __var__x) (Int___init__ 1)) (OptionalIntOrTuple_none)) (NDArray_scalar (Value_int (NDArray_size __var__x))) :ruleset array_api_ruleset)
(rewrite (sum (astype (TupleNDArray___getitem__ (unique_counts __var__x) (Int___init__ 1)) __var__dtype) (OptionalIntOrTuple_none)) (astype (NDArray_scalar (Value_int (NDArray_size __var__x))) __var__dtype) :ruleset array_api_ruleset)
(rewrite (NDArray_dtype (astype __var__x __var__dtype)) __var__dtype :ruleset array_api_ruleset)
(constructor DType_float64 () DType)
(rewrite (astype (NDArray_scalar (Value_int (Int___init__ __var__i))) (DType_float64)) (NDArray_scalar (Value_float (Float___init__ (to-f64 __var__i)))) :ruleset array_api_ruleset)
(sort OptionalInt)
(constructor concat (TupleNDArray OptionalInt) NDArray)
(constructor TupleNDArray___init__ (NDArray) TupleNDArray)
(constructor OptionalInt_none () OptionalInt)
(rewrite (concat (TupleNDArray___init__ __var__x) (OptionalInt_none)) __var__x :ruleset array_api_ruleset)
(rewrite (unique_values (unique_values __var__x)) (unique_values __var__x) :ruleset array_api_ruleset)
(rewrite (sum (NDArray___truediv__ __var__x (NDArray_scalar __var__v)) (OptionalIntOrTuple_none)) (NDArray___truediv__ (sum __var__x (OptionalIntOrTuple_none)) (NDArray_scalar __var__v)) :ruleset array_api_ruleset)
(constructor NDArray_ndim (NDArray) Int)
(sort OptionalDType)
(sort OptionalDevice)
(constructor asarray (NDArray OptionalDType OptionalBool OptionalDevice) NDArray)
(constructor OptionalDevice_none () OptionalDevice)
(rewrite (NDArray_ndim (asarray __var__a __var__d __var__ob (OptionalDevice_none))) (NDArray_ndim __var__a) :ruleset array_api_ruleset)
(constructor OptionalDType_none () OptionalDType)
(constructor OptionalBool_none () OptionalBool)
(rewrite (asarray __var__a (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none)) __var__a :ruleset array_api_ruleset)
(constructor TupleNDArray___add__ (TupleNDArray TupleNDArray) TupleNDArray)
(constructor TupleNDArray_EMPTY () TupleNDArray)
(rewrite (TupleNDArray___add__ __var__ti (TupleNDArray_EMPTY)) __var__ti :ruleset array_api_ruleset)
(rewrite (TupleNDArray_length (TupleNDArray___init__ __var__n)) (Int___init__ 1) :ruleset array_api_ruleset)
(rewrite (TupleNDArray_length (TupleNDArray___add__ __var__ti __var__ti2)) (Int___add__ (TupleNDArray_length __var__ti) (TupleNDArray_length __var__ti2)) :ruleset array_api_ruleset)
(rewrite (NDArray_ndim __var__x) (TupleInt_length (NDArray_shape __var__x)) :ruleset array_api_ruleset)
(constructor NDArray_to_value (NDArray) Value)
(rewrite (NDArray_to_value __var__x) (NDArray_index __var__x (TupleInt_EMPTY)) :ruleset array_api_ruleset)
(rewrite (NDArray___truediv__ (NDArray_scalar (Value_float __var__f)) (NDArray_scalar (Value_float __var__f))) (NDArray_scalar (Value_float (Float___init__ 1.0))) :ruleset array_api_ruleset)
(constructor NDArray___sub__ (NDArray NDArray) NDArray)
(rewrite (NDArray___sub__ (NDArray_scalar (Value_float __var__f)) (NDArray_scalar (Value_float __var__f))) (NDArray_scalar (Value_float (Float___init__ 0.0))) :ruleset array_api_ruleset)
(constructor NDArray___gt__ (NDArray NDArray) NDArray)
(rewrite (NDArray___gt__ (NDArray_scalar (Value_float (Float___init__ __var__fi1))) (NDArray_scalar (Value_float (Float___init__ __var__fi2)))) (NDArray_scalar (Value_bool (TRUE))) :when ((> __var__fi1 __var__fi2)) :ruleset array_api_ruleset)
