Average Error: 32.7 → 32.7
Time: 3.0s
Precision: binary64
\[\sqrt{1 + \frac{x - y}{\sqrt{p \cdot x + {\left(x - y\right)}^{2}}}}\]
↓
\[\sqrt{1 + \frac{x - y}{\sqrt{p \cdot x + {\left(x - y\right)}^{2}}}}\]
\sqrt{1 + \frac{x - y}{\sqrt{p \cdot x + {\left(x - y\right)}^{2}}}}
↓
\sqrt{1 + \frac{x - y}{\sqrt{p \cdot x + {\left(x - y\right)}^{2}}}}
double code(double x, double y, double p) {
	return ((double) sqrt(((double) (1.0 + ((double) (((double) (x - y)) / ((double) sqrt(((double) (((double) (p * x)) + ((double) pow(((double) (x - y)), 2.0))))))))))));
}
↓
double code(double x, double y, double p) {
	return ((double) sqrt(((double) (1.0 + ((double) (((double) (x - y)) / ((double) sqrt(((double) (((double) (p * x)) + ((double) pow(((double) (x - y)), 2.0))))))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus p

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 32.7

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

  2. Final simplification32.7

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

Reproduce

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