Average Error: 0.1 → 0.1
Time: 10.6s
Precision: 64
\[\sqrt{x + \sqrt{x}}\]
\[\sqrt{x + \sqrt{x}}\]
\sqrt{x + \sqrt{x}}
\sqrt{x + \sqrt{x}}
double f(double x) {
        double r1854352 = x;
        double r1854353 = sqrt(r1854352);
        double r1854354 = r1854352 + r1854353;
        double r1854355 = sqrt(r1854354);
        return r1854355;
}

double f(double x) {
        double r1854356 = x;
        double r1854357 = sqrt(r1854356);
        double r1854358 = r1854356 + r1854357;
        double r1854359 = sqrt(r1854358);
        return r1854359;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\sqrt{x + \sqrt{x}}\]
  2. Final simplification0.1

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

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(x+sqrt(x))"
  :precision binary64
  (sqrt (+ x (sqrt x))))