(rewrite (NDArray___gt__ (NDArray_scalar (Value_float (Float___init__ __var__fi1))) (NDArray_scalar (Value_float (Float___init__ __var__fi2)))) (NDArray_scalar (Value_bool (FALSE))) :when ((<= __var__fi1 __var__fi2)) :ruleset array_api_ruleset)
(constructor NDArray_T (NDArray) NDArray)
(rewrite (NDArray_T (NDArray_T __var__x)) __var__x :ruleset array_api_ruleset)
(constructor TupleValue___add__ (TupleValue TupleValue) TupleValue)
(constructor TupleValue_EMPTY () TupleValue)
(rewrite (TupleValue___add__ __var__ti (TupleValue_EMPTY)) __var__ti :ruleset array_api_ruleset)
(rewrite (TupleValue_length (TupleValue_EMPTY)) (Int___init__ 0) :ruleset array_api_ruleset)
(rewrite (TupleValue_length (TupleValue___init__ __var__v)) (Int___init__ 1) :ruleset array_api_ruleset)
(rewrite (TupleValue_length (TupleValue___add__ __var__ti __var__ti2)) (Int___add__ (TupleValue_length __var__ti) (TupleValue_length __var__ti2)) :ruleset array_api_ruleset)
(rewrite (TupleValue___getitem__ (TupleValue___init__ __var__v) (Int___init__ 0)) __var__v :ruleset array_api_ruleset)
(rewrite (TupleValue___getitem__ (TupleValue___add__ (TupleValue___init__ __var__v) __var__ti) (Int___init__ 0)) __var__v :ruleset array_api_ruleset)
(rule ((= __var__v (TupleValue___getitem__ (TupleValue___add__ (TupleValue___init__ __var__v2) __var__ti) (Int___init__ __var__k)))
(> __var__k 0))
((union __var__v (TupleValue___getitem__ __var__ti (Int___init__ (- __var__k 1)))))
:ruleset array_api_ruleset )
(rewrite (TupleValue_includes (TupleValue_EMPTY) __var__v) (FALSE) :ruleset array_api_ruleset)
(rewrite (TupleValue_includes (TupleValue___init__ __var__v) __var__v) (TRUE) :ruleset array_api_ruleset)
(rewrite (TupleValue_includes (TupleValue___init__ __var__v) __var__v2) (FALSE) :when ((!= __var__v __var__v2)) :ruleset array_api_ruleset)
(rewrite (TupleValue_includes (TupleValue___add__ __var__ti __var__ti2) __var__v) (Boolean___or__ (TupleValue_includes __var__ti __var__v) (TupleValue_includes __var__ti2 __var__v)) :ruleset array_api_ruleset)
(constructor DType_int64 () DType)
(rewrite (Value_dtype (Value_int __var__i)) (DType_int64) :ruleset array_api_ruleset)
(rewrite (Value_dtype (Value_float __var__f)) (DType_float64) :ruleset array_api_ruleset)
(constructor DType_bool () DType)
(rewrite (Value_dtype (Value_bool __var__b)) (DType_bool) :ruleset array_api_ruleset)
(constructor Value_to_bool (Value) Boolean)
(rewrite (Value_to_bool (Value_bool __var__b)) __var__b :ruleset array_api_ruleset)
(constructor Value_to_int (Value) Int)
(rewrite (Value_to_int (Value_int __var__i)) __var__i :ruleset array_api_ruleset)
(rewrite (Value_to_truthy_value (Value_bool __var__b)) (Value_bool __var__b) :ruleset array_api_ruleset)
(sort IsDtypeKind)
(constructor isdtype (DType IsDtypeKind) Boolean)
(constructor DType_float32 () DType)
(constructor IsDtypeKind_string (String) IsDtypeKind)
(rewrite (isdtype (DType_float32) (IsDtypeKind_string "integral")) (FALSE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_float64) (IsDtypeKind_string "integral")) (FALSE) :ruleset array_api_ruleset)
(constructor DType_object () DType)
(rewrite (isdtype (DType_object) (IsDtypeKind_string "integral")) (FALSE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_int64) (IsDtypeKind_string "integral")) (TRUE) :ruleset array_api_ruleset)
