Average Error: 0.0 → 0.0
Time: 19.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4
double f(double x, double y, double z) {
        double r225515 = 1.0;
        double r225516 = 4.0;
        double r225517 = x;
        double r225518 = y;
        double r225519 = 0.25;
        double r225520 = r225518 * r225519;
        double r225521 = r225517 + r225520;
        double r225522 = z;
        double r225523 = r225521 - r225522;
        double r225524 = r225516 * r225523;
        double r225525 = r225524 / r225518;
        double r225526 = r225515 + r225525;
        return r225526;
}
↓
double f(double x, double y, double z) {
        double r225527 = 2.0;
        double r225528 = x;
        double r225529 = y;
        double r225530 = r225528 / r225529;
        double r225531 = z;
        double r225532 = r225531 / r225529;
        double r225533 = r225530 - r225532;
        double r225534 = 4.0;
        double r225535 = r225533 * r225534;
        double r225536 = r225527 + r225535;
        return r225536;
}

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. Using strategy rm

  6. Applied div-sub0.0

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

  7. Final simplification0.0

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

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)))