Average Error: 0.0 → 0.0
Time: 1.9s
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 r278007 = x;
        double r278008 = y;
        double r278009 = 1.0;
        double r278010 = r278007 * r278008;
        double r278011 = 2.0;
        double r278012 = r278010 / r278011;
        double r278013 = r278009 + r278012;
        double r278014 = r278008 / r278013;
        double r278015 = r278007 - r278014;
        return r278015;
}
↓
double f(double x, double y) {
        double r278016 = x;
        double r278017 = y;
        double r278018 = 1.0;
        double r278019 = r278016 * r278017;
        double r278020 = 2.0;
        double r278021 = r278019 / r278020;
        double r278022 = r278018 + r278021;
        double r278023 = r278017 / r278022;
        double r278024 = r278016 - r278023;
        return r278024;
}

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 2019353 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))