Average Error: 0.1 → 0.0
Time: 7.5s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2.0\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2.0
double f(double x, double y, double z) {
        double r13198087 = 1.0;
        double r13198088 = 4.0;
        double r13198089 = x;
        double r13198090 = y;
        double r13198091 = 0.25;
        double r13198092 = r13198090 * r13198091;
        double r13198093 = r13198089 + r13198092;
        double r13198094 = z;
        double r13198095 = r13198093 - r13198094;
        double r13198096 = r13198088 * r13198095;
        double r13198097 = r13198096 / r13198090;
        double r13198098 = r13198087 + r13198097;
        return r13198098;
}
↓
double f(double x, double y, double z) {
        double r13198099 = 4.0;
        double r13198100 = x;
        double r13198101 = y;
        double r13198102 = r13198100 / r13198101;
        double r13198103 = z;
        double r13198104 = r13198103 / r13198101;
        double r13198105 = r13198102 - r13198104;
        double r13198106 = r13198099 * r13198105;
        double r13198107 = 2.0;
        double r13198108 = r13198106 + r13198107;
        return r13198108;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(0.25 - \frac{z - x}{y}\right) \cdot 4.0 + 1.0}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 2.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2.0}\]

  5. Final simplification0.0

    \[\leadsto 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2.0\]

Reproduce

herbie shell --seed 2019165 
(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)))