Average Error: 0.1 → 0.0
Time: 10.5s
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 r15542761 = 1.0;
        double r15542762 = 4.0;
        double r15542763 = x;
        double r15542764 = y;
        double r15542765 = 0.25;
        double r15542766 = r15542764 * r15542765;
        double r15542767 = r15542763 + r15542766;
        double r15542768 = z;
        double r15542769 = r15542767 - r15542768;
        double r15542770 = r15542762 * r15542769;
        double r15542771 = r15542770 / r15542764;
        double r15542772 = r15542761 + r15542771;
        return r15542772;
}
↓
double f(double x, double y, double z) {
        double r15542773 = 2.0;
        double r15542774 = 4.0;
        double r15542775 = z;
        double r15542776 = -r15542775;
        double r15542777 = x;
        double r15542778 = r15542776 + r15542777;
        double r15542779 = y;
        double r15542780 = r15542778 / r15542779;
        double r15542781 = r15542774 * r15542780;
        double r15542782 = r15542773 + r15542781;
        return r15542782;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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 2019172 
(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)))