Average Error: 0.5 → 0.1
Time: 21.7s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r25106917 = 60.0;
        double r25106918 = x;
        double r25106919 = y;
        double r25106920 = r25106918 - r25106919;
        double r25106921 = r25106917 * r25106920;
        double r25106922 = z;
        double r25106923 = t;
        double r25106924 = r25106922 - r25106923;
        double r25106925 = r25106921 / r25106924;
        double r25106926 = a;
        double r25106927 = 120.0;
        double r25106928 = r25106926 * r25106927;
        double r25106929 = r25106925 + r25106928;
        return r25106929;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25106930 = a;
        double r25106931 = 120.0;
        double r25106932 = x;
        double r25106933 = y;
        double r25106934 = r25106932 - r25106933;
        double r25106935 = 60.0;
        double r25106936 = z;
        double r25106937 = t;
        double r25106938 = r25106936 - r25106937;
        double r25106939 = r25106935 / r25106938;
        double r25106940 = r25106934 * r25106939;
        double r25106941 = fma(r25106930, r25106931, r25106940);
        return r25106941;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.5
Target0.1
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

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

  6. Applied associate-/r/0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 +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)))