Average Error: 0.2 → 0.0
Time: 3.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + 4 \cdot \frac{x - z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + 4 \cdot \frac{x - z}{y}
double f(double x, double y, double z) {
        double r255640 = 1.0;
        double r255641 = 4.0;
        double r255642 = x;
        double r255643 = y;
        double r255644 = 0.75;
        double r255645 = r255643 * r255644;
        double r255646 = r255642 + r255645;
        double r255647 = z;
        double r255648 = r255646 - r255647;
        double r255649 = r255641 * r255648;
        double r255650 = r255649 / r255643;
        double r255651 = r255640 + r255650;
        return r255651;
}
↓
double f(double x, double y, double z) {
        double r255652 = 4.0;
        double r255653 = x;
        double r255654 = z;
        double r255655 = r255653 - r255654;
        double r255656 = y;
        double r255657 = r255655 / r255656;
        double r255658 = r255652 * r255657;
        double r255659 = r255652 + r255658;
        return r255659;
}

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

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + 4 \cdot \left(0.75 + \frac{x - z}{y}\right)}\]

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))