Average Error: 0.2 → 0.2
Time: 24.2s
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 r535812 = x;
        double r535813 = y;
        double r535814 = r535813 - r535812;
        double r535815 = 6.0;
        double r535816 = r535814 * r535815;
        double r535817 = z;
        double r535818 = r535816 * r535817;
        double r535819 = r535812 + r535818;
        return r535819;
}
↓
double f(double x, double y, double z) {
        double r535820 = y;
        double r535821 = x;
        double r535822 = r535820 - r535821;
        double r535823 = 6.0;
        double r535824 = z;
        double r535825 = r535823 * r535824;
        double r535826 = fma(r535822, r535825, r535821);
        return r535826;
}

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 2019303 +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)))