Average Error: 0.1 → 0.0
Time: 9.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r310644 = 1.0;
        double r310645 = 4.0;
        double r310646 = x;
        double r310647 = y;
        double r310648 = 0.25;
        double r310649 = r310647 * r310648;
        double r310650 = r310646 + r310649;
        double r310651 = z;
        double r310652 = r310650 - r310651;
        double r310653 = r310645 * r310652;
        double r310654 = r310653 / r310647;
        double r310655 = r310644 + r310654;
        return r310655;
}
↓
double f(double x, double y, double z) {
        double r310656 = 2.0;
        double r310657 = x;
        double r310658 = z;
        double r310659 = r310657 - r310658;
        double r310660 = y;
        double r310661 = r310659 / r310660;
        double r310662 = 4.0;
        double r310663 = r310661 * r310662;
        double r310664 = r310656 + r310663;
        return r310664;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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

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

  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

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

  5. Final simplification0.0

    \[\leadsto 2 + \frac{x - z}{y} \cdot 4\]

Reproduce

herbie shell --seed 2020042 
(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)))