Average Error: 0.1 → 0.0
Time: 4.8s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x - y}{z} - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x - y}{z} - 2
double f(double x, double y, double z) {
        double r659842 = 4.0;
        double r659843 = x;
        double r659844 = y;
        double r659845 = r659843 - r659844;
        double r659846 = z;
        double r659847 = 0.5;
        double r659848 = r659846 * r659847;
        double r659849 = r659845 - r659848;
        double r659850 = r659842 * r659849;
        double r659851 = r659850 / r659846;
        return r659851;
}
↓
double f(double x, double y, double z) {
        double r659852 = 4.0;
        double r659853 = x;
        double r659854 = y;
        double r659855 = r659853 - r659854;
        double r659856 = z;
        double r659857 = r659855 / r659856;
        double r659858 = r659852 * r659857;
        double r659859 = 2.0;
        double r659860 = r659858 - r659859;
        return r659860;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} - 2}\]

  4. Final simplification0.0

    \[\leadsto 4 \cdot \frac{x - y}{z} - 2\]

Reproduce

herbie shell --seed 2019212 
(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))