Average Error: 0.3 → 0.2
Time: 5.0s
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 r849013 = x;
        double r849014 = y;
        double r849015 = r849014 - r849013;
        double r849016 = 6.0;
        double r849017 = r849015 * r849016;
        double r849018 = z;
        double r849019 = r849017 * r849018;
        double r849020 = r849013 + r849019;
        return r849020;
}
↓
double f(double x, double y, double z) {
        double r849021 = y;
        double r849022 = x;
        double r849023 = r849021 - r849022;
        double r849024 = 6.0;
        double r849025 = z;
        double r849026 = r849024 * r849025;
        double r849027 = fma(r849023, r849026, r849022);
        return r849027;
}

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 2020036 +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)))