Average Error: 0.2 → 0.2
Time: 12.8s
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 r74111 = x;
        double r74112 = 1.0;
        double r74113 = r74111 + r74112;
        double r74114 = sqrt(r74113);
        double r74115 = r74112 + r74114;
        double r74116 = r74111 / r74115;
        return r74116;
}
↓
double f(double x) {
        double r74117 = x;
        double r74118 = 1.0;
        double r74119 = r74117 + r74118;
        double r74120 = sqrt(r74119);
        double r74121 = r74118 + r74120;
        double r74122 = r74117 / r74121;
        return r74122;
}

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 2019235 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))