Average Error: 0.2 → 0.2
Time: 3.4s
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 r119149 = x;
        double r119150 = 1.0;
        double r119151 = r119149 + r119150;
        double r119152 = sqrt(r119151);
        double r119153 = r119150 + r119152;
        double r119154 = r119149 / r119153;
        return r119154;
}
↓
double f(double x) {
        double r119155 = x;
        double r119156 = 1.0;
        double r119157 = 1.0;
        double r119158 = r119155 + r119157;
        double r119159 = sqrt(r119158);
        double r119160 = r119157 + r119159;
        double r119161 = r119156 / r119160;
        double r119162 = r119155 * r119161;
        return r119162;
}

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 2019353 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))