Average Error: 0.4 → 0.1
Time: 22.6s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(\frac{60}{z - t}, x - y, 120 \cdot a\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(\frac{60}{z - t}, x - y, 120 \cdot a\right)
double f(double x, double y, double z, double t, double a) {
        double r38366709 = 60.0;
        double r38366710 = x;
        double r38366711 = y;
        double r38366712 = r38366710 - r38366711;
        double r38366713 = r38366709 * r38366712;
        double r38366714 = z;
        double r38366715 = t;
        double r38366716 = r38366714 - r38366715;
        double r38366717 = r38366713 / r38366716;
        double r38366718 = a;
        double r38366719 = 120.0;
        double r38366720 = r38366718 * r38366719;
        double r38366721 = r38366717 + r38366720;
        return r38366721;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r38366722 = 60.0;
        double r38366723 = z;
        double r38366724 = t;
        double r38366725 = r38366723 - r38366724;
        double r38366726 = r38366722 / r38366725;
        double r38366727 = x;
        double r38366728 = y;
        double r38366729 = r38366727 - r38366728;
        double r38366730 = 120.0;
        double r38366731 = a;
        double r38366732 = r38366730 * r38366731;
        double r38366733 = fma(r38366726, r38366729, r38366732);
        return r38366733;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.4
Target0.2
Herbie0.1
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.4

    \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{60}{z - t}, x - y, a \cdot 120\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\frac{60}{z - t}, x - y, 120 \cdot a\right)\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))