Average Error: 0.5 → 0.1
Time: 16.9s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, 60 \cdot \frac{x - y}{z - t}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, 60 \cdot \frac{x - y}{z - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r367907 = 60.0;
        double r367908 = x;
        double r367909 = y;
        double r367910 = r367908 - r367909;
        double r367911 = r367907 * r367910;
        double r367912 = z;
        double r367913 = t;
        double r367914 = r367912 - r367913;
        double r367915 = r367911 / r367914;
        double r367916 = a;
        double r367917 = 120.0;
        double r367918 = r367916 * r367917;
        double r367919 = r367915 + r367918;
        return r367919;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r367920 = 120.0;
        double r367921 = a;
        double r367922 = 60.0;
        double r367923 = x;
        double r367924 = y;
        double r367925 = r367923 - r367924;
        double r367926 = z;
        double r367927 = t;
        double r367928 = r367926 - r367927;
        double r367929 = r367925 / r367928;
        double r367930 = r367922 * r367929;
        double r367931 = fma(r367920, r367921, r367930);
        return r367931;
}

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

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

  4. Applied *-un-lft-identity0.4

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

  5. Applied times-frac0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019209 +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)))