Average Error: 0.3 → 0.2
Time: 16.9s
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 r849074 = x;
        double r849075 = y;
        double r849076 = r849075 - r849074;
        double r849077 = 6.0;
        double r849078 = r849076 * r849077;
        double r849079 = z;
        double r849080 = r849078 * r849079;
        double r849081 = r849074 + r849080;
        return r849081;
}
↓
double f(double x, double y, double z) {
        double r849082 = y;
        double r849083 = x;
        double r849084 = r849082 - r849083;
        double r849085 = 6.0;
        double r849086 = z;
        double r849087 = r849085 * r849086;
        double r849088 = fma(r849084, r849087, r849083);
        return r849088;
}

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 2020043 +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)))