Average Error: 0.0 → 0.0
Time: 7.9s
Precision: 64
\[\sqrt{x + 1} + \sqrt{\sqrt{x + 1}}\]
\[\sqrt{x + 1} + \sqrt{\sqrt{x + 1}}\]
\sqrt{x + 1} + \sqrt{\sqrt{x + 1}}
\sqrt{x + 1} + \sqrt{\sqrt{x + 1}}
double f(double x) {
        double r3630006 = x;
        double r3630007 = 1.0;
        double r3630008 = r3630006 + r3630007;
        double r3630009 = sqrt(r3630008);
        double r3630010 = sqrt(r3630009);
        double r3630011 = r3630009 + r3630010;
        return r3630011;
}

double f(double x) {
        double r3630012 = x;
        double r3630013 = 1.0;
        double r3630014 = r3630012 + r3630013;
        double r3630015 = sqrt(r3630014);
        double r3630016 = sqrt(r3630015);
        double r3630017 = r3630015 + r3630016;
        return r3630017;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\sqrt{x + 1} + \sqrt{\sqrt{x + 1}}\]
  2. Final simplification0.0

    \[\leadsto \sqrt{x + 1} + \sqrt{\sqrt{x + 1}}\]

Reproduce

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