Average Error: 0.1 → 0.0
Time: 13.0s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(0.75 + \frac{x - z}{y}\right) \cdot 4 + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(0.75 + \frac{x - z}{y}\right) \cdot 4 + 1
double f(double x, double y, double z) {
        double r392643 = 1.0;
        double r392644 = 4.0;
        double r392645 = x;
        double r392646 = y;
        double r392647 = 0.75;
        double r392648 = r392646 * r392647;
        double r392649 = r392645 + r392648;
        double r392650 = z;
        double r392651 = r392649 - r392650;
        double r392652 = r392644 * r392651;
        double r392653 = r392652 / r392646;
        double r392654 = r392643 + r392653;
        return r392654;
}
↓
double f(double x, double y, double z) {
        double r392655 = 0.75;
        double r392656 = x;
        double r392657 = z;
        double r392658 = r392656 - r392657;
        double r392659 = y;
        double r392660 = r392658 / r392659;
        double r392661 = r392655 + r392660;
        double r392662 = 4.0;
        double r392663 = r392661 * r392662;
        double r392664 = 1.0;
        double r392665 = r392663 + r392664;
        return r392665;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 
(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)))