Average Error: 0.1 → 0.0
Time: 18.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r151874 = 1.0;
        double r151875 = 4.0;
        double r151876 = x;
        double r151877 = y;
        double r151878 = 0.25;
        double r151879 = r151877 * r151878;
        double r151880 = r151876 + r151879;
        double r151881 = z;
        double r151882 = r151880 - r151881;
        double r151883 = r151875 * r151882;
        double r151884 = r151883 / r151877;
        double r151885 = r151874 + r151884;
        return r151885;
}
↓
double f(double x, double y, double z) {
        double r151886 = 2.0;
        double r151887 = 4.0;
        double r151888 = x;
        double r151889 = y;
        double r151890 = r151888 / r151889;
        double r151891 = z;
        double r151892 = r151891 / r151889;
        double r151893 = r151890 - r151892;
        double r151894 = r151887 * r151893;
        double r151895 = r151886 + r151894;
        return r151895;
}

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))