Average Error: 0.1 → 0.0
Time: 8.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \frac{\left(-z\right) + x}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \frac{\left(-z\right) + x}{y}
double f(double x, double y, double z) {
        double r15931616 = 1.0;
        double r15931617 = 4.0;
        double r15931618 = x;
        double r15931619 = y;
        double r15931620 = 0.25;
        double r15931621 = r15931619 * r15931620;
        double r15931622 = r15931618 + r15931621;
        double r15931623 = z;
        double r15931624 = r15931622 - r15931623;
        double r15931625 = r15931617 * r15931624;
        double r15931626 = r15931625 / r15931619;
        double r15931627 = r15931616 + r15931626;
        return r15931627;
}
↓
double f(double x, double y, double z) {
        double r15931628 = 2.0;
        double r15931629 = 4.0;
        double r15931630 = z;
        double r15931631 = -r15931630;
        double r15931632 = x;
        double r15931633 = r15931631 + r15931632;
        double r15931634 = y;
        double r15931635 = r15931633 / r15931634;
        double r15931636 = r15931629 * r15931635;
        double r15931637 = r15931628 + r15931636;
        return r15931637;
}

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 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(0.25 - \frac{z - x}{y}\right) + 1}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{2 + 4 \cdot \frac{\left(-z\right) + x}{y}}\]

  5. Final simplification0.0

    \[\leadsto 2 + 4 \cdot \frac{\left(-z\right) + x}{y}\]

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))