Average Error: 0.2 → 0.2
Time: 13.7s
Precision: 64
\[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
↓
\[x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}\]
\frac{x}{1.0 + \sqrt{x + 1.0}}
↓
x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}
double f(double x) {
        double r7729125 = x;
        double r7729126 = 1.0;
        double r7729127 = r7729125 + r7729126;
        double r7729128 = sqrt(r7729127);
        double r7729129 = r7729126 + r7729128;
        double r7729130 = r7729125 / r7729129;
        return r7729130;
}
↓
double f(double x) {
        double r7729131 = x;
        double r7729132 = 1.0;
        double r7729133 = 1.0;
        double r7729134 = r7729131 + r7729133;
        double r7729135 = sqrt(r7729134);
        double r7729136 = r7729133 + r7729135;
        double r7729137 = r7729132 / r7729136;
        double r7729138 = r7729131 * r7729137;
        return r7729138;
}

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

    \[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
  2. Using strategy rm

  3. Applied div-inv0.2

    \[\leadsto \color{blue}{x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}}\]

  4. Final simplification0.2

    \[\leadsto x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))