Average Error: 0.2 → 0.2
Time: 9.6s
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 r77157 = x;
        double r77158 = 1.0;
        double r77159 = r77157 + r77158;
        double r77160 = sqrt(r77159);
        double r77161 = r77158 + r77160;
        double r77162 = r77157 / r77161;
        return r77162;
}
↓
double f(double x) {
        double r77163 = x;
        double r77164 = 1.0;
        double r77165 = r77163 + r77164;
        double r77166 = sqrt(r77165);
        double r77167 = r77164 + r77166;
        double r77168 = r77163 / r77167;
        return r77168;
}

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 2019322 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))