Average Error: 0.5 → 0.1
Time: 20.5s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)
double f(double x, double y, double z, double t, double a) {
        double r34000896 = 60.0;
        double r34000897 = x;
        double r34000898 = y;
        double r34000899 = r34000897 - r34000898;
        double r34000900 = r34000896 * r34000899;
        double r34000901 = z;
        double r34000902 = t;
        double r34000903 = r34000901 - r34000902;
        double r34000904 = r34000900 / r34000903;
        double r34000905 = a;
        double r34000906 = 120.0;
        double r34000907 = r34000905 * r34000906;
        double r34000908 = r34000904 + r34000907;
        return r34000908;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r34000909 = a;
        double r34000910 = 120.0;
        double r34000911 = 60.0;
        double r34000912 = z;
        double r34000913 = t;
        double r34000914 = r34000912 - r34000913;
        double r34000915 = x;
        double r34000916 = y;
        double r34000917 = r34000915 - r34000916;
        double r34000918 = r34000914 / r34000917;
        double r34000919 = r34000911 / r34000918;
        double r34000920 = fma(r34000909, r34000910, r34000919);
        return r34000920;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.5
Target0.2
Herbie0.1
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.5

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

  2. Simplified0.5

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

  4. Applied associate-/l*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 +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)))