Average Error: 0.0 → 0.0
Time: 10.7s
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 r229500 = x;
        double r229501 = y;
        double r229502 = 1.0;
        double r229503 = r229500 * r229501;
        double r229504 = 2.0;
        double r229505 = r229503 / r229504;
        double r229506 = r229502 + r229505;
        double r229507 = r229501 / r229506;
        double r229508 = r229500 - r229507;
        return r229508;
}
↓
double f(double x, double y) {
        double r229509 = x;
        double r229510 = y;
        double r229511 = r229509 * r229510;
        double r229512 = 2.0;
        double r229513 = r229511 / r229512;
        double r229514 = 1.0;
        double r229515 = r229513 + r229514;
        double r229516 = r229510 / r229515;
        double r229517 = r229509 - r229516;
        return r229517;
}

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 2019179 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))