Average Error: 0.2 → 0.0
Time: 17.8s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\frac{x - y}{z} - 0.5\right) \cdot 4\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\frac{x - y}{z} - 0.5\right) \cdot 4
double f(double x, double y, double z) {
        double r39537834 = 4.0;
        double r39537835 = x;
        double r39537836 = y;
        double r39537837 = r39537835 - r39537836;
        double r39537838 = z;
        double r39537839 = 0.5;
        double r39537840 = r39537838 * r39537839;
        double r39537841 = r39537837 - r39537840;
        double r39537842 = r39537834 * r39537841;
        double r39537843 = r39537842 / r39537838;
        return r39537843;
}
↓
double f(double x, double y, double z) {
        double r39537844 = x;
        double r39537845 = y;
        double r39537846 = r39537844 - r39537845;
        double r39537847 = z;
        double r39537848 = r39537846 / r39537847;
        double r39537849 = 0.5;
        double r39537850 = r39537848 - r39537849;
        double r39537851 = 4.0;
        double r39537852 = r39537850 * r39537851;
        return r39537852;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +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))