Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{\frac{x \cdot y}{2} + 1}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{\frac{x \cdot y}{2} + 1}
double f(double x, double y) {
        double r398659 = x;
        double r398660 = y;
        double r398661 = 1.0;
        double r398662 = r398659 * r398660;
        double r398663 = 2.0;
        double r398664 = r398662 / r398663;
        double r398665 = r398661 + r398664;
        double r398666 = r398660 / r398665;
        double r398667 = r398659 - r398666;
        return r398667;
}
↓
double f(double x, double y) {
        double r398668 = x;
        double r398669 = y;
        double r398670 = r398668 * r398669;
        double r398671 = 2.0;
        double r398672 = r398670 / r398671;
        double r398673 = 1.0;
        double r398674 = r398672 + r398673;
        double r398675 = r398669 / r398674;
        double r398676 = r398668 - r398675;
        return r398676;
}

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

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))