Average Error: 0.1 → 0.0
Time: 16.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2
double f(double x, double y, double z) {
        double r23343 = 1.0;
        double r23344 = 4.0;
        double r23345 = x;
        double r23346 = y;
        double r23347 = 0.25;
        double r23348 = r23346 * r23347;
        double r23349 = r23345 + r23348;
        double r23350 = z;
        double r23351 = r23349 - r23350;
        double r23352 = r23344 * r23351;
        double r23353 = r23352 / r23346;
        double r23354 = r23343 + r23353;
        return r23354;
}
↓
double f(double x, double y, double z) {
        double r23355 = 4.0;
        double r23356 = x;
        double r23357 = y;
        double r23358 = r23356 / r23357;
        double r23359 = z;
        double r23360 = r23359 / r23357;
        double r23361 = r23358 - r23360;
        double r23362 = r23355 * r23361;
        double r23363 = 2.0;
        double r23364 = r23362 + r23363;
        return r23364;
}

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 0.1

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

  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

    \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 2}\]
  5. Using strategy rm

  6. Applied div-sub0.0

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

  7. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2\]

Reproduce

herbie shell --seed 2019315 
(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)))