Average Error: 17.7 → 0.0
Time: 2.1s
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 r561493 = x;
        double r561494 = y;
        double r561495 = r561493 * r561494;
        double r561496 = r561494 * r561494;
        double r561497 = r561495 + r561496;
        double r561498 = z;
        double r561499 = r561494 * r561498;
        double r561500 = r561497 - r561499;
        double r561501 = r561500 - r561496;
        return r561501;
}
↓
double f(double x, double y, double z) {
        double r561502 = y;
        double r561503 = x;
        double r561504 = z;
        double r561505 = r561503 - r561504;
        double r561506 = 0.0;
        double r561507 = fma(r561502, r561505, r561506);
        return r561507;
}

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 2020021 +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)))