(constructor DType_int32 () DType)
(rewrite (isdtype (DType_int32) (IsDtypeKind_string "integral")) (TRUE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_float32) (IsDtypeKind_string "real floating")) (TRUE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_float64) (IsDtypeKind_string "real floating")) (TRUE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_object) (IsDtypeKind_string "real floating")) (FALSE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_int64) (IsDtypeKind_string "real floating")) (FALSE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_int32) (IsDtypeKind_string "real floating")) (FALSE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_float32) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_float64) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_object) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_int64) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset)
(rewrite (isdtype (DType_int32) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset)
(constructor IsDtypeKind_NULL () IsDtypeKind)
(rewrite (isdtype __var__d (IsDtypeKind_NULL)) (FALSE) :ruleset array_api_ruleset)
(constructor IsDtypeKind_dtype (DType) IsDtypeKind)
(rewrite (isdtype __var__d (IsDtypeKind_dtype __var__d)) (TRUE) :ruleset array_api_ruleset)
(constructor IsDtypeKind___or__ (IsDtypeKind IsDtypeKind) IsDtypeKind :cost 10)
(rewrite (isdtype __var__d (IsDtypeKind___or__ __var__k1 __var__k2)) (Boolean___or__ (isdtype __var__d __var__k1) (isdtype __var__d __var__k2)) :ruleset array_api_ruleset)
(rewrite (IsDtypeKind___or__ __var__k1 (IsDtypeKind_NULL)) __var__k1 :ruleset array_api_ruleset)
(constructor DType___eq__ (DType DType) Boolean)
(rewrite (DType___eq__ (DType_float64) (DType_float64)) (TRUE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_float64) (DType_float32)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_float64) (DType_int32)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_float64) (DType_int64)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_float64) (DType_object)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_float32) (DType_float64)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_float32) (DType_float32)) (TRUE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_float32) (DType_int32)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_float32) (DType_int64)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_float32) (DType_object)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_int32) (DType_float64)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_int32) (DType_float32)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_int32) (DType_int32)) (TRUE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_int32) (DType_int64)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_int32) (DType_object)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_int64) (DType_float64)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_int64) (DType_float32)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_int64) (DType_int32)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_int64) (DType_int64)) (TRUE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_int64) (DType_object)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_object) (DType_float64)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_object) (DType_float32)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_object) (DType_int32)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_object) (DType_int64)) (FALSE) :ruleset array_api_ruleset)
