Average Error: 0.1 → 0.0
Time: 3.0s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(\left(0.25 + \frac{x}{y}\right) - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
1 + 4 \cdot \left(\left(0.25 + \frac{x}{y}\right) - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r297631 = 1.0;
        double r297632 = 4.0;
        double r297633 = x;
        double r297634 = y;
        double r297635 = 0.25;
        double r297636 = r297634 * r297635;
        double r297637 = r297633 + r297636;
        double r297638 = z;
        double r297639 = r297637 - r297638;
        double r297640 = r297632 * r297639;
        double r297641 = r297640 / r297634;
        double r297642 = r297631 + r297641;
        return r297642;
}
↓
double f(double x, double y, double z) {
        double r297643 = 1.0;
        double r297644 = 4.0;
        double r297645 = 0.25;
        double r297646 = x;
        double r297647 = y;
        double r297648 = r297646 / r297647;
        double r297649 = r297645 + r297648;
        double r297650 = z;
        double r297651 = r297650 / r297647;
        double r297652 = r297649 - r297651;
        double r297653 = r297644 * r297652;
        double r297654 = r297643 + r297653;
        return r297654;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020089 
(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)))