Average Error: 0.2 → 0.2
Time: 5.3s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 + \sqrt{x + 1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 + \sqrt{x + 1}}
double f(double x) {
        double r380 = x;
        double r381 = 1.0;
        double r382 = r380 + r381;
        double r383 = sqrt(r382);
        double r384 = r381 + r383;
        double r385 = r380 / r384;
        return r385;
}
↓
double f(double x) {
        double r386 = x;
        double r387 = 1.0;
        double r388 = r386 + r387;
        double r389 = sqrt(r388);
        double r390 = r387 + r389;
        double r391 = r386 / r390;
        return r391;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))