Average Error: 0.0 → 0.0
Time: 17.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r208315 = 1.0;
        double r208316 = 4.0;
        double r208317 = x;
        double r208318 = y;
        double r208319 = 0.25;
        double r208320 = r208318 * r208319;
        double r208321 = r208317 + r208320;
        double r208322 = z;
        double r208323 = r208321 - r208322;
        double r208324 = r208316 * r208323;
        double r208325 = r208324 / r208318;
        double r208326 = r208315 + r208325;
        return r208326;
}
↓
double f(double x, double y, double z) {
        double r208327 = 2.0;
        double r208328 = x;
        double r208329 = z;
        double r208330 = r208328 - r208329;
        double r208331 = y;
        double r208332 = r208330 / r208331;
        double r208333 = 4.0;
        double r208334 = r208332 * r208333;
        double r208335 = r208327 + r208334;
        return r208335;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  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

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

  5. Final simplification0.0

    \[\leadsto 2 + \frac{x - z}{y} \cdot 4\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))