Average Error: 0.1 → 0.0
Time: 2.0m
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4
double f(double x, double y, double z) {
        double r7871734 = 1.0;
        double r7871735 = 4.0;
        double r7871736 = x;
        double r7871737 = y;
        double r7871738 = 0.25;
        double r7871739 = r7871737 * r7871738;
        double r7871740 = r7871736 + r7871739;
        double r7871741 = z;
        double r7871742 = r7871740 - r7871741;
        double r7871743 = r7871735 * r7871742;
        double r7871744 = r7871743 / r7871737;
        double r7871745 = r7871734 + r7871744;
        return r7871745;
}
↓
double f(double x, double y, double z) {
        double r7871746 = 2.0;
        double r7871747 = x;
        double r7871748 = y;
        double r7871749 = r7871747 / r7871748;
        double r7871750 = z;
        double r7871751 = r7871750 / r7871748;
        double r7871752 = r7871749 - r7871751;
        double r7871753 = 4.0;
        double r7871754 = r7871752 * r7871753;
        double r7871755 = r7871746 + r7871754;
        return r7871755;
}

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

Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 2}\]
  5. Using strategy rm

  6. Applied div-sub0.0

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

  7. Final simplification0.0

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

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