Average Error: 0.1 → 0.0
Time: 14.3s
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 r19383702 = 1.0;
        double r19383703 = 4.0;
        double r19383704 = x;
        double r19383705 = y;
        double r19383706 = 0.25;
        double r19383707 = r19383705 * r19383706;
        double r19383708 = r19383704 + r19383707;
        double r19383709 = z;
        double r19383710 = r19383708 - r19383709;
        double r19383711 = r19383703 * r19383710;
        double r19383712 = r19383711 / r19383705;
        double r19383713 = r19383702 + r19383712;
        return r19383713;
}
↓
double f(double x, double y, double z) {
        double r19383714 = 2.0;
        double r19383715 = 4.0;
        double r19383716 = x;
        double r19383717 = y;
        double r19383718 = r19383716 / r19383717;
        double r19383719 = z;
        double r19383720 = r19383719 / r19383717;
        double r19383721 = r19383718 - r19383720;
        double r19383722 = r19383715 * r19383721;
        double r19383723 = r19383714 + r19383722;
        return r19383723;
}

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

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(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)))