Average Error: 0.4 → 0.1
Time: 10.7s
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 r789081 = 60.0;
        double r789082 = x;
        double r789083 = y;
        double r789084 = r789082 - r789083;
        double r789085 = r789081 * r789084;
        double r789086 = z;
        double r789087 = t;
        double r789088 = r789086 - r789087;
        double r789089 = r789085 / r789088;
        double r789090 = a;
        double r789091 = 120.0;
        double r789092 = r789090 * r789091;
        double r789093 = r789089 + r789092;
        return r789093;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r789094 = 120.0;
        double r789095 = a;
        double r789096 = 60.0;
        double r789097 = z;
        double r789098 = t;
        double r789099 = r789097 - r789098;
        double r789100 = x;
        double r789101 = y;
        double r789102 = r789100 - r789101;
        double r789103 = r789099 / r789102;
        double r789104 = r789096 / r789103;
        double r789105 = fma(r789094, r789095, r789104);
        return r789105;
}

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 2019350 +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)))