Average Error: 0.0 → 0.0
Time: 2.7s
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 r300031 = x;
        double r300032 = y;
        double r300033 = 1.0;
        double r300034 = r300031 * r300032;
        double r300035 = 2.0;
        double r300036 = r300034 / r300035;
        double r300037 = r300033 + r300036;
        double r300038 = r300032 / r300037;
        double r300039 = r300031 - r300038;
        return r300039;
}
↓
double f(double x, double y) {
        double r300040 = x;
        double r300041 = y;
        double r300042 = 1.0;
        double r300043 = r300040 * r300041;
        double r300044 = 2.0;
        double r300045 = r300043 / r300044;
        double r300046 = r300042 + r300045;
        double r300047 = r300041 / r300046;
        double r300048 = r300040 - r300047;
        return r300048;
}

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)))))