Average Error: 0.0 → 0.0
Time: 6.4s
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 r162001 = x;
        double r162002 = y;
        double r162003 = 1.0;
        double r162004 = r162001 * r162002;
        double r162005 = 2.0;
        double r162006 = r162004 / r162005;
        double r162007 = r162003 + r162006;
        double r162008 = r162002 / r162007;
        double r162009 = r162001 - r162008;
        return r162009;
}
↓
double f(double x, double y) {
        double r162010 = x;
        double r162011 = y;
        double r162012 = 1.0;
        double r162013 = r162010 * r162011;
        double r162014 = 2.0;
        double r162015 = r162013 / r162014;
        double r162016 = r162012 + r162015;
        double r162017 = r162011 / r162016;
        double r162018 = r162010 - r162017;
        return r162018;
}

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 2019308 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))