Average Error: 0.0 → 0.0
Time: 3.6s
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 r167438 = x;
        double r167439 = y;
        double r167440 = 1.0;
        double r167441 = r167438 * r167439;
        double r167442 = 2.0;
        double r167443 = r167441 / r167442;
        double r167444 = r167440 + r167443;
        double r167445 = r167439 / r167444;
        double r167446 = r167438 - r167445;
        return r167446;
}
↓
double f(double x, double y) {
        double r167447 = x;
        double r167448 = y;
        double r167449 = 1.0;
        double r167450 = r167447 * r167448;
        double r167451 = 2.0;
        double r167452 = r167450 / r167451;
        double r167453 = r167449 + r167452;
        double r167454 = r167448 / r167453;
        double r167455 = r167447 - r167454;
        return r167455;
}

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 2019209 +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)))))