symbolica 0.20.0

A blazing fast computer algebra system
Documentation 
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use symbolica::{
    atom::AtomCore,
    domains::rational::Q,
    parse,
    poly::evaluate::{BorrowedHornerScheme, InstructionSetPrinter},
};

use symbolica::poly::polynomial::MultivariatePolynomial;
use wide::f64x4;

// a large test polynomial
const SIGMA: &str = "+32*amel2^3*zk^2*xcp3 +32*amel2^3*zk^2*xcp1 -48*amel2^3*zk^2*x1*xcp3 -48*amel2^3*zk^2*x1*xcp1 +32*amel2^4*x5^2*xcp3 +32*amel2^4*x5^2*xcp1 +64*amel2^4*x4*x5*xcp3 -128*amel2^4*x4*x5*xcp2 +64*amel2^4*x4*x5*xcp1 +64*amel2^4*x4^2*xcp3 -128*amel2^4*x4^2*xcp2 +64*amel2^4*x4^2*xcp1 -128*amel2^4*x3*x5*xcp2 +64*amel2^4*x3*x4*xcp3 -128*amel2^4*x3*x4*xcp2 +64*amel2^4*x3*x4*xcp1 +32*amel2^4*x3^2*xcp3 +32*amel2^4*x3^2*xcp1 -64*amel2^4*x1*xcp3 -64*amel2^4*x1*xcp1 +32*amel2^4*x1*x5*xcp3 +32*amel2^4*x1*x5*xcp1 -32*amel2^4*x1*x5^2*xcp3 -32*amel2^4*x1*x5^2*xcp1 +64*amel2^4*x1*x4*xcp3 -192*amel2^4*x1*x4*xcp2 +64*amel2^4*x1*x4*xcp1 -64*amel2^4*x1*x4*x5*xcp3 +128*amel2^4*x1*x4*x5*xcp2 -64*amel2^4*x1*x4*x5*xcp1 -64*amel2^4*x1*x4^2*xcp3 +128*amel2^4*x1*x4^2*xcp2 -64*amel2^4*x1*x4^2*xcp1 +96*amel2^4*x1*x3*xcp3 -192*amel2^4*x1*x3*xcp2 +96*amel2^4*x1*x3*xcp1 +128*amel2^4*x1*x3*x5*xcp2 -64*amel2^4*x1*x3*x4*xcp3 +128*amel2^4*x1*x3*x4*xcp2 -64*amel2^4*x1*x3*x4*xcp1 -32*amel2^4*x1*x3^2*xcp3 -32*amel2^4*x1*x3^2*xcp1 +64*amel2^4*x1^2*xcp3 +64*amel2^4*x1^2*xcp1 -64*amel2^4*x1^2*x5*xcp3 -64*amel2^4*x1^2*x5*xcp1 -64*amel2^4*x1^2*x4*xcp3 -64*amel2^4*x1^2*x4*xcp1 -64*amel2^4*x1^2*x3*xcp3 -64*amel2^4*x1^2*x3*xcp1 -32*amel2^4*x1^3*xcp3 -32*amel2^4*x1^3*xcp1 +48*e2e1*amel2^2*zk^2*xcp3 +32*e2e1*amel2^2*zk^2*xcp2 +48*e2e1*amel2^2*zk^2*xcp1 -48*e2e1*amel2^2*zk^2*x5*xcp3 +64*e2e1*amel2^2*zk^2*x5*xcp2 -48*e2e1*amel2^2*zk^2*x5*xcp1 -96*e2e1*amel2^2*zk^2*x4*xcp3 -96*e2e1*amel2^2*zk^2*x4*xcp1 -64*e2e1*amel2^2*zk^2*x3*xcp2 -48*e2e1*amel2^2*zk^2*x1*xcp3 -48*e2e1*amel2^2*zk^2*x1*xcp1 +256*e2e1*amel2^3*x5*xcp2 +32*e2e1*amel2^3*x5^2*xcp3 -128*e2e1*amel2^3*x5^2*xcp2 +32*e2e1*amel2^3*x5^2*xcp1 -32*e2e1*amel2^3*x5^3*xcp3 -32*e2e1*amel2^3*x5^3*xcp1 -64*e2e1*amel2^3*x4*xcp3 +256*e2e1*amel2^3*x4*xcp2 -64*e2e1*amel2^3*x4*xcp1 +128*e2e1*amel2^3*x4*x5*xcp3 -448*e2e1*amel2^3*x4*x5*xcp2 +128*e2e1*amel2^3*x4*x5*xcp1 -128*e2e1*amel2^3*x4*x5^2*xcp3 +64*e2e1*amel2^3*x4*x5^2*xcp2 -128*e2e1*amel2^3*x4*x5^2*xcp1 +192*e2e1*amel2^3*x4^2*xcp3 -384*e2e1*amel2^3*x4^2*xcp2 +192*e2e1*amel2^3*x4^2*xcp1 -192*e2e1*amel2^3*x4^2*x5*xcp3 +256*e2e1*amel2^3*x4^2*x5*xcp2 -192*e2e1*amel2^3*x4^2*x5*xcp1 -128*e2e1*amel2^3*x4^3*xcp3 +128*e2e1*amel2^3*x4^3*xcp2 -128*e2e1*amel2^3*x4^3*xcp1 +64*e2e1*amel2^3*x3*xcp3 +64*e2e1*amel2^3*x3*xcp1 -448*e2e1*amel2^3*x3*x5*xcp2 +64*e2e1*amel2^3*x3*x5^2*xcp2 +192*e2e1*amel2^3*x3*x4*xcp3 -576*e2e1*amel2^3*x3*x4*xcp2 +192*e2e1*amel2^3*x3*x4*xcp1 -64*e2e1*amel2^3*x3*x4*x5*xcp3 +384*e2e1*amel2^3*x3*x4*x5*xcp2 -64*e2e1*amel2^3*x3*x4*x5*xcp1 -128*e2e1*amel2^3*x3*x4^2*xcp3 +128*e2e1*amel2^3*x3*x4^2*xcp2 -128*e2e1*amel2^3*x3*x4^2*xcp1 +32*e2e1*amel2^3*x3^2*xcp3 -64*e2e1*amel2^3*x3^2*xcp2 +32*e2e1*amel2^3*x3^2*xcp1 -32*e2e1*amel2^3*x3^2*x5*xcp3 +128*e2e1*amel2^3*x3^2*x5*xcp2 -32*e2e1*amel2^3*x3^2*x5*xcp1 -64*e2e1*amel2^3*x3^2*x4*xcp3 -64*e2e1*amel2^3*x3^2*x4*xcp2 -64*e2e1*amel2^3*x3^2*x4*xcp1 -64*e2e1*amel2^3*x3^3*xcp2 -64*e2e1*amel2^3*x1*xcp3 +128*e2e1*amel2^3*x1*xcp2 -64*e2e1*amel2^3*x1*xcp1 +32*e2e1*amel2^3*x1*x5*xcp3 -448*e2e1*amel2^3*x1*x5*xcp2 +32*e2e1*amel2^3*x1*x5*xcp1 -96*e2e1*amel2^3*x1*x5^2*xcp3 +256*e2e1*amel2^3*x1*x5^2*xcp2 -96*e2e1*amel2^3*x1*x5^2*xcp1 +192*e2e1*amel2^3*x1*x4*xcp3 -768*e2e1*amel2^3*x1*x4*xcp2 +192*e2e1*amel2^3*x1*x4*xcp1 -320*e2e1*amel2^3*x1*x4*x5*xcp3 +768*e2e1*amel2^3*x1*x4*x5*xcp2 -320*e2e1*amel2^3*x1*x4*x5*xcp1 -256*e2e1*amel2^3*x1*x4^2*xcp3 +512*e2e1*amel2^3*x1*x4^2*xcp2 -256*e2e1*amel2^3*x1*x4^2*xcp1 +160*e2e1*amel2^3*x1*x3*xcp3 -448*e2e1*amel2^3*x1*x3*xcp2 +160*e2e1*amel2^3*x1*x3*xcp1 -64*e2e1*amel2^3*x1*x3*x5*xcp3 +512*e2e1*amel2^3*x1*x3*x5*xcp2 -64*e2e1*amel2^3*x1*x3*x5*xcp1 -256*e2e1*amel2^3*x1*x3*x4*xcp3 +512*e2e1*amel2^3*x1*x3*x4*xcp2 -256*e2e1*amel2^3*x1*x3*x4*xcp1 -32*e2e1*amel2^3*x1*x3^2*xcp3 -32*e2e1*amel2^3*x1*x3^2*xcp1 +128*e2e1*amel2^3*x1^2*xcp3 -64*e2e1*amel2^3*x1^2*xcp2 +128*e2e1*amel2^3*x1^2*xcp1 -96*e2e1*amel2^3*x1^2*x5*xcp3 +128*e2e1*amel2^3*x1^2*x5*xcp2 -96*e2e1*amel2^3*x1^2*x5*xcp1 -192*e2e1*amel2^3*x1^2*x4*xcp3 +64*e2e1*amel2^3*x1^2*x4*xcp2 -192*e2e1*amel2^3*x1^2*x4*xcp1 -128*e2e1*amel2^3*x1^2*x3*xcp3 -64*e2e1*amel2^3*x1^2*x3*xcp2 -128*e2e1*amel2^3*x1^2*x3*xcp1 -32*e2e1*amel2^3*x1^3*xcp3 -32*e2e1*amel2^3*x1^3*xcp1 +96*e2e1^2*amel2*zk^2*xcp2 -48*e2e1^2*amel2*zk^2*x5*xcp3 -32*e2e1^2*amel2*zk^2*x5*xcp2 -48*e2e1^2*amel2*zk^2*x5*xcp1 -96*e2e1^2*amel2*zk^2*x4*xcp3 -32*e2e1^2*amel2*zk^2*x4*xcp2 -96*e2e1^2*amel2*zk^2*x4*xcp1 -96*e2e1^2*amel2*zk^2*x3*xcp3 +32*e2e1^2*amel2*zk^2*x3*xcp2 -96*e2e1^2*amel2*zk^2*x3*xcp1 -96*e2e1^2*amel2*zk^2*x1*xcp2 +384*e2e1^2*amel2^2*x5*xcp2 +128*e2e1^2*amel2^2*x5^2*xcp2 -32*e2e1^2*amel2^2*x5^3*xcp3 -192*e2e1^2*amel2^2*x5^3*xcp2 -32*e2e1^2*amel2^2*x5^3*xcp1 -64*e2e1^2*amel2^2*x4*xcp3 +512*e2e1^2*amel2^2*x4*xcp2 -64*e2e1^2*amel2^2*x4*xcp1 +64*e2e1^2*amel2^2*x4*x5*xcp3 -256*e2e1^2*amel2^2*x4*x5*xcp2 +64*e2e1^2*amel2^2*x4*x5*xcp1 -192*e2e1^2*amel2^2*x4*x5^2*xcp3 -192*e2e1^2*amel2^2*x4*x5^2*xcp2 -192*e2e1^2*amel2^2*x4*x5^2*xcp1 +128*e2e1^2*amel2^2*x4^2*xcp3 -384*e2e1^2*amel2^2*x4^2*xcp2 +128*e2e1^2*amel2^2*x4^2*xcp1 -384*e2e1^2*amel2^2*x4^2*x5*xcp3 +256*e2e1^2*amel2^2*x4^2*x5*xcp2 -384*e2e1^2*amel2^2*x4^2*x5*xcp1 -256*e2e1^2*amel2^2*x4^3*xcp3 +256*e2e1^2*amel2^2*x4^3*xcp2 -256*e2e1^2*amel2^2*x4^3*xcp1 +64*e2e1^2*amel2^2*x3*xcp3 +128*e2e1^2*amel2^2*x3*xcp2 +64*e2e1^2*amel2^2*x3*xcp1 -64*e2e1^2*amel2^2*x3*x5*xcp3 -640*e2e1^2*amel2^2*x3*x5*xcp2 -64*e2e1^2*amel2^2*x3*x5*xcp1 -64*e2e1^2*amel2^2*x3*x5^2*xcp3 +64*e2e1^2*amel2^2*x3*x5^2*xcp2 -64*e2e1^2*amel2^2*x3*x5^2*xcp1 +64*e2e1^2*amel2^2*x3*x4*xcp3 -896*e2e1^2*amel2^2*x3*x4*xcp2 +64*e2e1^2*amel2^2*x3*x4*xcp1 -256*e2e1^2*amel2^2*x3*x4*x5*xcp3 +768*e2e1^2*amel2^2*x3*x4*x5*xcp2 -256*e2e1^2*amel2^2*x3*x4*x5*xcp1 -384*e2e1^2*amel2^2*x3*x4^2*xcp3 +640*e2e1^2*amel2^2*x3*x4^2*xcp2 -384*e2e1^2*amel2^2*x3*x4^2*xcp1 -256*e2e1^2*amel2^2*x3^2*xcp2 -32*e2e1^2*amel2^2*x3^2*x5*xcp3 +320*e2e1^2*amel2^2*x3^2*x5*xcp2 -32*e2e1^2*amel2^2*x3^2*x5*xcp1 -192*e2e1^2*amel2^2*x3^2*x4*xcp3 +320*e2e1^2*amel2^2*x3^2*x4*xcp2 -192*e2e1^2*amel2^2*x3^2*x4*xcp1 -64*e2e1^2*amel2^2*x3^3*xcp3 +64*e2e1^2*amel2^2*x3^3*xcp2 -64*e2e1^2*amel2^2*x3^3*xcp1 +64*e2e1^2*amel2^2*x1*xcp3 +256*e2e1^2*amel2^2*x1*xcp2 +64*e2e1^2*amel2^2*x1*xcp1 -32*e2e1^2*amel2^2*x1*x5*xcp3 -640*e2e1^2*amel2^2*x1*x5*xcp2 -32*e2e1^2*amel2^2*x1*x5*xcp1 -64*e2e1^2*amel2^2*x1*x5^2*xcp3 +320*e2e1^2*amel2^2*x1*x5^2*xcp2 -64*e2e1^2*amel2^2*x1*x5^2*xcp1 +192*e2e1^2*amel2^2*x1*x4*xcp3 -832*e2e1^2*amel2^2*x1*x4*xcp2 +192*e2e1^2*amel2^2*x1*x4*xcp1 -320*e2e1^2*amel2^2*x1*x4*x5*xcp3 +1024*e2e1^2*amel2^2*x1*x4*x5*xcp2 -320*e2e1^2*amel2^2*x1*x4*x5*xcp1 -320*e2e1^2*amel2^2*x1*x4^2*xcp3 +512*e2e1^2*amel2^2*x1*x4^2*xcp2 -320*e2e1^2*amel2^2*x1*x4^2*xcp1 +32*e2e1^2*amel2^2*x1*x3*xcp3 -576*e2e1^2*amel2^2*x1*x3*xcp2 +32*e2e1^2*amel2^2*x1*x3*xcp1 -256*e2e1^2*amel2^2*x1*x3*x5*xcp3 +896*e2e1^2*amel2^2*x1*x3*x5*xcp2 -256*e2e1^2*amel2^2*x1*x3*x5*xcp1 -448*e2e1^2*amel2^2*x1*x3*x4*xcp3 +768*e2e1^2*amel2^2*x1*x3*x4*xcp2 -448*e2e1^2*amel2^2*x1*x3*x4*xcp1 -128*e2e1^2*amel2^2*x1*x3^2*xcp3 +192*e2e1^2*amel2^2*x1*x3^2*xcp2 -128*e2e1^2*amel2^2*x1*x3^2*xcp1 +32*e2e1^2*amel2^2*x1^2*xcp3 +32*e2e1^2*amel2^2*x1^2*xcp1 -32*e2e1^2*amel2^2*x1^2*x5*xcp3 +64*e2e1^2*amel2^2*x1^2*x5*xcp2 -32*e2e1^2*amel2^2*x1^2*x5*xcp1 -128*e2e1^2*amel2^2*x1^2*x4*xcp3 +64*e2e1^2*amel2^2*x1^2*x4*xcp2 -128*e2e1^2*amel2^2*x1^2*x4*xcp1 -128*e2e1^2*amel2^2*x1^2*x3*xcp3 -64*e2e1^2*amel2^2*x1^2*x3*xcp2 -128*e2e1^2*amel2^2*x1^2*x3*xcp1 -64*e2e1^2*amel2^2*x1^3*xcp2 -32*e2e1^3*zk^2*xcp2 -32*e2e1^3*zk^2*x4*xcp2 +32*e2e1^3*zk^2*x3*xcp2 -64*e2e1^3*amel2*x5*xcp3 +128*e2e1^3*amel2*x5*xcp2 -64*e2e1^3*amel2*x5*xcp1 +32*e2e1^3*amel2*x5^2*xcp3 +320*e2e1^3*amel2*x5^2*xcp2 +32*e2e1^3*amel2*x5^2*xcp1 -256*e2e1^3*amel2*x5^3*xcp2 +384*e2e1^3*amel2*x4*xcp2 +192*e2e1^3*amel2*x4*x5*xcp2 -64*e2e1^3*amel2*x4*x5^2*xcp3 -512*e2e1^3*amel2*x4*x5^2*xcp2 -64*e2e1^3*amel2*x4*x5^2*xcp1 -256*e2e1^3*amel2*x4^2*xcp2 -192*e2e1^3*amel2*x4^2*x5*xcp3 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fn main() {
    let poly: MultivariatePolynomial<_, u8> = parse!(SIGMA).to_polynomial(&Q, None);

