Average Error: 20.6 → 20.6
Time: 721.0ms
Precision: binary64
\[\sqrt{a \cdot a + b}\]
↓
\[\sqrt{a \cdot a + b}\]
\sqrt{a \cdot a + b}
↓
\sqrt{a \cdot a + b}
double code(double a, double b) {
	return ((double) sqrt(((double) (((double) (a * a)) + b))));
}
↓
double code(double a, double b) {
	return ((double) sqrt(((double) (((double) (a * a)) + 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 20.6

    \[\sqrt{a \cdot a + b}\]

  2. Final simplification20.6

    \[\leadsto \sqrt{a \cdot a + b}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a b)
  :name "(sqrt (+ (* a a) b))"
  :precision binary64
  (sqrt (+ (* a a) b)))