Average Error: 0.2 → 0.0
Time: 13.1s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)
double f(double x, double y, double z) {
        double r545854 = 4.0;
        double r545855 = x;
        double r545856 = y;
        double r545857 = r545855 - r545856;
        double r545858 = z;
        double r545859 = 0.5;
        double r545860 = r545858 * r545859;
        double r545861 = r545857 - r545860;
        double r545862 = r545854 * r545861;
        double r545863 = r545862 / r545858;
        return r545863;
}
↓
double f(double x, double y, double z) {
        double r545864 = 4.0;
        double r545865 = x;
        double r545866 = z;
        double r545867 = r545865 / r545866;
        double r545868 = y;
        double r545869 = r545868 / r545866;
        double r545870 = 0.5;
        double r545871 = r545869 + r545870;
        double r545872 = r545867 - r545871;
        double r545873 = r545864 * r545872;
        return r545873;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.2

    \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(\frac{x - y}{z} - 0.5\right)}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0.5\right)\]

  5. Applied associate--l-0.0

    \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)}\]

  6. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4 (/ x z)) (+ 2 (* 4 (/ y z))))

  (/ (* 4 (- (- x y) (* z 0.5))) z))