Average Error: 0.4 → 0.1
Time: 10.9s
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 r770920 = 60.0;
        double r770921 = x;
        double r770922 = y;
        double r770923 = r770921 - r770922;
        double r770924 = r770920 * r770923;
        double r770925 = z;
        double r770926 = t;
        double r770927 = r770925 - r770926;
        double r770928 = r770924 / r770927;
        double r770929 = a;
        double r770930 = 120.0;
        double r770931 = r770929 * r770930;
        double r770932 = r770928 + r770931;
        return r770932;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r770933 = 120.0;
        double r770934 = a;
        double r770935 = 60.0;
        double r770936 = z;
        double r770937 = t;
        double r770938 = r770936 - r770937;
        double r770939 = x;
        double r770940 = y;
        double r770941 = r770939 - r770940;
        double r770942 = r770938 / r770941;
        double r770943 = r770935 / r770942;
        double r770944 = fma(r770933, r770934, r770943);
        return r770944;
}

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. Simplified0.4

    \[\leadsto \color{blue}{\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
  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 2020047 +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)))