Average Error: 0.5 → 0.1
Time: 9.3s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \frac{60}{\frac{z - t}{x - y}}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, \frac{60}{\frac{z - t}{x - y}}\right)
double f(double x, double y, double z, double t, double a) {
        double r1000905 = 60.0;
        double r1000906 = x;
        double r1000907 = y;
        double r1000908 = r1000906 - r1000907;
        double r1000909 = r1000905 * r1000908;
        double r1000910 = z;
        double r1000911 = t;
        double r1000912 = r1000910 - r1000911;
        double r1000913 = r1000909 / r1000912;
        double r1000914 = a;
        double r1000915 = 120.0;
        double r1000916 = r1000914 * r1000915;
        double r1000917 = r1000913 + r1000916;
        return r1000917;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1000918 = 120.0;
        double r1000919 = a;
        double r1000920 = 60.0;
        double r1000921 = z;
        double r1000922 = t;
        double r1000923 = r1000921 - r1000922;
        double r1000924 = x;
        double r1000925 = y;
        double r1000926 = r1000924 - r1000925;
        double r1000927 = r1000923 / r1000926;
        double r1000928 = r1000920 / r1000927;
        double r1000929 = fma(r1000918, r1000919, r1000928);
        return r1000929;
}

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. Simplified0.4

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

  4. Applied associate-/l*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60 (/ (- z t) (- x y))) (* a 120))

  (+ (/ (* 60 (- x y)) (- z t)) (* a 120)))