Average Error: 16.1 → 16.1
Time: 470.0ms
Precision: binary64
\[\sqrt{1 + a \cdot a}\]
↓
\[\sqrt{1 + a \cdot a}\]
\sqrt{1 + a \cdot a}
↓
\sqrt{1 + a \cdot a}
double code(double a) {
	return ((double) sqrt(((double) (1.0 + ((double) (a * a))))));
}
↓
double code(double a) {
	return ((double) sqrt(((double) (1.0 + ((double) (a * a))))));
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.1

    \[\sqrt{1 + a \cdot a}\]

  2. Final simplification16.1

    \[\leadsto \sqrt{1 + a \cdot a}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a)
  :name "(sqrt (+ 1 (* a a)))"
  :precision binary64
  (sqrt (+ 1.0 (* a a))))