    let (h, _ops, scheme) = poly.optimize_horner_scheme(4000);
    let mut i = h.to_instr(poly.nvars());

    println!(
        "Number of operations={}, with scheme={:?}",
        BorrowedHornerScheme::from(&h).op_count_cse(),
        scheme,
    );

    i.fuse_operations();

    for _ in 0..100_000 {
        if !i.common_pair_elimination() {
            break;
        }
        i.fuse_operations();
    }

    let op_count = i.op_count();
    let o = i.to_output(poly.variables.as_ref().to_vec(), true);
    let o_f64 = o.convert::<f64>();

    println!("Writing output to evaluate.cpp");
    std::fs::write(
        "evaluate.cpp",
        format!(
            "{}",
            InstructionSetPrinter {
                name: "sigma".to_string(),
                instr: &o,
                mode: symbolica::poly::evaluate::InstructionSetMode::CPP(
                    symbolica::poly::evaluate::InstructionSetModeCPPSettings {
                        write_header_and_test: true,
                        always_pass_output_array: false,
                    }
                )
            }
        ),
    )
    .unwrap();

    let mut evaluator = o_f64.evaluator();

    println!("Final number of operations={op_count}");
    println!(
        "Evaluation = {}",
        evaluator
            .evaluate_with_input(&(0..poly.nvars()).map(|x| x as f64 + 1.).collect::<Vec<_>>())[0]
    );

    // evaluate with simd
    let o_f64x4 = o.convert::<f64x4>();
    let mut evaluator = o_f64x4.evaluator();

    println!(
        "Evaluation with simd = {:?}",
        evaluator.evaluate_with_input(
            &(0..poly.nvars())
                .map(|x| f64x4::new([x as f64 + 1., x as f64 + 2., x as f64 + 3., x as f64 + 4.]))
                .collect::<Vec<_>>()
        )[0]
    );
}