Average Error: 0.1 → 0.0
Time: 19.6s
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 r17663014 = 1.0;
        double r17663015 = 4.0;
        double r17663016 = x;
        double r17663017 = y;
        double r17663018 = 0.25;
        double r17663019 = r17663017 * r17663018;
        double r17663020 = r17663016 + r17663019;
        double r17663021 = z;
        double r17663022 = r17663020 - r17663021;
        double r17663023 = r17663015 * r17663022;
        double r17663024 = r17663023 / r17663017;
        double r17663025 = r17663014 + r17663024;
        return r17663025;
}
↓
double f(double x, double y, double z) {
        double r17663026 = 2.0;
        double r17663027 = 4.0;
        double r17663028 = x;
        double r17663029 = y;
        double r17663030 = r17663028 / r17663029;
        double r17663031 = z;
        double r17663032 = r17663031 / r17663029;
        double r17663033 = r17663030 - r17663032;
        double r17663034 = r17663027 * r17663033;
        double r17663035 = r17663026 + r17663034;
        return r17663035;
}

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

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(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)))