Average Error: 0.1 → 0.0
Time: 2.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(1 + 0.25 \cdot 4\right) + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(1 + 0.25 \cdot 4\right) + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4
double f(double x, double y, double z) {
        double r369455 = 1.0;
        double r369456 = 4.0;
        double r369457 = x;
        double r369458 = y;
        double r369459 = 0.25;
        double r369460 = r369458 * r369459;
        double r369461 = r369457 + r369460;
        double r369462 = z;
        double r369463 = r369461 - r369462;
        double r369464 = r369456 * r369463;
        double r369465 = r369464 / r369458;
        double r369466 = r369455 + r369465;
        return r369466;
}
↓
double f(double x, double y, double z) {
        double r369467 = 1.0;
        double r369468 = 0.25;
        double r369469 = 4.0;
        double r369470 = r369468 * r369469;
        double r369471 = r369467 + r369470;
        double r369472 = x;
        double r369473 = y;
        double r369474 = r369472 / r369473;
        double r369475 = z;
        double r369476 = r369475 / r369473;
        double r369477 = r369474 - r369476;
        double r369478 = r369477 * r369469;
        double r369479 = r369471 + r369478;
        return r369479;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Using strategy rm

  4. Applied div-sub0.0

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

  5. Applied associate-+r-0.0

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

  7. Applied associate--l+0.0

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

  8. Applied distribute-rgt-in0.0

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

  9. Applied associate-+r+0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 
(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)))