Average Error: 4.6 → 4.6
Time: 1.2s
Precision: binary64
\[\frac{b \cdot a}{\sqrt{1 + {\left(\frac{1}{b}\right)}^{2}}}\]
↓
\[\frac{b \cdot a}{\sqrt{1 + {\left(\frac{1}{b}\right)}^{2}}}\]
\frac{b \cdot a}{\sqrt{1 + {\left(\frac{1}{b}\right)}^{2}}}
↓
\frac{b \cdot a}{\sqrt{1 + {\left(\frac{1}{b}\right)}^{2}}}
double code(double b, double a) {
	return ((double) (((double) (b * a)) / ((double) sqrt(((double) (1.0 + ((double) pow(((double) (1.0 / b)), 2.0))))))));
}
↓
double code(double b, double a) {
	return ((double) (((double) (b * a)) / ((double) sqrt(((double) (1.0 + ((double) pow(((double) (1.0 / b)), 2.0))))))));
}

Error

Bits error versus b

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.6

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

  2. Final simplification4.6

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

Reproduce

herbie shell --seed 2020152 
(FPCore (b a)
  :name "(/ (* b a) (sqrt (+ 1 (pow (/ 1 b) 2))))"
  :precision binary64
  (/ (* b a) (sqrt (+ 1.0 (pow (/ 1.0 b) 2.0)))))