Average Error: 0.0 → 0.0
Time: 784.0ms
Precision: binary64
\[\sqrt{x + 1} + \sqrt{\sqrt{x + 1}}\]
↓
\[\sqrt{x + 1} + \sqrt{\sqrt{x + 1}}\]
\sqrt{x + 1} + \sqrt{\sqrt{x + 1}}
↓
\sqrt{x + 1} + \sqrt{\sqrt{x + 1}}
double code(double x) {
	return ((double) (((double) sqrt(((double) (x + 1.0)))) + ((double) sqrt(((double) sqrt(((double) (x + 1.0))))))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (x + 1.0)))) + ((double) sqrt(((double) sqrt(((double) (x + 1.0))))))));
}

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 2020153 
(FPCore (x)
  :name "(+ (sqrt (+ x 1)) (sqrt (sqrt (+ x 1))))"
  :precision binary64
  (+ (sqrt (+ x 1.0)) (sqrt (sqrt (+ x 1.0)))))