Average Error: 0.2 → 0.2
Time: 13.0s
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 r8175281 = x;
        double r8175282 = 1.0;
        double r8175283 = r8175281 + r8175282;
        double r8175284 = sqrt(r8175283);
        double r8175285 = r8175282 + r8175284;
        double r8175286 = r8175281 / r8175285;
        return r8175286;
}
↓
double f(double x) {
        double r8175287 = x;
        double r8175288 = 1.0;
        double r8175289 = r8175288 + r8175287;
        double r8175290 = sqrt(r8175289);
        double r8175291 = r8175288 + r8175290;
        double r8175292 = r8175287 / r8175291;
        return r8175292;
}

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 2019162 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))