Average Error: 5.8 → 5.8
Time: 1.2s
Precision: binary64
\[\frac{1}{\sqrt{1 + {\left(\frac{p}{q - r}\right)}^{2}}}\]
↓
\[\frac{1}{\sqrt{1 + {\left(\frac{p}{q - r}\right)}^{2}}}\]
\frac{1}{\sqrt{1 + {\left(\frac{p}{q - r}\right)}^{2}}}
↓
\frac{1}{\sqrt{1 + {\left(\frac{p}{q - r}\right)}^{2}}}
double code(double p, double q, double r) {
	return ((double) (1.0 / ((double) sqrt(((double) (1.0 + ((double) pow(((double) (p / ((double) (q - r)))), 2.0))))))));
}
↓
double code(double p, double q, double r) {
	return ((double) (1.0 / ((double) sqrt(((double) (1.0 + ((double) pow(((double) (p / ((double) (q - r)))), 2.0))))))));
}

Error

Bits error versus p

Bits error versus q

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 5.8

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

  2. Final simplification5.8

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

Reproduce

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