Average Error: 0.4 → 0.2
Time: 6.0s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \frac{\frac{60}{z - t}}{\frac{1}{x - y}}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, \frac{\frac{60}{z - t}}{\frac{1}{x - y}}\right)
double f(double x, double y, double z, double t, double a) {
        double r876708 = 60.0;
        double r876709 = x;
        double r876710 = y;
        double r876711 = r876709 - r876710;
        double r876712 = r876708 * r876711;
        double r876713 = z;
        double r876714 = t;
        double r876715 = r876713 - r876714;
        double r876716 = r876712 / r876715;
        double r876717 = a;
        double r876718 = 120.0;
        double r876719 = r876717 * r876718;
        double r876720 = r876716 + r876719;
        return r876720;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r876721 = 120.0;
        double r876722 = a;
        double r876723 = 60.0;
        double r876724 = z;
        double r876725 = t;
        double r876726 = r876724 - r876725;
        double r876727 = r876723 / r876726;
        double r876728 = 1.0;
        double r876729 = x;
        double r876730 = y;
        double r876731 = r876729 - r876730;
        double r876732 = r876728 / r876731;
        double r876733 = r876727 / r876732;
        double r876734 = fma(r876721, r876722, r876733);
        return r876734;
}

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

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. Using strategy rm

  6. Applied div-inv0.2

    \[\leadsto \mathsf{fma}\left(120, a, \frac{60}{\color{blue}{\left(z - t\right) \cdot \frac{1}{x - y}}}\right)\]

  7. Applied associate-/r*0.2

    \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{\frac{\frac{60}{z - t}}{\frac{1}{x - y}}}\right)\]

  8. Final simplification0.2

    \[\leadsto \mathsf{fma}\left(120, a, \frac{\frac{60}{z - t}}{\frac{1}{x - y}}\right)\]

Reproduce

herbie shell --seed 2020100 +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)))