Average Error: 0.0 → 0.0
Time: 4.2s
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 r291973 = x;
        double r291974 = y;
        double r291975 = 1.0;
        double r291976 = r291973 * r291974;
        double r291977 = 2.0;
        double r291978 = r291976 / r291977;
        double r291979 = r291975 + r291978;
        double r291980 = r291974 / r291979;
        double r291981 = r291973 - r291980;
        return r291981;
}
↓
double f(double x, double y) {
        double r291982 = x;
        double r291983 = y;
        double r291984 = 1.0;
        double r291985 = r291982 * r291983;
        double r291986 = 2.0;
        double r291987 = r291985 / r291986;
        double r291988 = r291984 + r291987;
        double r291989 = r291983 / r291988;
        double r291990 = r291982 - r291989;
        return r291990;
}

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 2020047 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))