Average Error: 0.2 → 0.2
Time: 9.6s
Precision: 64
\[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
↓
\[\frac{x}{1.0 + \sqrt{1.0 + x}}\]
\frac{x}{1.0 + \sqrt{x + 1.0}}
↓
\frac{x}{1.0 + \sqrt{1.0 + x}}
double f(double x) {
        double r2266018 = x;
        double r2266019 = 1.0;
        double r2266020 = r2266018 + r2266019;
        double r2266021 = sqrt(r2266020);
        double r2266022 = r2266019 + r2266021;
        double r2266023 = r2266018 / r2266022;
        return r2266023;
}
↓
double f(double x) {
        double r2266024 = x;
        double r2266025 = 1.0;
        double r2266026 = r2266025 + r2266024;
        double r2266027 = sqrt(r2266026);
        double r2266028 = r2266025 + r2266027;
        double r2266029 = r2266024 / r2266028;
        return r2266029;
}

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

    \[\frac{x}{1.0 + \sqrt{x + 1.0}}\]

  2. Final simplification0.2

    \[\leadsto \frac{x}{1.0 + \sqrt{1.0 + x}}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))