(rewrite (DType___eq__ (DType_object) (DType_object)) (TRUE) :ruleset array_api_ruleset)
(constructor cast_Callable__UnstableFn_Int__Int___Int___Int___lambda_idx_fn__i__idx_fn_i_+_Int_1___ (UnstableFn_Int_Int Int) Int)
(rewrite (cast_Callable__UnstableFn_Int__Int___Int___Int___lambda_idx_fn__i__idx_fn_i_+_Int_1___ __var__idx_fn __var__i) (unstable-app __var__idx_fn (Int___add__ __var__i (Int___init__ 1))) :ruleset array_api_ruleset)
(rewrite (index_vec_int __var__vs (Int___init__ __var__k)) (vec-get __var__vs __var__k) :ruleset array_api_ruleset)
(rewrite (TupleInt_length (TupleInt___init__ __var__i __var__idx_fn)) __var__i :ruleset array_api_ruleset)
(rewrite (TupleInt___getitem__ (TupleInt___init__ __var__i __var__idx_fn) __var__i2) (unstable-app __var__idx_fn __var__i2) :ruleset array_api_ruleset)
(rewrite (TupleInt_fold (TupleInt___init__ (Int___init__ 0) __var__idx_fn) __var__i __var__f) __var__i :ruleset array_api_ruleset)
(rewrite (TupleInt_fold (TupleInt___init__ (Int___init__ __var__k) __var__idx_fn) __var__i __var__f) (unstable-app __var__f (TupleInt_fold (TupleInt___init__ (Int___init__ (- __var__k 1)) (unstable-fn "cast_Callable__UnstableFn_Int__Int___Int___Int___lambda_idx_fn__i__idx_fn_i_+_Int_1___" __var__idx_fn)) __var__i __var__f) (unstable-app __var__idx_fn (Int___init__ 0))) :when ((!= __var__k 0)) :ruleset array_api_ruleset)
(rewrite (TupleInt_fold_boolean (TupleInt___init__ (Int___init__ 0) __var__idx_fn) __var__b __var__bool_f) __var__b :ruleset array_api_ruleset)
(rewrite (TupleInt_fold_boolean (TupleInt___init__ (Int___init__ __var__k) __var__idx_fn) __var__b __var__bool_f) (unstable-app __var__bool_f (TupleInt_fold_boolean (TupleInt___init__ (Int___init__ (- __var__k 1)) (unstable-fn "cast_Callable__UnstableFn_Int__Int___Int___Int___lambda_idx_fn__i__idx_fn_i_+_Int_1___" __var__idx_fn)) __var__b __var__bool_f) (unstable-app __var__idx_fn (Int___init__ 0))) :when ((!= __var__k 0)) :ruleset array_api_ruleset)
(constructor bottom_indexing (Int) Int)
(rewrite (TupleInt_EMPTY) (TupleInt___init__ (Int___init__ 0) (unstable-fn "bottom_indexing")) :ruleset array_api_ruleset)
(rewrite (Float_abs (Float___init__ __var__f)) (Float___init__ __var__f) :when ((>= __var__f 0.0)) :ruleset array_api_ruleset)
(rewrite (Float_abs (Float___init__ __var__f)) (Float___init__ (neg __var__f)) :when ((< __var__f 0.0)) :ruleset array_api_ruleset)
(constructor Float_rational (BigRat) Float :cost 2)
(rewrite (Float___init__ __var__f) (Float_rational (bigrat (bigint (to-i64 __var__f)) (bigint 1))) :when ((= (to-f64 (to-i64 __var__f)) __var__f)) :ruleset array_api_ruleset)
(constructor Float_from_int (Int) Float)
(rewrite (Float_from_int (Int___init__ __var__i)) (Float_rational (bigrat (bigint __var__i) (bigint 1))) :ruleset array_api_ruleset)
(constructor Float___add__ (Float Float) Float)
(rewrite (Float___add__ (Float___init__ __var__f) (Float___init__ __var__f2)) (Float___init__ (+ __var__f __var__f2)) :ruleset array_api_ruleset)
(constructor Float___sub__ (Float Float) Float)
