Average Error: 0.1 → 0.0
Time: 10.3s
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 r15514408 = 1.0;
        double r15514409 = 4.0;
        double r15514410 = x;
        double r15514411 = y;
        double r15514412 = 0.25;
        double r15514413 = r15514411 * r15514412;
        double r15514414 = r15514410 + r15514413;
        double r15514415 = z;
        double r15514416 = r15514414 - r15514415;
        double r15514417 = r15514409 * r15514416;
        double r15514418 = r15514417 / r15514411;
        double r15514419 = r15514408 + r15514418;
        return r15514419;
}
↓
double f(double x, double y, double z) {
        double r15514420 = 2.0;
        double r15514421 = 4.0;
        double r15514422 = z;
        double r15514423 = -r15514422;
        double r15514424 = x;
        double r15514425 = r15514423 + r15514424;
        double r15514426 = y;
        double r15514427 = r15514425 / r15514426;
        double r15514428 = r15514421 * r15514427;
        double r15514429 = r15514420 + r15514428;
        return r15514429;
}

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)))