Average Error: 0.1 → 0.0
Time: 1.5s
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 r248439 = 1.0;
        double r248440 = 4.0;
        double r248441 = x;
        double r248442 = y;
        double r248443 = 0.25;
        double r248444 = r248442 * r248443;
        double r248445 = r248441 + r248444;
        double r248446 = z;
        double r248447 = r248445 - r248446;
        double r248448 = r248440 * r248447;
        double r248449 = r248448 / r248442;
        double r248450 = r248439 + r248449;
        return r248450;
}
↓
double f(double x, double y, double z) {
        double r248451 = 2.0;
        double r248452 = 4.0;
        double r248453 = x;
        double r248454 = z;
        double r248455 = r248453 - r248454;
        double r248456 = y;
        double r248457 = r248455 / r248456;
        double r248458 = r248452 * r248457;
        double r248459 = r248451 + r248458;
        return r248459;
}

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

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

  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 2020034 
(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)))