Average Error: 0.0 → 0.1
Time: 2.6s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - y \cdot \frac{1}{1 + \frac{x \cdot y}{2}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - y \cdot \frac{1}{1 + \frac{x \cdot y}{2}}
double f(double x, double y) {
        double r265139 = x;
        double r265140 = y;
        double r265141 = 1.0;
        double r265142 = r265139 * r265140;
        double r265143 = 2.0;
        double r265144 = r265142 / r265143;
        double r265145 = r265141 + r265144;
        double r265146 = r265140 / r265145;
        double r265147 = r265139 - r265146;
        return r265147;
}
↓
double f(double x, double y) {
        double r265148 = x;
        double r265149 = y;
        double r265150 = 1.0;
        double r265151 = 1.0;
        double r265152 = r265148 * r265149;
        double r265153 = 2.0;
        double r265154 = r265152 / r265153;
        double r265155 = r265151 + r265154;
        double r265156 = r265150 / r265155;
        double r265157 = r265149 * r265156;
        double r265158 = r265148 - r265157;
        return r265158;
}

Error

Bits error versus x

Bits error versus y

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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. Using strategy rm

  3. Applied div-inv0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))