Average Error: 0.1 → 0.0
Time: 1.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)
double f(double x, double y, double z) {
        double r326753 = 1.0;
        double r326754 = 4.0;
        double r326755 = x;
        double r326756 = y;
        double r326757 = 0.25;
        double r326758 = r326756 * r326757;
        double r326759 = r326755 + r326758;
        double r326760 = z;
        double r326761 = r326759 - r326760;
        double r326762 = r326754 * r326761;
        double r326763 = r326762 / r326756;
        double r326764 = r326753 + r326763;
        return r326764;
}
↓
double f(double x, double y, double z) {
        double r326765 = 1.0;
        double r326766 = 4.0;
        double r326767 = 0.25;
        double r326768 = x;
        double r326769 = y;
        double r326770 = r326768 / r326769;
        double r326771 = z;
        double r326772 = r326771 / r326769;
        double r326773 = r326770 - r326772;
        double r326774 = r326767 + r326773;
        double r326775 = r326766 * r326774;
        double r326776 = r326765 + r326775;
        return r326776;
}

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 0.1

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

  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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019354 
(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)))