(rewrite (Float___sub__ (Float___init__ __var__f) (Float___init__ __var__f2)) (Float___init__ (- __var__f __var__f2)) :ruleset array_api_ruleset)
(constructor Float___mul__ (Float Float) Float)
(rewrite (Float___mul__ (Float___init__ __var__f) (Float___init__ __var__f2)) (Float___init__ (* __var__f __var__f2)) :ruleset array_api_ruleset)
(constructor Float___truediv__ (Float Float) Float)
(rewrite (Float___truediv__ (Float_rational __var__r) (Float_rational __var__r1)) (Float_rational (/ __var__r __var__r1)) :ruleset array_api_ruleset)
(rewrite (Float___add__ (Float_rational __var__r) (Float_rational __var__r1)) (Float_rational (+ __var__r __var__r1)) :ruleset array_api_ruleset)
(rewrite (Float___sub__ (Float_rational __var__r) (Float_rational __var__r1)) (Float_rational (- __var__r __var__r1)) :ruleset array_api_ruleset)
(rewrite (Float___mul__ (Float_rational __var__r) (Float_rational __var__r1)) (Float_rational (* __var__r __var__r1)) :ruleset array_api_ruleset)
(rewrite (Int___eq__ (Int___init__ __var__i) (Int___init__ __var__i)) (TRUE) :ruleset array_api_ruleset)
(rule ((= __var__r (Int___eq__ (Int___init__ __var__i) (Int___init__ __var__j)))
(!= __var__i __var__j))
((union __var__r (FALSE)))
:ruleset array_api_ruleset )
(constructor Int___ge__ (Int Int) Boolean)
(rewrite (Int___ge__ (Int___init__ __var__i) (Int___init__ __var__i)) (TRUE) :ruleset array_api_ruleset)
(rule ((= __var__r (Int___ge__ (Int___init__ __var__i) (Int___init__ __var__j)))
(> __var__i __var__j))
((union __var__r (TRUE)))
:ruleset array_api_ruleset )
(rule ((= __var__r (Int___ge__ (Int___init__ __var__i) (Int___init__ __var__j)))
(< __var__i __var__j))
((union __var__r (FALSE)))
:ruleset array_api_ruleset )
(rewrite (Int___lt__ (Int___init__ __var__i) (Int___init__ __var__i)) (FALSE) :ruleset array_api_ruleset)
(rule ((= __var__r (Int___lt__ (Int___init__ __var__i) (Int___init__ __var__j)))
(< __var__i __var__j))
((union __var__r (TRUE)))
:ruleset array_api_ruleset )
(rule ((= __var__r (Int___lt__ (Int___init__ __var__i) (Int___init__ __var__j)))
(> __var__i __var__j))
((union __var__r (FALSE)))
:ruleset array_api_ruleset )
(constructor Int___gt__ (Int Int) Boolean)
(rewrite (Int___gt__ (Int___init__ __var__i) (Int___init__ __var__i)) (FALSE) :ruleset array_api_ruleset)
(rule ((= __var__r (Int___gt__ (Int___init__ __var__i) (Int___init__ __var__j)))
(> __var__i __var__j))
((union __var__r (TRUE)))
:ruleset array_api_ruleset )
(rule ((= __var__r (Int___gt__ (Int___init__ __var__i) (Int___init__ __var__j)))
(< __var__i __var__j))
((union __var__r (FALSE)))
:ruleset array_api_ruleset )
(function Int_i64 (Int) i64 :no-merge)
(rule ((= __var__o (Int___init__ __var__j)))
((set (Int_i64 __var__o) __var__j))
:ruleset array_api_ruleset )
(rewrite (Int___add__ (Int___init__ __var__i) (Int___init__ __var__j)) (Int___init__ (+ __var__i __var__j)) :ruleset array_api_ruleset)
(rewrite (Int___sub__ (Int___init__ __var__i) (Int___init__ __var__j)) (Int___init__ (- __var__i __var__j)) :ruleset array_api_ruleset)
(rewrite (Int___mul__ (Int___init__ __var__i) (Int___init__ __var__j)) (Int___init__ (* __var__i __var__j)) :ruleset array_api_ruleset)
(constructor Int___truediv__ (Int Int) Int)
(rewrite (Int___truediv__ (Int___init__ __var__i) (Int___init__ __var__j)) (Int___init__ (/ __var__i __var__j)) :ruleset array_api_ruleset)
