Average Error: 0.3 → 0.1
Time: 11.0s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \frac{60}{\frac{z - t}{x - y}}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, \frac{60}{\frac{z - t}{x - y}}\right)
double f(double x, double y, double z, double t, double a) {
        double r749311 = 60.0;
        double r749312 = x;
        double r749313 = y;
        double r749314 = r749312 - r749313;
        double r749315 = r749311 * r749314;
        double r749316 = z;
        double r749317 = t;
        double r749318 = r749316 - r749317;
        double r749319 = r749315 / r749318;
        double r749320 = a;
        double r749321 = 120.0;
        double r749322 = r749320 * r749321;
        double r749323 = r749319 + r749322;
        return r749323;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r749324 = 120.0;
        double r749325 = a;
        double r749326 = 60.0;
        double r749327 = z;
        double r749328 = t;
        double r749329 = r749327 - r749328;
        double r749330 = x;
        double r749331 = y;
        double r749332 = r749330 - r749331;
        double r749333 = r749329 / r749332;
        double r749334 = r749326 / r749333;
        double r749335 = fma(r749324, r749325, r749334);
        return r749335;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.3
Target0.2
Herbie0.1
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.3

    \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
  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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019351 +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)))