Average Error: 0.3 → 0.2
Time: 13.9s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[\mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
\mathsf{fma}\left(y - x, 6 \cdot z, x\right)
double f(double x, double y, double z) {
        double r904513 = x;
        double r904514 = y;
        double r904515 = r904514 - r904513;
        double r904516 = 6.0;
        double r904517 = r904515 * r904516;
        double r904518 = z;
        double r904519 = r904517 * r904518;
        double r904520 = r904513 + r904519;
        return r904520;
}
↓
double f(double x, double y, double z) {
        double r904521 = y;
        double r904522 = x;
        double r904523 = r904521 - r904522;
        double r904524 = 6.0;
        double r904525 = z;
        double r904526 = r904524 * r904525;
        double r904527 = fma(r904523, r904526, r904522);
        return r904527;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.3
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.3

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)}\]

  3. Final simplification0.2

    \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6 z) (- x y)))

  (+ x (* (* (- y x) 6) z)))