Average Error: 0.1 → 0.0
Time: 21.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2
double f(double x, double y, double z) {
        double r226814 = 1.0;
        double r226815 = 4.0;
        double r226816 = x;
        double r226817 = y;
        double r226818 = 0.25;
        double r226819 = r226817 * r226818;
        double r226820 = r226816 + r226819;
        double r226821 = z;
        double r226822 = r226820 - r226821;
        double r226823 = r226815 * r226822;
        double r226824 = r226823 / r226817;
        double r226825 = r226814 + r226824;
        return r226825;
}
↓
double f(double x, double y, double z) {
        double r226826 = 4.0;
        double r226827 = x;
        double r226828 = y;
        double r226829 = r226827 / r226828;
        double r226830 = z;
        double r226831 = r226830 / r226828;
        double r226832 = r226829 - r226831;
        double r226833 = r226826 * r226832;
        double r226834 = 2.0;
        double r226835 = r226833 + r226834;
        return r226835;
}

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

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

  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

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

Reproduce

herbie shell --seed 2019325 
(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)))