Average Error: 0.1 → 0.0
Time: 13.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \frac{\left(x - z\right) \cdot 4}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \frac{\left(x - z\right) \cdot 4}{y}
double f(double x, double y, double z) {
        double r220235 = 1.0;
        double r220236 = 4.0;
        double r220237 = x;
        double r220238 = y;
        double r220239 = 0.25;
        double r220240 = r220238 * r220239;
        double r220241 = r220237 + r220240;
        double r220242 = z;
        double r220243 = r220241 - r220242;
        double r220244 = r220236 * r220243;
        double r220245 = r220244 / r220238;
        double r220246 = r220235 + r220245;
        return r220246;
}
↓
double f(double x, double y, double z) {
        double r220247 = 2.0;
        double r220248 = x;
        double r220249 = z;
        double r220250 = r220248 - r220249;
        double r220251 = 4.0;
        double r220252 = r220250 * r220251;
        double r220253 = y;
        double r220254 = r220252 / r220253;
        double r220255 = r220247 + r220254;
        return r220255;
}

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. Applied associate-*r/0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

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)))