Average Error: 0.0 → 0.0
Time: 13.9s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{\frac{x \cdot y}{2} + 1}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{\frac{x \cdot y}{2} + 1}
double f(double x, double y) {
        double r12948946 = x;
        double r12948947 = y;
        double r12948948 = 1.0;
        double r12948949 = r12948946 * r12948947;
        double r12948950 = 2.0;
        double r12948951 = r12948949 / r12948950;
        double r12948952 = r12948948 + r12948951;
        double r12948953 = r12948947 / r12948952;
        double r12948954 = r12948946 - r12948953;
        return r12948954;
}
↓
double f(double x, double y) {
        double r12948955 = x;
        double r12948956 = y;
        double r12948957 = r12948955 * r12948956;
        double r12948958 = 2.0;
        double r12948959 = r12948957 / r12948958;
        double r12948960 = 1.0;
        double r12948961 = r12948959 + r12948960;
        double r12948962 = r12948956 / r12948961;
        double r12948963 = r12948955 - r12948962;
        return r12948963;
}

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

    \[\leadsto x - \frac{y}{\frac{x \cdot y}{2} + 1}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))