Average Error: 0.2 → 0.2
Time: 4.0s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 \cdot \left(1 + \sqrt{x + 1}\right)}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 \cdot \left(1 + \sqrt{x + 1}\right)}
double f(double x) {
        double r102472 = x;
        double r102473 = 1.0;
        double r102474 = r102472 + r102473;
        double r102475 = sqrt(r102474);
        double r102476 = r102473 + r102475;
        double r102477 = r102472 / r102476;
        return r102477;
}
↓
double f(double x) {
        double r102478 = x;
        double r102479 = 1.0;
        double r102480 = 1.0;
        double r102481 = r102478 + r102480;
        double r102482 = sqrt(r102481);
        double r102483 = r102480 + r102482;
        double r102484 = r102479 * r102483;
        double r102485 = r102478 / r102484;
        return r102485;
}

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 *-un-lft-identity0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))