Average Error: 0.1 → 0.0
Time: 16.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.25 - \left(\frac{z}{y} - \frac{x}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.25 - \left(\frac{z}{y} - \frac{x}{y}\right)\right)
double f(double x, double y, double z) {
        double r13647334 = 1.0;
        double r13647335 = 4.0;
        double r13647336 = x;
        double r13647337 = y;
        double r13647338 = 0.25;
        double r13647339 = r13647337 * r13647338;
        double r13647340 = r13647336 + r13647339;
        double r13647341 = z;
        double r13647342 = r13647340 - r13647341;
        double r13647343 = r13647335 * r13647342;
        double r13647344 = r13647343 / r13647337;
        double r13647345 = r13647334 + r13647344;
        return r13647345;
}
↓
double f(double x, double y, double z) {
        double r13647346 = 1.0;
        double r13647347 = 4.0;
        double r13647348 = 0.25;
        double r13647349 = z;
        double r13647350 = y;
        double r13647351 = r13647349 / r13647350;
        double r13647352 = x;
        double r13647353 = r13647352 / r13647350;
        double r13647354 = r13647351 - r13647353;
        double r13647355 = r13647348 - r13647354;
        double r13647356 = r13647347 * r13647355;
        double r13647357 = r13647346 + r13647356;
        return r13647357;
}

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. Using strategy rm

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(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)))