Average Error: 0.1 → 0.0
Time: 17.5s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4
double f(double x, double y, double z) {
        double r196430897 = 4.0;
        double r196430898 = x;
        double r196430899 = y;
        double r196430900 = r196430898 - r196430899;
        double r196430901 = z;
        double r196430902 = 0.5;
        double r196430903 = r196430901 * r196430902;
        double r196430904 = r196430900 - r196430903;
        double r196430905 = r196430897 * r196430904;
        double r196430906 = r196430905 / r196430901;
        return r196430906;
}
↓
double f(double x, double y, double z) {
        double r196430907 = x;
        double r196430908 = z;
        double r196430909 = r196430907 / r196430908;
        double r196430910 = y;
        double r196430911 = r196430910 / r196430908;
        double r196430912 = r196430909 - r196430911;
        double r196430913 = 0.5;
        double r196430914 = r196430912 - r196430913;
        double r196430915 = 4.0;
        double r196430916 = r196430914 * r196430915;
        return r196430916;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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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. Using strategy rm

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 +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))