Average Error: 0.1 → 0.2
Time: 7.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\frac{4}{y} \cdot \left(x - z\right) + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\frac{4}{y} \cdot \left(x - z\right) + 2
double f(double x, double y, double z) {
        double r203904 = 1.0;
        double r203905 = 4.0;
        double r203906 = x;
        double r203907 = y;
        double r203908 = 0.25;
        double r203909 = r203907 * r203908;
        double r203910 = r203906 + r203909;
        double r203911 = z;
        double r203912 = r203910 - r203911;
        double r203913 = r203905 * r203912;
        double r203914 = r203913 / r203907;
        double r203915 = r203904 + r203914;
        return r203915;
}
↓
double f(double x, double y, double z) {
        double r203916 = 4.0;
        double r203917 = y;
        double r203918 = r203916 / r203917;
        double r203919 = x;
        double r203920 = z;
        double r203921 = r203919 - r203920;
        double r203922 = r203918 * r203921;
        double r203923 = 2.0;
        double r203924 = r203922 + r203923;
        return r203924;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019297 
(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)))