Average Error: 0.0 → 0.0
Time: 12.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}
double f(double x, double y, double z) {
        double r910639 = 1.0;
        double r910640 = 4.0;
        double r910641 = x;
        double r910642 = y;
        double r910643 = 0.25;
        double r910644 = r910642 * r910643;
        double r910645 = r910641 + r910644;
        double r910646 = z;
        double r910647 = r910645 - r910646;
        double r910648 = r910640 * r910647;
        double r910649 = r910648 / r910642;
        double r910650 = r910639 + r910649;
        return r910650;
}
↓
double f(double x, double y, double z) {
        double r910651 = 4.0;
        double r910652 = x;
        double r910653 = y;
        double r910654 = r910652 / r910653;
        double r910655 = r910651 * r910654;
        double r910656 = 2.0;
        double r910657 = r910655 + r910656;
        double r910658 = z;
        double r910659 = r910658 / r910653;
        double r910660 = r910651 * r910659;
        double r910661 = r910657 - r910660;
        return r910661;
}

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. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 
(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)))