Average Error: 0.5 → 0.1
Time: 18.8s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)
double f(double x, double y, double z, double t, double a) {
        double r651629 = 60.0;
        double r651630 = x;
        double r651631 = y;
        double r651632 = r651630 - r651631;
        double r651633 = r651629 * r651632;
        double r651634 = z;
        double r651635 = t;
        double r651636 = r651634 - r651635;
        double r651637 = r651633 / r651636;
        double r651638 = a;
        double r651639 = 120.0;
        double r651640 = r651638 * r651639;
        double r651641 = r651637 + r651640;
        return r651641;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r651642 = a;
        double r651643 = 120.0;
        double r651644 = 60.0;
        double r651645 = z;
        double r651646 = t;
        double r651647 = r651645 - r651646;
        double r651648 = x;
        double r651649 = y;
        double r651650 = r651648 - r651649;
        double r651651 = r651647 / r651650;
        double r651652 = r651644 / r651651;
        double r651653 = fma(r651642, r651643, r651652);
        return r651653;
}

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. Simplified0.5

    \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
  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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 +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)))