Average Error: 0.3 → 0.2
Time: 21.6s
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 r752298 = x;
        double r752299 = y;
        double r752300 = r752299 - r752298;
        double r752301 = 6.0;
        double r752302 = r752300 * r752301;
        double r752303 = z;
        double r752304 = r752302 * r752303;
        double r752305 = r752298 + r752304;
        return r752305;
}
↓
double f(double x, double y, double z) {
        double r752306 = y;
        double r752307 = x;
        double r752308 = r752306 - r752307;
        double r752309 = 6.0;
        double r752310 = z;
        double r752311 = r752309 * r752310;
        double r752312 = fma(r752308, r752311, r752307);
        return r752312;
}

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 2019304 +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)))