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 r194002 = x;
        double r194003 = y;
        double r194004 = 1.0;
        double r194005 = r194002 * r194003;
        double r194006 = 2.0;
        double r194007 = r194005 / r194006;
        double r194008 = r194004 + r194007;
        double r194009 = r194003 / r194008;
        double r194010 = r194002 - r194009;
        return r194010;
}
↓
double f(double x, double y) {
        double r194011 = x;
        double r194012 = y;
        double r194013 = 1.0;
        double r194014 = r194011 * r194012;
        double r194015 = 2.0;
        double r194016 = r194014 / r194015;
        double r194017 = r194013 + r194016;
        double r194018 = r194012 / r194017;
        double r194019 = r194011 - r194018;
        return r194019;
}

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 2020027 +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)))))