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 r199968 = x;
        double r199969 = y;
        double r199970 = 1.0;
        double r199971 = r199968 * r199969;
        double r199972 = 2.0;
        double r199973 = r199971 / r199972;
        double r199974 = r199970 + r199973;
        double r199975 = r199969 / r199974;
        double r199976 = r199968 - r199975;
        return r199976;
}
↓
double f(double x, double y) {
        double r199977 = x;
        double r199978 = y;
        double r199979 = 1.0;
        double r199980 = r199977 * r199978;
        double r199981 = 2.0;
        double r199982 = r199980 / r199981;
        double r199983 = r199979 + r199982;
        double r199984 = r199978 / r199983;
        double r199985 = r199977 - r199984;
        return r199985;
}

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