Average Error: 0.2 → 0.0
Time: 10.4s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) + 1
double f(double x, double y, double z) {
        double r243463 = 1.0;
        double r243464 = 4.0;
        double r243465 = x;
        double r243466 = y;
        double r243467 = 0.25;
        double r243468 = r243466 * r243467;
        double r243469 = r243465 + r243468;
        double r243470 = z;
        double r243471 = r243469 - r243470;
        double r243472 = r243464 * r243471;
        double r243473 = r243472 / r243466;
        double r243474 = r243463 + r243473;
        return r243474;
}
↓
double f(double x, double y, double z) {
        double r243475 = 4.0;
        double r243476 = 0.25;
        double r243477 = x;
        double r243478 = y;
        double r243479 = r243477 / r243478;
        double r243480 = z;
        double r243481 = r243480 / r243478;
        double r243482 = r243479 - r243481;
        double r243483 = r243476 + r243482;
        double r243484 = r243475 * r243483;
        double r243485 = 1.0;
        double r243486 = r243484 + r243485;
        return r243486;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Derivation

  1. Initial program 0.2

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

  2. Simplified0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  7. Applied div-sub0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019298 
(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)))