Average Error: 0.1 → 0.0
Time: 13.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r272701 = 1.0;
        double r272702 = 4.0;
        double r272703 = x;
        double r272704 = y;
        double r272705 = 0.25;
        double r272706 = r272704 * r272705;
        double r272707 = r272703 + r272706;
        double r272708 = z;
        double r272709 = r272707 - r272708;
        double r272710 = r272702 * r272709;
        double r272711 = r272710 / r272704;
        double r272712 = r272701 + r272711;
        return r272712;
}
↓
double f(double x, double y, double z) {
        double r272713 = 2.0;
        double r272714 = x;
        double r272715 = z;
        double r272716 = r272714 - r272715;
        double r272717 = y;
        double r272718 = r272716 / r272717;
        double r272719 = 4.0;
        double r272720 = r272718 * r272719;
        double r272721 = r272713 + r272720;
        return r272721;
}

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. Using strategy rm

  6. Applied sub-div0.0

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

  7. Final simplification0.0

    \[\leadsto 2 + \frac{x - z}{y} \cdot 4\]

Reproduce

herbie shell --seed 2019194 
(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)))