Average Error: 0.1 → 0.0
Time: 1.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)
double f(double x, double y, double z) {
        double r236913 = 1.0;
        double r236914 = 4.0;
        double r236915 = x;
        double r236916 = y;
        double r236917 = 0.25;
        double r236918 = r236916 * r236917;
        double r236919 = r236915 + r236918;
        double r236920 = z;
        double r236921 = r236919 - r236920;
        double r236922 = r236914 * r236921;
        double r236923 = r236922 / r236916;
        double r236924 = r236913 + r236923;
        return r236924;
}
↓
double f(double x, double y, double z) {
        double r236925 = 1.0;
        double r236926 = 4.0;
        double r236927 = 0.25;
        double r236928 = x;
        double r236929 = y;
        double r236930 = r236928 / r236929;
        double r236931 = z;
        double r236932 = r236931 / r236929;
        double r236933 = r236930 - r236932;
        double r236934 = r236927 + r236933;
        double r236935 = r236926 * r236934;
        double r236936 = r236925 + r236935;
        return r236936;
}

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

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019362 
(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)))