Average Error: 0.5 → 0.1
Time: 11.0s
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 r1058839 = 60.0;
        double r1058840 = x;
        double r1058841 = y;
        double r1058842 = r1058840 - r1058841;
        double r1058843 = r1058839 * r1058842;
        double r1058844 = z;
        double r1058845 = t;
        double r1058846 = r1058844 - r1058845;
        double r1058847 = r1058843 / r1058846;
        double r1058848 = a;
        double r1058849 = 120.0;
        double r1058850 = r1058848 * r1058849;
        double r1058851 = r1058847 + r1058850;
        return r1058851;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1058852 = 120.0;
        double r1058853 = a;
        double r1058854 = 60.0;
        double r1058855 = x;
        double r1058856 = y;
        double r1058857 = r1058855 - r1058856;
        double r1058858 = z;
        double r1058859 = t;
        double r1058860 = r1058858 - r1058859;
        double r1058861 = r1058857 / r1058860;
        double r1058862 = r1058854 * r1058861;
        double r1058863 = fma(r1058852, r1058853, r1058862);
        return r1058863;
}

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 2020046 +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)))