Average Error: 0.1 → 0.0
Time: 11.7s
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 r19321838 = 1.0;
        double r19321839 = 4.0;
        double r19321840 = x;
        double r19321841 = y;
        double r19321842 = 0.25;
        double r19321843 = r19321841 * r19321842;
        double r19321844 = r19321840 + r19321843;
        double r19321845 = z;
        double r19321846 = r19321844 - r19321845;
        double r19321847 = r19321839 * r19321846;
        double r19321848 = r19321847 / r19321841;
        double r19321849 = r19321838 + r19321848;
        return r19321849;
}
↓
double f(double x, double y, double z) {
        double r19321850 = 4.0;
        double r19321851 = x;
        double r19321852 = y;
        double r19321853 = r19321851 / r19321852;
        double r19321854 = z;
        double r19321855 = r19321854 / r19321852;
        double r19321856 = r19321853 - r19321855;
        double r19321857 = r19321850 * r19321856;
        double r19321858 = 2.0;
        double r19321859 = r19321857 + r19321858;
        return r19321859;
}

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

    \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 2}\]
  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 2019174 
(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)))