Average Error: 17.2 → 0.0
Time: 1.1s
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 r503358 = x;
        double r503359 = y;
        double r503360 = r503358 * r503359;
        double r503361 = r503359 * r503359;
        double r503362 = r503360 + r503361;
        double r503363 = z;
        double r503364 = r503359 * r503363;
        double r503365 = r503362 - r503364;
        double r503366 = r503365 - r503361;
        return r503366;
}
↓
double f(double x, double y, double z) {
        double r503367 = y;
        double r503368 = x;
        double r503369 = z;
        double r503370 = r503368 - r503369;
        double r503371 = 0.0;
        double r503372 = fma(r503367, r503370, r503371);
        return r503372;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.2

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

  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 2020047 +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)))