Average Error: 0.5 → 0.1
Time: 7.2s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, 60 \cdot \left(\frac{x}{z - t} - \frac{y}{z - t}\right)\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, 60 \cdot \left(\frac{x}{z - t} - \frac{y}{z - t}\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r1425785 = 60.0;
        double r1425786 = x;
        double r1425787 = y;
        double r1425788 = r1425786 - r1425787;
        double r1425789 = r1425785 * r1425788;
        double r1425790 = z;
        double r1425791 = t;
        double r1425792 = r1425790 - r1425791;
        double r1425793 = r1425789 / r1425792;
        double r1425794 = a;
        double r1425795 = 120.0;
        double r1425796 = r1425794 * r1425795;
        double r1425797 = r1425793 + r1425796;
        return r1425797;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1425798 = 120.0;
        double r1425799 = a;
        double r1425800 = 60.0;
        double r1425801 = x;
        double r1425802 = z;
        double r1425803 = t;
        double r1425804 = r1425802 - r1425803;
        double r1425805 = r1425801 / r1425804;
        double r1425806 = y;
        double r1425807 = r1425806 / r1425804;
        double r1425808 = r1425805 - r1425807;
        double r1425809 = r1425800 * r1425808;
        double r1425810 = fma(r1425798, r1425799, r1425809);
        return r1425810;
}

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. Simplified0.4

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

  8. Applied div-sub0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 +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)))