Average Error: 0.2 → 0.0
Time: 14.7s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4.0 \cdot \left(0.75 - \frac{z - x}{y}\right) + 1.0\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4.0 \cdot \left(0.75 - \frac{z - x}{y}\right) + 1.0
double f(double x, double y, double z) {
        double r17052626 = 1.0;
        double r17052627 = 4.0;
        double r17052628 = x;
        double r17052629 = y;
        double r17052630 = 0.75;
        double r17052631 = r17052629 * r17052630;
        double r17052632 = r17052628 + r17052631;
        double r17052633 = z;
        double r17052634 = r17052632 - r17052633;
        double r17052635 = r17052627 * r17052634;
        double r17052636 = r17052635 / r17052629;
        double r17052637 = r17052626 + r17052636;
        return r17052637;
}
↓
double f(double x, double y, double z) {
        double r17052638 = 4.0;
        double r17052639 = 0.75;
        double r17052640 = z;
        double r17052641 = x;
        double r17052642 = r17052640 - r17052641;
        double r17052643 = y;
        double r17052644 = r17052642 / r17052643;
        double r17052645 = r17052639 - r17052644;
        double r17052646 = r17052638 * r17052645;
        double r17052647 = 1.0;
        double r17052648 = r17052646 + r17052647;
        return r17052648;
}

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 0.2

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(0.75 - \frac{z - x}{y}\right) \cdot 4.0 + 1.0}\]

  3. Final simplification0.0

    \[\leadsto 4.0 \cdot \left(0.75 - \frac{z - x}{y}\right) + 1.0\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))