Average Error: 0.4 → 0.1
Time: 21.3s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)
double f(double x, double y, double z, double t, double a) {
        double r711302 = 60.0;
        double r711303 = x;
        double r711304 = y;
        double r711305 = r711303 - r711304;
        double r711306 = r711302 * r711305;
        double r711307 = z;
        double r711308 = t;
        double r711309 = r711307 - r711308;
        double r711310 = r711306 / r711309;
        double r711311 = a;
        double r711312 = 120.0;
        double r711313 = r711311 * r711312;
        double r711314 = r711310 + r711313;
        return r711314;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r711315 = a;
        double r711316 = 120.0;
        double r711317 = 60.0;
        double r711318 = z;
        double r711319 = t;
        double r711320 = r711318 - r711319;
        double r711321 = x;
        double r711322 = y;
        double r711323 = r711321 - r711322;
        double r711324 = r711320 / r711323;
        double r711325 = r711317 / r711324;
        double r711326 = fma(r711315, r711316, r711325);
        return r711326;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.4
Target0.2
Herbie0.1
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.4

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

  2. Simplified0.3

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

  4. Applied associate-/l*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 +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)))