Average Error: 0.1 → 0.0
Time: 1.7s
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 r388390 = 1.0;
        double r388391 = 4.0;
        double r388392 = x;
        double r388393 = y;
        double r388394 = 0.25;
        double r388395 = r388393 * r388394;
        double r388396 = r388392 + r388395;
        double r388397 = z;
        double r388398 = r388396 - r388397;
        double r388399 = r388391 * r388398;
        double r388400 = r388399 / r388393;
        double r388401 = r388390 + r388400;
        return r388401;
}
↓
double f(double x, double y, double z) {
        double r388402 = 2.0;
        double r388403 = 4.0;
        double r388404 = x;
        double r388405 = y;
        double r388406 = r388404 / r388405;
        double r388407 = z;
        double r388408 = r388407 / r388405;
        double r388409 = r388406 - r388408;
        double r388410 = r388403 * r388409;
        double r388411 = r388402 + r388410;
        return r388411;
}

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

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

  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

    \[\leadsto \color{blue}{2 + 4 \cdot \frac{x - z}{y}}\]
  5. Using strategy rm

  6. Applied div-sub0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(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)))