Average Error: 0.1 → 0.0
Time: 33.0s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x - y}{z} - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x - y}{z} - 0.5\right)
double f(double x, double y, double z) {
        double r40618781 = 4.0;
        double r40618782 = x;
        double r40618783 = y;
        double r40618784 = r40618782 - r40618783;
        double r40618785 = z;
        double r40618786 = 0.5;
        double r40618787 = r40618785 * r40618786;
        double r40618788 = r40618784 - r40618787;
        double r40618789 = r40618781 * r40618788;
        double r40618790 = r40618789 / r40618785;
        return r40618790;
}
↓
double f(double x, double y, double z) {
        double r40618791 = 4.0;
        double r40618792 = x;
        double r40618793 = y;
        double r40618794 = r40618792 - r40618793;
        double r40618795 = z;
        double r40618796 = r40618794 / r40618795;
        double r40618797 = 0.5;
        double r40618798 = r40618796 - r40618797;
        double r40618799 = r40618791 * r40618798;
        return r40618799;
}

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

Original0.1
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))