Average Error: 0.5 → 0.1
Time: 9.6s
Precision: 64
\[\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0\]
↓
\[\mathsf{fma}\left(a, 120.0, 60.0 \cdot \frac{x - y}{z - t}\right)\]
\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0
↓
\mathsf{fma}\left(a, 120.0, 60.0 \cdot \frac{x - y}{z - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r9226176 = 60.0;
        double r9226177 = x;
        double r9226178 = y;
        double r9226179 = r9226177 - r9226178;
        double r9226180 = r9226176 * r9226179;
        double r9226181 = z;
        double r9226182 = t;
        double r9226183 = r9226181 - r9226182;
        double r9226184 = r9226180 / r9226183;
        double r9226185 = a;
        double r9226186 = 120.0;
        double r9226187 = r9226185 * r9226186;
        double r9226188 = r9226184 + r9226187;
        return r9226188;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r9226189 = a;
        double r9226190 = 120.0;
        double r9226191 = 60.0;
        double r9226192 = x;
        double r9226193 = y;
        double r9226194 = r9226192 - r9226193;
        double r9226195 = z;
        double r9226196 = t;
        double r9226197 = r9226195 - r9226196;
        double r9226198 = r9226194 / r9226197;
        double r9226199 = r9226191 * r9226198;
        double r9226200 = fma(r9226189, r9226190, r9226199);
        return r9226200;
}

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
\[\frac{60.0}{\frac{z - t}{x - y}} + a \cdot 120.0\]

Derivation

  1. Initial program 0.5

    \[\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0\]

  2. Simplified0.4

    \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120.0, \frac{\left(x - y\right) \cdot 60.0}{z - t}\right)}\]
  3. Using strategy rm

  4. Applied associate-/l*0.1

    \[\leadsto \mathsf{fma}\left(a, 120.0, \color{blue}{\frac{x - y}{\frac{z - t}{60.0}}}\right)\]
  5. Using strategy rm

  6. Applied associate-/r/0.1

    \[\leadsto \mathsf{fma}\left(a, 120.0, \color{blue}{\frac{x - y}{z - t} \cdot 60.0}\right)\]

  7. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(a, 120.0, 60.0 \cdot \frac{x - y}{z - t}\right)\]

Reproduce

herbie shell --seed 2019156 +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)))