Average Error: 14.2 → 14.2
Time: 1.8s
Precision: binary64
\[\frac{\sqrt{1 - \frac{r}{q}}}{\sqrt{\frac{p}{q} + {\left(1 - \frac{r}{q}\right)}^{2}}}\]
↓
\[\frac{\sqrt{1 - \frac{r}{q}}}{\sqrt{\frac{p}{q} + {\left(1 - \frac{r}{q}\right)}^{2}}}\]
\frac{\sqrt{1 - \frac{r}{q}}}{\sqrt{\frac{p}{q} + {\left(1 - \frac{r}{q}\right)}^{2}}}
↓
\frac{\sqrt{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) (((double) sqrt(((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) (((double) sqrt(((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 14.2

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

  2. Final simplification14.2

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

Reproduce

herbie shell --seed 2020153 
(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)))))