Average Error: 0.0 → 0.0
Time: 8.1s
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 r278947 = x;
        double r278948 = y;
        double r278949 = 1.0;
        double r278950 = r278947 * r278948;
        double r278951 = 2.0;
        double r278952 = r278950 / r278951;
        double r278953 = r278949 + r278952;
        double r278954 = r278948 / r278953;
        double r278955 = r278947 - r278954;
        return r278955;
}
↓
double f(double x, double y) {
        double r278956 = x;
        double r278957 = y;
        double r278958 = 1.0;
        double r278959 = r278956 * r278957;
        double r278960 = 2.0;
        double r278961 = r278959 / r278960;
        double r278962 = r278958 + r278961;
        double r278963 = r278957 / r278962;
        double r278964 = r278956 - r278963;
        return r278964;
}

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)))))