Average Error: 0.0 → 0.0
Time: 1.5s
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 r231995 = x;
        double r231996 = y;
        double r231997 = 1.0;
        double r231998 = r231995 * r231996;
        double r231999 = 2.0;
        double r232000 = r231998 / r231999;
        double r232001 = r231997 + r232000;
        double r232002 = r231996 / r232001;
        double r232003 = r231995 - r232002;
        return r232003;
}
↓
double f(double x, double y) {
        double r232004 = x;
        double r232005 = y;
        double r232006 = 1.0;
        double r232007 = r232004 * r232005;
        double r232008 = 2.0;
        double r232009 = r232007 / r232008;
        double r232010 = r232006 + r232009;
        double r232011 = r232005 / r232010;
        double r232012 = r232004 - r232011;
        return r232012;
}

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 2020064 +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)))))