Average Error: 0.2 → 0.2
Time: 28.8s
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 r518590 = x;
        double r518591 = y;
        double r518592 = r518591 - r518590;
        double r518593 = 6.0;
        double r518594 = r518592 * r518593;
        double r518595 = z;
        double r518596 = r518594 * r518595;
        double r518597 = r518590 + r518596;
        return r518597;
}
↓
double f(double x, double y, double z) {
        double r518598 = y;
        double r518599 = x;
        double r518600 = r518598 - r518599;
        double r518601 = 6.0;
        double r518602 = z;
        double r518603 = r518601 * r518602;
        double r518604 = fma(r518600, r518603, r518599);
        return r518604;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

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

Derivation

  1. Initial program 0.2

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

  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 2019323 +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)))