Average Error: 0.2 → 0.0
Time: 14.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r172876 = 1.0;
        double r172877 = 4.0;
        double r172878 = x;
        double r172879 = y;
        double r172880 = 0.75;
        double r172881 = r172879 * r172880;
        double r172882 = r172878 + r172881;
        double r172883 = z;
        double r172884 = r172882 - r172883;
        double r172885 = r172877 * r172884;
        double r172886 = r172885 / r172879;
        double r172887 = r172876 + r172886;
        return r172887;
}
↓
double f(double x, double y, double z) {
        double r172888 = 4.0;
        double r172889 = x;
        double r172890 = z;
        double r172891 = r172889 - r172890;
        double r172892 = y;
        double r172893 = r172891 / r172892;
        double r172894 = r172893 * r172888;
        double r172895 = r172888 + r172894;
        return r172895;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Derivation

  1. Initial program 0.2

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + \left(\frac{x - z}{y} + 0.75\right) \cdot 4}\]

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))