Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[\mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
\mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2
double f(double x, double y) {
        double r525504 = 2.0;
        double r525505 = x;
        double r525506 = r525505 * r525505;
        double r525507 = y;
        double r525508 = r525505 * r525507;
        double r525509 = r525506 + r525508;
        double r525510 = r525504 * r525509;
        return r525510;
}
↓
double f(double x, double y) {
        double r525511 = x;
        double r525512 = y;
        double r525513 = r525511 * r525512;
        double r525514 = fma(r525511, r525511, r525513);
        double r525515 = 2.0;
        double r525516 = r525514 * r525515;
        return r525516;
}

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0.0
Herbie0.0
\[\left(x \cdot 2\right) \cdot \left(x + y\right)\]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x + x \cdot y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (* x 2) (+ x y))

  (* 2 (+ (* x x) (* x y))))