Average Error: 0.4 → 0.5
Time: 4.5s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \frac{60}{\frac{z}{x - y} - \frac{t}{x - y}}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, \frac{60}{\frac{z}{x - y} - \frac{t}{x - y}}\right)
double f(double x, double y, double z, double t, double a) {
        double r1120977 = 60.0;
        double r1120978 = x;
        double r1120979 = y;
        double r1120980 = r1120978 - r1120979;
        double r1120981 = r1120977 * r1120980;
        double r1120982 = z;
        double r1120983 = t;
        double r1120984 = r1120982 - r1120983;
        double r1120985 = r1120981 / r1120984;
        double r1120986 = a;
        double r1120987 = 120.0;
        double r1120988 = r1120986 * r1120987;
        double r1120989 = r1120985 + r1120988;
        return r1120989;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1120990 = 120.0;
        double r1120991 = a;
        double r1120992 = 60.0;
        double r1120993 = z;
        double r1120994 = x;
        double r1120995 = y;
        double r1120996 = r1120994 - r1120995;
        double r1120997 = r1120993 / r1120996;
        double r1120998 = t;
        double r1120999 = r1120998 / r1120996;
        double r1121000 = r1120997 - r1120999;
        double r1121001 = r1120992 / r1121000;
        double r1121002 = fma(r1120990, r1120991, r1121001);
        return r1121002;
}

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
Herbie0.5
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

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-sub0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2020060 +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)))