Average Error: 0.2 → 0.0
Time: 8.9s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r812629 = 1.0;
        double r812630 = 4.0;
        double r812631 = x;
        double r812632 = y;
        double r812633 = 0.75;
        double r812634 = r812632 * r812633;
        double r812635 = r812631 + r812634;
        double r812636 = z;
        double r812637 = r812635 - r812636;
        double r812638 = r812630 * r812637;
        double r812639 = r812638 / r812632;
        double r812640 = r812629 + r812639;
        return r812640;
}
↓
double f(double x, double y, double z) {
        double r812641 = 4.0;
        double r812642 = 1.0;
        double r812643 = x;
        double r812644 = y;
        double r812645 = r812643 / r812644;
        double r812646 = r812642 + r812645;
        double r812647 = z;
        double r812648 = r812647 / r812644;
        double r812649 = r812646 - r812648;
        double r812650 = r812641 * r812649;
        return r812650;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

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

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(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)))