Average Error: 0.0 → 0.0
Time: 8.2s
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 r115702 = x;
        double r115703 = y;
        double r115704 = 1.0;
        double r115705 = r115702 * r115703;
        double r115706 = 2.0;
        double r115707 = r115705 / r115706;
        double r115708 = r115704 + r115707;
        double r115709 = r115703 / r115708;
        double r115710 = r115702 - r115709;
        return r115710;
}
↓
double f(double x, double y) {
        double r115711 = x;
        double r115712 = y;
        double r115713 = 1.0;
        double r115714 = r115711 * r115712;
        double r115715 = 2.0;
        double r115716 = r115714 / r115715;
        double r115717 = r115713 + r115716;
        double r115718 = r115712 / r115717;
        double r115719 = r115711 - r115718;
        return r115719;
}

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 2019326 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))