Average Error: 9.9 → 9.9
Time: 698.0ms
Precision: binary64
\[\frac{a}{\sqrt{1 + b \cdot b}}\]
↓
\[\frac{a}{\sqrt{1 + b \cdot b}}\]
\frac{a}{\sqrt{1 + b \cdot b}}
↓
\frac{a}{\sqrt{1 + b \cdot b}}
double code(double a, double b) {
	return ((double) (a / ((double) sqrt(((double) (1.0 + ((double) (b * b))))))));
}
↓
double code(double a, double b) {
	return ((double) (a / ((double) sqrt(((double) (1.0 + ((double) (b * 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 9.9

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

  2. Final simplification9.9

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

Reproduce

herbie shell --seed 2020152 
(FPCore (a b)
  :name "(/ a (sqrt (+ 1 (* b b))))"
  :precision binary64
  (/ a (sqrt (+ 1.0 (* b b)))))