Average Error: 21.4 → 21.4
Time: 1.1s
Precision: binary64
\[\frac{1}{\sqrt{1 + \frac{3 \cdot {p}^{2}}{{pi}^{2}}}}\]
↓
\[\frac{1}{\sqrt{1 + \frac{3 \cdot {p}^{2}}{{pi}^{2}}}}\]
\frac{1}{\sqrt{1 + \frac{3 \cdot {p}^{2}}{{pi}^{2}}}}
↓
\frac{1}{\sqrt{1 + \frac{3 \cdot {p}^{2}}{{pi}^{2}}}}
double code(double p, double pi) {
	return ((double) (1.0 / ((double) sqrt(((double) (1.0 + ((double) (((double) (3.0 * ((double) pow(p, 2.0)))) / ((double) pow(pi, 2.0))))))))));
}
↓
double code(double p, double pi) {
	return ((double) (1.0 / ((double) sqrt(((double) (1.0 + ((double) (((double) (3.0 * ((double) pow(p, 2.0)))) / ((double) pow(pi, 2.0))))))))));
}

Error

Bits error versus p

Bits error versus pi

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 21.4

    \[\frac{1}{\sqrt{1 + \frac{3 \cdot {p}^{2}}{{pi}^{2}}}}\]

  2. Final simplification21.4

    \[\leadsto \frac{1}{\sqrt{1 + \frac{3 \cdot {p}^{2}}{{pi}^{2}}}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (p pi)
  :name "(/ 1 (sqrt (+ 1 (/ (* 3 (pow p 2)) (pow pi 2)))))"
  :precision binary64
  (/ 1.0 (sqrt (+ 1.0 (/ (* 3.0 (pow p 2.0)) (pow pi 2.0))))))