Average Error: 0.1 → 0.0
Time: 21.1s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2.0\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2.0
double f(double x, double y, double z) {
        double r17688269 = 1.0;
        double r17688270 = 4.0;
        double r17688271 = x;
        double r17688272 = y;
        double r17688273 = 0.25;
        double r17688274 = r17688272 * r17688273;
        double r17688275 = r17688271 + r17688274;
        double r17688276 = z;
        double r17688277 = r17688275 - r17688276;
        double r17688278 = r17688270 * r17688277;
        double r17688279 = r17688278 / r17688272;
        double r17688280 = r17688269 + r17688279;
        return r17688280;
}
↓
double f(double x, double y, double z) {
        double r17688281 = 4.0;
        double r17688282 = x;
        double r17688283 = y;
        double r17688284 = r17688282 / r17688283;
        double r17688285 = z;
        double r17688286 = r17688285 / r17688283;
        double r17688287 = r17688284 - r17688286;
        double r17688288 = r17688281 * r17688287;
        double r17688289 = 2.0;
        double r17688290 = r17688288 + r17688289;
        return r17688290;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(0.25 - \frac{z - x}{y}\right) + 1.0}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 2.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2.0}\]

  5. Final simplification0.0

    \[\leadsto 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2.0\]

Reproduce

herbie shell --seed 2019165 
(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)))