Average Error: 0.1 → 0.0
Time: 8.4s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \left(0.25 - \frac{z - x}{y}\right) + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \left(0.25 - \frac{z - x}{y}\right) + 1
double f(double x, double y, double z) {
        double r13231856 = 1.0;
        double r13231857 = 4.0;
        double r13231858 = x;
        double r13231859 = y;
        double r13231860 = 0.25;
        double r13231861 = r13231859 * r13231860;
        double r13231862 = r13231858 + r13231861;
        double r13231863 = z;
        double r13231864 = r13231862 - r13231863;
        double r13231865 = r13231857 * r13231864;
        double r13231866 = r13231865 / r13231859;
        double r13231867 = r13231856 + r13231866;
        return r13231867;
}
↓
double f(double x, double y, double z) {
        double r13231868 = 4.0;
        double r13231869 = 0.25;
        double r13231870 = z;
        double r13231871 = x;
        double r13231872 = r13231870 - r13231871;
        double r13231873 = y;
        double r13231874 = r13231872 / r13231873;
        double r13231875 = r13231869 - r13231874;
        double r13231876 = r13231868 * r13231875;
        double r13231877 = 1.0;
        double r13231878 = r13231876 + r13231877;
        return r13231878;
}

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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Derivation

  1. Initial program 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(0.25 - \frac{z - x}{y}\right) \cdot 4 + 1}\]

  3. Final simplification0.0

    \[\leadsto 4 \cdot \left(0.25 - \frac{z - x}{y}\right) + 1\]

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))