Average Error: 0.1 → 0.0
Time: 18.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r166699 = 1.0;
        double r166700 = 4.0;
        double r166701 = x;
        double r166702 = y;
        double r166703 = 0.25;
        double r166704 = r166702 * r166703;
        double r166705 = r166701 + r166704;
        double r166706 = z;
        double r166707 = r166705 - r166706;
        double r166708 = r166700 * r166707;
        double r166709 = r166708 / r166702;
        double r166710 = r166699 + r166709;
        return r166710;
}
↓
double f(double x, double y, double z) {
        double r166711 = 2.0;
        double r166712 = 4.0;
        double r166713 = x;
        double r166714 = y;
        double r166715 = r166713 / r166714;
        double r166716 = z;
        double r166717 = r166716 / r166714;
        double r166718 = r166715 - r166717;
        double r166719 = r166712 * r166718;
        double r166720 = r166711 + r166719;
        return r166720;
}

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(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)))