Average Error: 0.2 → 0.2
Time: 13.3s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 + \sqrt{1 + x}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 + \sqrt{1 + x}}
double f(double x) {
        double r3725380 = x;
        double r3725381 = 1.0;
        double r3725382 = r3725380 + r3725381;
        double r3725383 = sqrt(r3725382);
        double r3725384 = r3725381 + r3725383;
        double r3725385 = r3725380 / r3725384;
        return r3725385;
}
↓
double f(double x) {
        double r3725386 = x;
        double r3725387 = 1.0;
        double r3725388 = r3725387 + r3725386;
        double r3725389 = sqrt(r3725388);
        double r3725390 = r3725387 + r3725389;
        double r3725391 = r3725386 / r3725390;
        return r3725391;
}

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

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))