Average Error: 0.1 → 0.1
Time: 1.2s
Precision: binary64
\[\sqrt{\frac{\left(x - y\right) + 1}{x + y}}\]
↓
\[\sqrt{\frac{\left(x - y\right) + 1}{x + y}}\]
\sqrt{\frac{\left(x - y\right) + 1}{x + y}}
↓
\sqrt{\frac{\left(x - y\right) + 1}{x + y}}
double code(double x, double y) {
	return ((double) sqrt(((double) (((double) (((double) (x - y)) + 1.0)) / ((double) (x + y))))));
}
↓
double code(double x, double y) {
	return ((double) sqrt(((double) (((double) (((double) (x - y)) + 1.0)) / ((double) (x + y))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(sqrt (/ (+ (- x y) 1) (+ x y)))"
  :precision binary64
  (sqrt (/ (+ (- x y) 1.0) (+ x y))))