Average Error: 0.0 → 0.0
Time: 8.1s
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 r11325951 = x;
        double r11325952 = y;
        double r11325953 = 1.0;
        double r11325954 = r11325951 * r11325952;
        double r11325955 = 2.0;
        double r11325956 = r11325954 / r11325955;
        double r11325957 = r11325953 + r11325956;
        double r11325958 = r11325952 / r11325957;
        double r11325959 = r11325951 - r11325958;
        return r11325959;
}
↓
double f(double x, double y) {
        double r11325960 = x;
        double r11325961 = y;
        double r11325962 = r11325960 * r11325961;
        double r11325963 = 2.0;
        double r11325964 = r11325962 / r11325963;
        double r11325965 = 1.0;
        double r11325966 = r11325964 + r11325965;
        double r11325967 = r11325961 / r11325966;
        double r11325968 = r11325960 - r11325967;
        return r11325968;
}

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 2019169 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))