Average Error: 0.2 → 0.2
Time: 3.2s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[x \cdot \frac{1}{1 + \sqrt{x + 1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
x \cdot \frac{1}{1 + \sqrt{x + 1}}
double f(double x) {
        double r88172 = x;
        double r88173 = 1.0;
        double r88174 = r88172 + r88173;
        double r88175 = sqrt(r88174);
        double r88176 = r88173 + r88175;
        double r88177 = r88172 / r88176;
        return r88177;
}
↓
double f(double x) {
        double r88178 = x;
        double r88179 = 1.0;
        double r88180 = 1.0;
        double r88181 = r88178 + r88180;
        double r88182 = sqrt(r88181);
        double r88183 = r88180 + r88182;
        double r88184 = r88179 / r88183;
        double r88185 = r88178 * r88184;
        return r88185;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{x}{1 + \sqrt{x + 1}}\]
  2. Using strategy rm

  3. Applied div-inv0.2

    \[\leadsto \color{blue}{x \cdot \frac{1}{1 + \sqrt{x + 1}}}\]

  4. Final simplification0.2

    \[\leadsto x \cdot \frac{1}{1 + \sqrt{x + 1}}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))