Average Error: 27.8 → 27.8
Time: 1.3s
Precision: binary64
\[\frac{1 - \frac{r}{q}}{\sqrt{p \cdot p + {\left(1 - \frac{r}{q}\right)}^{2}}}\]
↓
\[\frac{1 - \frac{r}{q}}{\sqrt{p \cdot p + {\left(1 - \frac{r}{q}\right)}^{2}}}\]
\frac{1 - \frac{r}{q}}{\sqrt{p \cdot p + {\left(1 - \frac{r}{q}\right)}^{2}}}
↓
\frac{1 - \frac{r}{q}}{\sqrt{p \cdot p + {\left(1 - \frac{r}{q}\right)}^{2}}}
double code(double r, double q, double p) {
	return ((double) (((double) (1.0 - ((double) (r / q)))) / ((double) sqrt(((double) (((double) (p * p)) + ((double) pow(((double) (1.0 - ((double) (r / q)))), 2.0))))))));
}
↓
double code(double r, double q, double p) {
	return ((double) (((double) (1.0 - ((double) (r / q)))) / ((double) sqrt(((double) (((double) (p * p)) + ((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 27.8

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

  2. Final simplification27.8

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

Reproduce

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