Average Error: 0.2 → 0.0
Time: 1.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)
double f(double x, double y, double z) {
        double r279621 = 1.0;
        double r279622 = 4.0;
        double r279623 = x;
        double r279624 = y;
        double r279625 = 0.75;
        double r279626 = r279624 * r279625;
        double r279627 = r279623 + r279626;
        double r279628 = z;
        double r279629 = r279627 - r279628;
        double r279630 = r279622 * r279629;
        double r279631 = r279630 / r279624;
        double r279632 = r279621 + r279631;
        return r279632;
}
↓
double f(double x, double y, double z) {
        double r279633 = 1.0;
        double r279634 = 4.0;
        double r279635 = 0.75;
        double r279636 = x;
        double r279637 = y;
        double r279638 = r279636 / r279637;
        double r279639 = z;
        double r279640 = r279639 / r279637;
        double r279641 = r279638 - r279640;
        double r279642 = r279635 + r279641;
        double r279643 = r279634 * r279642;
        double r279644 = r279633 + r279643;
        return r279644;
}

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 0.2

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

  2. Simplified0.0

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))