(constructor Int___mod__ (Int Int) Int)
(rewrite (Int___mod__ (Int___init__ __var__i) (Int___init__ __var__j)) (Int___init__ (% __var__i __var__j)) :ruleset array_api_ruleset)
(constructor Int___and__ (Int Int) Int)
(rewrite (Int___and__ (Int___init__ __var__i) (Int___init__ __var__j)) (Int___init__ (& __var__i __var__j)) :ruleset array_api_ruleset)
(constructor Int___or__ (Int Int) Int)
(rewrite (Int___or__ (Int___init__ __var__i) (Int___init__ __var__j)) (Int___init__ (| __var__i __var__j)) :ruleset array_api_ruleset)
(constructor Int___xor__ (Int Int) Int)
(rewrite (Int___xor__ (Int___init__ __var__i) (Int___init__ __var__j)) (Int___init__ (^ __var__i __var__j)) :ruleset array_api_ruleset)
(constructor Int___lshift__ (Int Int) Int)
(rewrite (Int___lshift__ (Int___init__ __var__i) (Int___init__ __var__j)) (Int___init__ (<< __var__i __var__j)) :ruleset array_api_ruleset)
(constructor Int___rshift__ (Int Int) Int)
(rewrite (Int___rshift__ (Int___init__ __var__i) (Int___init__ __var__j)) (Int___init__ (>> __var__i __var__j)) :ruleset array_api_ruleset)
(constructor Int___invert__ (Int) Int)
(rewrite (Int___invert__ (Int___init__ __var__i)) (Int___init__ (not-i64 __var__i)) :ruleset array_api_ruleset)
(rewrite (Int_if_ (TRUE) __var__o __var__b) __var__o :ruleset array_api_ruleset)
(rewrite (Int_if_ (FALSE) __var__o __var__b) __var__b :ruleset array_api_ruleset)
(function Boolean_bool (Boolean) bool :no-merge)
(rule ((= __var__x (TRUE)))
((set (Boolean_bool __var__x) true))
:ruleset array_api_ruleset )
(rule ((= __var__x (FALSE)))
((set (Boolean_bool __var__x) false))
:ruleset array_api_ruleset )
(rewrite (Boolean___or__ (TRUE) __var__x) (TRUE) :ruleset array_api_ruleset)
(rewrite (Boolean___or__ (FALSE) __var__x) __var__x :ruleset array_api_ruleset)
(constructor Boolean___and__ (Boolean Boolean) Boolean)
(rewrite (Boolean___and__ (TRUE) __var__x) __var__x :ruleset array_api_ruleset)
(rewrite (Boolean___and__ (FALSE) __var__x) (FALSE) :ruleset array_api_ruleset)
(constructor Boolean_if_int (Boolean Int Int) Int)
(rewrite (Boolean_if_int (TRUE) __var__i __var__j) __var__i :ruleset array_api_ruleset)
(rewrite (Boolean_if_int (FALSE) __var__i __var__j) __var__j :ruleset array_api_ruleset)
(constructor Boolean___invert__ (Boolean) Boolean)
(rewrite (Boolean___invert__ (TRUE)) (FALSE) :ruleset array_api_ruleset)
(rewrite (Boolean___invert__ (FALSE)) (TRUE) :ruleset array_api_ruleset)
(ruleset ruleset_5218390416)
(constructor NDArray___eq__ (NDArray NDArray) NDArray)
(rewrite (NDArray___eq__ (TupleNDArray___getitem__ (unique_inverse __var__x) (Int___init__ 1)) (NDArray_scalar (Value_int __var__i))) (NDArray___eq__ __var__x (NDArray_scalar (NDArray_index (unique_values __var__x) (TupleInt_from_vec (vec-of __var__i))))) :subsume :ruleset ruleset_5218390416)
(constructor count_values (NDArray NDArray) TupleValue :unextractable)
(rewrite (TupleNDArray___getitem__ (unique_counts __var__x) (Int___init__ 1)) (NDArray_vector (count_values __var__x (unique_values __var__x))) :subsume :ruleset ruleset_5218390416)
(rewrite (count_values __var__x (NDArray_vector (TupleValue___add__ (TupleValue___init__ __var__v) __var__tv))) (TupleValue___add__ (TupleValue___init__ (NDArray_to_value (sum (NDArray___eq__ __var__x (NDArray_scalar __var__v)) (OptionalIntOrTuple_none)))) (count_values __var__x (NDArray_vector __var__tv))) :subsume :ruleset ruleset_5218390416)
