Average Error: 17.7 → 0.0
Time: 3.1s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[\mathsf{fma}\left(y, x - z, 0\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
\mathsf{fma}\left(y, x - z, 0\right)
double f(double x, double y, double z) {
        double r466371 = x;
        double r466372 = y;
        double r466373 = r466371 * r466372;
        double r466374 = r466372 * r466372;
        double r466375 = r466373 + r466374;
        double r466376 = z;
        double r466377 = r466372 * r466376;
        double r466378 = r466375 - r466377;
        double r466379 = r466378 - r466374;
        return r466379;
}
↓
double f(double x, double y, double z) {
        double r466380 = y;
        double r466381 = x;
        double r466382 = z;
        double r466383 = r466381 - r466382;
        double r466384 = 0.0;
        double r466385 = fma(r466380, r466383, r466384);
        return r466385;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.7
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.7

    \[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - z, 0\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x - z, 0\right)\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (- (+ (* x y) (* y y)) (* y z)) (* y y)))