Average Error: 15.6 → 15.6
Time: 1.8s
Precision: binary64
\[\sqrt{\frac{1 - \frac{r}{q}}{\sqrt{\frac{p}{q} + {\left(1 - \frac{r}{q}\right)}^{2}}}}\]
↓
\[\sqrt{\frac{1 - \frac{r}{q}}{\sqrt{\frac{p}{q} + {\left(1 - \frac{r}{q}\right)}^{2}}}}\]
\sqrt{\frac{1 - \frac{r}{q}}{\sqrt{\frac{p}{q} + {\left(1 - \frac{r}{q}\right)}^{2}}}}
↓
\sqrt{\frac{1 - \frac{r}{q}}{\sqrt{\frac{p}{q} + {\left(1 - \frac{r}{q}\right)}^{2}}}}
double code(double r, double q, double p) {
	return ((double) sqrt(((double) (((double) (1.0 - ((double) (r / q)))) / ((double) sqrt(((double) (((double) (p / q)) + ((double) pow(((double) (1.0 - ((double) (r / q)))), 2.0))))))))));
}
↓
double code(double r, double q, double p) {
	return ((double) sqrt(((double) (((double) (1.0 - ((double) (r / q)))) / ((double) sqrt(((double) (((double) (p / q)) + ((double) pow(((double) (1.0 - ((double) (r / q)))), 2.0))))))))));
}

Error

Bits error versus r

Bits error versus q

Bits error versus p

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.6

    \[\sqrt{\frac{1 - \frac{r}{q}}{\sqrt{\frac{p}{q} + {\left(1 - \frac{r}{q}\right)}^{2}}}}\]

  2. Final simplification15.6

    \[\leadsto \sqrt{\frac{1 - \frac{r}{q}}{\sqrt{\frac{p}{q} + {\left(1 - \frac{r}{q}\right)}^{2}}}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (r q p)
  :name "(sqrt (/ (- 1 (/ r q)) (sqrt (+ (/ p q) (pow (- 1 (/ r q)) 2)))))"
  :precision binary64
  (sqrt (/ (- 1.0 (/ r q)) (sqrt (+ (/ p q) (pow (- 1.0 (/ r q)) 2.0))))))