(rewrite (count_values __var__x (NDArray_vector (TupleValue___init__ __var__v))) (TupleValue___init__ (NDArray_to_value (sum (NDArray___eq__ __var__x (NDArray_scalar __var__v)) (OptionalIntOrTuple_none)))) :subsume :ruleset ruleset_5218390416)
(constructor std (NDArray OptionalIntOrTuple) NDArray)
(sort IntOrTuple)
(constructor OptionalIntOrTuple_some (IntOrTuple) OptionalIntOrTuple)
(constructor IntOrTuple_int (Int) IntOrTuple)
(constructor ndarray-sqrt (NDArray) NDArray)
(constructor mean (NDArray OptionalIntOrTuple Boolean) NDArray)
(constructor square (NDArray) NDArray)
(rewrite (std __var__x (OptionalIntOrTuple_some (IntOrTuple_int __var__i))) (ndarray-sqrt (mean (square (NDArray___sub__ __var__x (mean __var__x (OptionalIntOrTuple_some (IntOrTuple_int __var__i)) (TRUE)))) (OptionalIntOrTuple_some (IntOrTuple_int __var__i)) (FALSE))) :subsume :ruleset ruleset_5218390416)
(rewrite (mean __var__x (OptionalIntOrTuple_some (IntOrTuple_int __var__i)) (FALSE)) (NDArray___truediv__ (sum __var__x (OptionalIntOrTuple_some (IntOrTuple_int __var__i))) (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape __var__x) __var__i)))) :subsume :ruleset ruleset_5218390416)
(constructor expand_dims (NDArray Int) NDArray)
(rewrite (mean __var__x (OptionalIntOrTuple_some (IntOrTuple_int __var__i)) (TRUE)) (expand_dims (NDArray___truediv__ (sum __var__x (OptionalIntOrTuple_some (IntOrTuple_int __var__i))) (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape __var__x) __var__i)))) __var__i) :subsume :ruleset ruleset_5218390416)
(constructor NDArray___matmul__ (NDArray NDArray) NDArray)
(constructor NDArray_var (String) NDArray :cost 200)
(constructor NDArray___setitem__ (NDArray IndexKey NDArray) NDArray)
(constructor zeros (TupleInt OptionalDType OptionalDevice) NDArray)
(constructor OptionalDType_some (DType) OptionalDType)
(sort Device)
(constructor OptionalDevice_some (Device) OptionalDevice)
(constructor NDArray_device (NDArray) Device)
(sort MultiAxisIndexKey)
(constructor IndexKey_multi_axis (MultiAxisIndexKey) IndexKey)
(sort MultiAxisIndexKeyItem)
(sort Vec_MultiAxisIndexKeyItem (Vec MultiAxisIndexKeyItem))
(constructor MultiAxisIndexKey_from_vec (Vec_MultiAxisIndexKeyItem) MultiAxisIndexKey)
(constructor MultiAxisIndexKeyItem_int (Int) MultiAxisIndexKeyItem)
(sort Slice)
(constructor MultiAxisIndexKeyItem_slice (Slice) MultiAxisIndexKeyItem)
(constructor Slice___init__ (OptionalInt OptionalInt OptionalInt) Slice)
(constructor IndexKey_ndarray (NDArray) IndexKey)
(constructor NDArray___mul__ (NDArray NDArray) NDArray)
(constructor OptionalInt_some (Int) OptionalInt)
(constructor IndexKey_slice (Slice) IndexKey)
(push)
(let $desugar_simplify_1 (NDArray___getitem__ (NDArray___matmul__ (NDArray___sub__ (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") (DType_float64)) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none)) (NDArray___matmul__ (NDArray___truediv__ (astype (TupleNDArray___getitem__ (unique_counts (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none)) (TupleInt_from_vec (vec-of (Int___init__ -1))) (OptionalBool_none)) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 1)) (NDArray_dtype (asarray 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