Average Error: 16.1 → 16.1
Time: 925.0ms
Precision: binary64
\[\frac{\sqrt{1 + {\left(\frac{1}{b}\right)}^{2}}}{\frac{1}{b}}\]
↓
\[\frac{\sqrt{1 + {\left(\frac{1}{b}\right)}^{2}}}{\frac{1}{b}}\]
\frac{\sqrt{1 + {\left(\frac{1}{b}\right)}^{2}}}{\frac{1}{b}}
↓
\frac{\sqrt{1 + {\left(\frac{1}{b}\right)}^{2}}}{\frac{1}{b}}
double code(double b) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) pow(((double) (1.0 / b)), 2.0)))))) / ((double) (1.0 / b))));
}
↓
double code(double b) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) pow(((double) (1.0 / b)), 2.0)))))) / ((double) (1.0 / b))));
}

Error

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.1

    \[\frac{\sqrt{1 + {\left(\frac{1}{b}\right)}^{2}}}{\frac{1}{b}}\]

  2. Final simplification16.1

    \[\leadsto \frac{\sqrt{1 + {\left(\frac{1}{b}\right)}^{2}}}{\frac{1}{b}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (b)
  :name "(/ (sqrt (+ 1 (pow (/ 1 b) 2))) (/ 1 b))"
  :precision binary64
  (/ (sqrt (+ 1.0 (pow (/ 1.0 b) 2.0))) (/ 1.0 b)))