Average Error: 23.6 → 23.6
Time: 1.4s
Precision: binary64
\[\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{\left(4 \cdot p\right) \cdot p + x \cdot x}}\right)}\]
↓
\[\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{\left(4 \cdot p\right) \cdot p + x \cdot x}}\right)}\]
\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{\left(4 \cdot p\right) \cdot p + x \cdot x}}\right)}
↓
\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{\left(4 \cdot p\right) \cdot p + x \cdot x}}\right)}
double code(double x, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (x / ((double) sqrt(((double) (((double) (((double) (4.0 * p)) * p)) + ((double) (x * x))))))))))))));
}
↓
double code(double x, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (x / ((double) sqrt(((double) (((double) (((double) (4.0 * p)) * p)) + ((double) (x * x))))))))))))));
}

Error

Bits error versus x

Bits error versus p

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 23.6

    \[\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{\left(4 \cdot p\right) \cdot p + x \cdot x}}\right)}\]

  2. Final simplification23.6

    \[\leadsto \sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{\left(4 \cdot p\right) \cdot p + x \cdot x}}\right)}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x p)
  :name "(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))"
  :precision binary64
  (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))