Average Error: 0.1 → 0.0
Time: 10.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r328820 = 1.0;
        double r328821 = 4.0;
        double r328822 = x;
        double r328823 = y;
        double r328824 = 0.25;
        double r328825 = r328823 * r328824;
        double r328826 = r328822 + r328825;
        double r328827 = z;
        double r328828 = r328826 - r328827;
        double r328829 = r328821 * r328828;
        double r328830 = r328829 / r328823;
        double r328831 = r328820 + r328830;
        return r328831;
}
↓
double f(double x, double y, double z) {
        double r328832 = 2.0;
        double r328833 = x;
        double r328834 = z;
        double r328835 = r328833 - r328834;
        double r328836 = y;
        double r328837 = r328835 / r328836;
        double r328838 = 4.0;
        double r328839 = r328837 * r328838;
        double r328840 = r328832 + r328839;
        return r328840;
}

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

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

  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

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

  5. Final simplification0.0

    \[\leadsto 2 + \frac{x - z}{y} \cdot 4\]

Reproduce

herbie shell --seed 2020042 
(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)))