Average Error: 0.0 → 0.0
Time: 8.4s
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 r490035 = x;
        double r490036 = y;
        double r490037 = 1.0;
        double r490038 = r490035 * r490036;
        double r490039 = 2.0;
        double r490040 = r490038 / r490039;
        double r490041 = r490037 + r490040;
        double r490042 = r490036 / r490041;
        double r490043 = r490035 - r490042;
        return r490043;
}
↓
double f(double x, double y) {
        double r490044 = x;
        double r490045 = y;
        double r490046 = 1.0;
        double r490047 = r490044 * r490045;
        double r490048 = 2.0;
        double r490049 = r490047 / r490048;
        double r490050 = r490046 + r490049;
        double r490051 = r490045 / r490050;
        double r490052 = r490044 - r490051;
        return r490052;
}

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 2020042 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))