Module build 

Smart constructors for building derivative expressions — useful when writing a custom Rule, which returns f'(u) as an sqlparser::ast::Expr.

Functions

add

a + b, dropping a structurally-zero operand.

cast_double

Wrap e in a CAST(... AS DOUBLE). Self-delimiting, so it never needs precedence parentheses as an operand.

div

a / b, folding 0 / _ = 0 and a / 1 = a.

finite_num

A numeric literal for a value that might not be finite — the checked counterpart of num. Emits the literal if v is finite, else a typed DiffError::NotImplemented: a non-finite value has no valid SQL literal (inf/NaN are not numbers), so a derivative that would carry one must fail loud, never emit invalid SQL (#33). Use this for every value derived from user input or an arithmetic that can overflow (e.g. ln(base), an out-of-range exponent). This is the single seam through which computed constants become literals.

func

Build an unqualified scalar function call name(args...).

func1

f(x) — a unary call, the common case for chain-rule outer derivatives.

mul

a * b, folding 0 * _ = 0 and 1 * b = b (and the mirror cases).

neg

-a, folding -0 = 0 and -(-e) = e, and parenthesizing a binary operand (-(a + b), -(a / b)), since unary minus binds tighter than either.

one

The constant 1.0 — the derivative of wrt itself.

sign

The mathematical sign of u, as a CASE that behaves identically on every engine:

square

e * e.

sub

a - b, dropping a zero right operand and turning 0 - b into -b.

zero

The constant 0.0 — the derivative of anything independent of wrt.