Average Error: 0.1 → 0.0
Time: 17.9s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r161087 = 1.0;
        double r161088 = 4.0;
        double r161089 = x;
        double r161090 = y;
        double r161091 = 0.25;
        double r161092 = r161090 * r161091;
        double r161093 = r161089 + r161092;
        double r161094 = z;
        double r161095 = r161093 - r161094;
        double r161096 = r161088 * r161095;
        double r161097 = r161096 / r161090;
        double r161098 = r161087 + r161097;
        return r161098;
}
↓
double f(double x, double y, double z) {
        double r161099 = 2.0;
        double r161100 = 4.0;
        double r161101 = x;
        double r161102 = y;
        double r161103 = r161101 / r161102;
        double r161104 = z;
        double r161105 = r161104 / r161102;
        double r161106 = r161103 - r161105;
        double r161107 = r161100 * r161106;
        double r161108 = r161099 + r161107;
        return r161108;
}

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. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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)))