Average Error: 0.2 → 0.0
Time: 19.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \frac{x - z}{y} + 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \frac{x - z}{y} + 4
double f(double x, double y, double z) {
        double r144468 = 1.0;
        double r144469 = 4.0;
        double r144470 = x;
        double r144471 = y;
        double r144472 = 0.75;
        double r144473 = r144471 * r144472;
        double r144474 = r144470 + r144473;
        double r144475 = z;
        double r144476 = r144474 - r144475;
        double r144477 = r144469 * r144476;
        double r144478 = r144477 / r144471;
        double r144479 = r144468 + r144478;
        return r144479;
}
↓
double f(double x, double y, double z) {
        double r144480 = 4.0;
        double r144481 = x;
        double r144482 = z;
        double r144483 = r144481 - r144482;
        double r144484 = y;
        double r144485 = r144483 / r144484;
        double r144486 = r144480 * r144485;
        double r144487 = r144486 + r144480;
        return r144487;
}

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

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

  2. Simplified0.0

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(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)))