Average Error: 0.1 → 0.0
Time: 13.0s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \frac{x - z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \frac{x - z}{y}
double f(double x, double y, double z) {
        double r298237 = 1.0;
        double r298238 = 4.0;
        double r298239 = x;
        double r298240 = y;
        double r298241 = 0.25;
        double r298242 = r298240 * r298241;
        double r298243 = r298239 + r298242;
        double r298244 = z;
        double r298245 = r298243 - r298244;
        double r298246 = r298238 * r298245;
        double r298247 = r298246 / r298240;
        double r298248 = r298237 + r298247;
        return r298248;
}
↓
double f(double x, double y, double z) {
        double r298249 = 2.0;
        double r298250 = 4.0;
        double r298251 = x;
        double r298252 = z;
        double r298253 = r298251 - r298252;
        double r298254 = y;
        double r298255 = r298253 / r298254;
        double r298256 = r298250 * r298255;
        double r298257 = r298249 + r298256;
        return r298257;
}

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

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(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)))