Average Error: 0.1 → 0.0
Time: 14.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \frac{x - z}{y} + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \frac{x - z}{y} + 2
double f(double x, double y, double z) {
        double r304291 = 1.0;
        double r304292 = 4.0;
        double r304293 = x;
        double r304294 = y;
        double r304295 = 0.25;
        double r304296 = r304294 * r304295;
        double r304297 = r304293 + r304296;
        double r304298 = z;
        double r304299 = r304297 - r304298;
        double r304300 = r304292 * r304299;
        double r304301 = r304300 / r304294;
        double r304302 = r304291 + r304301;
        return r304302;
}
↓
double f(double x, double y, double z) {
        double r304303 = 4.0;
        double r304304 = x;
        double r304305 = z;
        double r304306 = r304304 - r304305;
        double r304307 = y;
        double r304308 = r304306 / r304307;
        double r304309 = r304303 * r304308;
        double r304310 = 2.0;
        double r304311 = r304309 + r304310;
        return r304311;
}

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

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 
(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)))