Average Error: 0.1 → 0.0
Time: 1.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}
double f(double x, double y, double z) {
        double r314273 = 1.0;
        double r314274 = 4.0;
        double r314275 = x;
        double r314276 = y;
        double r314277 = 0.25;
        double r314278 = r314276 * r314277;
        double r314279 = r314275 + r314278;
        double r314280 = z;
        double r314281 = r314279 - r314280;
        double r314282 = r314274 * r314281;
        double r314283 = r314282 / r314276;
        double r314284 = r314273 + r314283;
        return r314284;
}
↓
double f(double x, double y, double z) {
        double r314285 = 4.0;
        double r314286 = x;
        double r314287 = y;
        double r314288 = r314286 / r314287;
        double r314289 = r314285 * r314288;
        double r314290 = 2.0;
        double r314291 = r314289 + r314290;
        double r314292 = z;
        double r314293 = r314292 / r314287;
        double r314294 = r314285 * r314293;
        double r314295 = r314291 - r314294;
        return r314295;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 
(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)))