Average Error: 0.2 → 0.0
Time: 16.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4 + \left(4 \cdot 0.75 + 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4 + \left(4 \cdot 0.75 + 1\right)
double f(double x, double y, double z) {
        double r172471 = 1.0;
        double r172472 = 4.0;
        double r172473 = x;
        double r172474 = y;
        double r172475 = 0.75;
        double r172476 = r172474 * r172475;
        double r172477 = r172473 + r172476;
        double r172478 = z;
        double r172479 = r172477 - r172478;
        double r172480 = r172472 * r172479;
        double r172481 = r172480 / r172474;
        double r172482 = r172471 + r172481;
        return r172482;
}
↓
double f(double x, double y, double z) {
        double r172483 = x;
        double r172484 = y;
        double r172485 = r172483 / r172484;
        double r172486 = z;
        double r172487 = r172486 / r172484;
        double r172488 = r172485 - r172487;
        double r172489 = 4.0;
        double r172490 = r172488 * r172489;
        double r172491 = 0.75;
        double r172492 = r172489 * r172491;
        double r172493 = 1.0;
        double r172494 = r172492 + r172493;
        double r172495 = r172490 + r172494;
        return r172495;
}

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

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(\frac{x - z}{y} + 0.75\right) + 1}\]
  3. Using strategy rm

  4. Applied distribute-rgt-in0.0

    \[\leadsto \color{blue}{\left(\frac{x - z}{y} \cdot 4 + 0.75 \cdot 4\right)} + 1\]

  5. Applied associate-+l+0.0

    \[\leadsto \color{blue}{\frac{x - z}{y} \cdot 4 + \left(0.75 \cdot 4 + 1\right)}\]

  6. Simplified0.0

    \[\leadsto \frac{x - z}{y} \cdot 4 + \color{blue}{\left(4 \cdot 0.75 + 1\right)}\]
  7. Using strategy rm

  8. Applied div-sub0.0

    \[\leadsto \color{blue}{\left(\frac{x}{y} - \frac{z}{y}\right)} \cdot 4 + \left(4 \cdot 0.75 + 1\right)\]

  9. Final simplification0.0

    \[\leadsto \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4 + \left(4 \cdot 0.75 + 1\right)\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))