Average Error: 0.2 → 0.2
Time: 9.4s
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 r2255195 = x;
        double r2255196 = 1.0;
        double r2255197 = r2255195 + r2255196;
        double r2255198 = sqrt(r2255197);
        double r2255199 = r2255196 + r2255198;
        double r2255200 = r2255195 / r2255199;
        return r2255200;
}
↓
double f(double x) {
        double r2255201 = x;
        double r2255202 = 1.0;
        double r2255203 = r2255202 + r2255201;
        double r2255204 = sqrt(r2255203);
        double r2255205 = r2255202 + r2255204;
        double r2255206 = r2255201 / r2255205;
        return r2255206;
}

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