Average Error: 0.5 → 0.1
Time: 18.3s
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 r600696 = 60.0;
        double r600697 = x;
        double r600698 = y;
        double r600699 = r600697 - r600698;
        double r600700 = r600696 * r600699;
        double r600701 = z;
        double r600702 = t;
        double r600703 = r600701 - r600702;
        double r600704 = r600700 / r600703;
        double r600705 = a;
        double r600706 = 120.0;
        double r600707 = r600705 * r600706;
        double r600708 = r600704 + r600707;
        return r600708;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r600709 = 120.0;
        double r600710 = a;
        double r600711 = 60.0;
        double r600712 = x;
        double r600713 = y;
        double r600714 = r600712 - r600713;
        double r600715 = z;
        double r600716 = t;
        double r600717 = r600715 - r600716;
        double r600718 = r600714 / r600717;
        double r600719 = r600711 * r600718;
        double r600720 = fma(r600709, r600710, r600719);
        return r600720;
}

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

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

  4. Applied *-un-lft-identity0.5

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

  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 2019198 +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)))