Average Error: 0.2 → 0.0
Time: 1.3s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \frac{x - z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \frac{x - z}{y}
double f(double x, double y, double z) {
        double r347686 = 1.0;
        double r347687 = 4.0;
        double r347688 = x;
        double r347689 = y;
        double r347690 = 0.25;
        double r347691 = r347689 * r347690;
        double r347692 = r347688 + r347691;
        double r347693 = z;
        double r347694 = r347692 - r347693;
        double r347695 = r347687 * r347694;
        double r347696 = r347695 / r347689;
        double r347697 = r347686 + r347696;
        return r347697;
}
↓
double f(double x, double y, double z) {
        double r347698 = 2.0;
        double r347699 = 4.0;
        double r347700 = x;
        double r347701 = z;
        double r347702 = r347700 - r347701;
        double r347703 = y;
        double r347704 = r347702 / r347703;
        double r347705 = r347699 * r347704;
        double r347706 = r347698 + r347705;
        return r347706;
}

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 0.2

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

  2. Simplified0.0

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

  3. 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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020021 
(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)))