Average Error: 0.2 → 0.2
Time: 3.2s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{{\left(1 + \sqrt{x + 1}\right)}^{1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{{\left(1 + \sqrt{x + 1}\right)}^{1}}
double f(double x) {
        double r142506 = x;
        double r142507 = 1.0;
        double r142508 = r142506 + r142507;
        double r142509 = sqrt(r142508);
        double r142510 = r142507 + r142509;
        double r142511 = r142506 / r142510;
        return r142511;
}
↓
double f(double x) {
        double r142512 = x;
        double r142513 = 1.0;
        double r142514 = r142512 + r142513;
        double r142515 = sqrt(r142514);
        double r142516 = r142513 + r142515;
        double r142517 = 1.0;
        double r142518 = pow(r142516, r142517);
        double r142519 = r142512 / r142518;
        return r142519;
}

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 pow10.2

    \[\leadsto \frac{x}{\color{blue}{{\left(1 + \sqrt{x + 1}\right)}^{1}}}\]

  4. Final simplification0.2

    \[\leadsto \frac{x}{{\left(1 + \sqrt{x + 1}\right)}^{1}}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))