Average Error: 0.0 → 0.0
Time: 1.4s
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 r229014 = x;
        double r229015 = y;
        double r229016 = 1.0;
        double r229017 = r229014 * r229015;
        double r229018 = 2.0;
        double r229019 = r229017 / r229018;
        double r229020 = r229016 + r229019;
        double r229021 = r229015 / r229020;
        double r229022 = r229014 - r229021;
        return r229022;
}
↓
double f(double x, double y) {
        double r229023 = x;
        double r229024 = y;
        double r229025 = 1.0;
        double r229026 = r229023 * r229024;
        double r229027 = 2.0;
        double r229028 = r229026 / r229027;
        double r229029 = r229025 + r229028;
        double r229030 = r229024 / r229029;
        double r229031 = r229023 - r229030;
        return r229031;
}

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 2020018 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))