Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{1 + \frac{x \cdot y}{2}}
double f(double x, double y) {
        double r149764 = x;
        double r149765 = y;
        double r149766 = 1.0;
        double r149767 = r149764 * r149765;
        double r149768 = 2.0;
        double r149769 = r149767 / r149768;
        double r149770 = r149766 + r149769;
        double r149771 = r149765 / r149770;
        double r149772 = r149764 - r149771;
        return r149772;
}
↓
double f(double x, double y) {
        double r149773 = x;
        double r149774 = y;
        double r149775 = 1.0;
        double r149776 = r149773 * r149774;
        double r149777 = 2.0;
        double r149778 = r149776 / r149777;
        double r149779 = r149775 + r149778;
        double r149780 = r149774 / r149779;
        double r149781 = r149773 - r149780;
        return r149781;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]

  2. Final simplification0.0

    \[\leadsto x - \frac{y}{1 + \frac{x \cdot y}{2}}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))