Average Error: 0.1 → 0.1
Time: 1.0s
Precision: binary64
\[\sqrt{2^{a} + 2^{b}}\]
↓
\[\sqrt{2^{a} + 2^{b}}\]
\sqrt{2^{a} + 2^{b}}
↓
\sqrt{2^{a} + 2^{b}}
double code(double a, double b) {
	return ((double) sqrt(((double) (((double) exp2(a)) + ((double) exp2(b))))));
}
↓
double code(double a, double b) {
	return ((double) sqrt(((double) (((double) exp2(a)) + ((double) exp2(b))))));
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\sqrt{2^{a} + 2^{b}}\]

  2. Final simplification0.1

    \[\leadsto \sqrt{2^{a} + 2^{b}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a b)
  :name "(sqrt (+ (exp2 a) (exp2 b)))"
  :precision binary64
  (sqrt (+ (exp2 a) (exp2 b))))