Average Error: 0.1 → 0.1
Time: 30.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \frac{\left(x - z\right) \cdot 4}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \frac{\left(x - z\right) \cdot 4}{y}
double f(double x, double y, double z) {
        double r11765867 = 1.0;
        double r11765868 = 4.0;
        double r11765869 = x;
        double r11765870 = y;
        double r11765871 = 0.25;
        double r11765872 = r11765870 * r11765871;
        double r11765873 = r11765869 + r11765872;
        double r11765874 = z;
        double r11765875 = r11765873 - r11765874;
        double r11765876 = r11765868 * r11765875;
        double r11765877 = r11765876 / r11765870;
        double r11765878 = r11765867 + r11765877;
        return r11765878;
}
↓
double f(double x, double y, double z) {
        double r11765879 = 2.0;
        double r11765880 = x;
        double r11765881 = z;
        double r11765882 = r11765880 - r11765881;
        double r11765883 = 4.0;
        double r11765884 = r11765882 * r11765883;
        double r11765885 = y;
        double r11765886 = r11765884 / r11765885;
        double r11765887 = r11765879 + r11765886;
        return r11765887;
}

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

Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

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, C"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))