Average Error: 0.1 → 0.1
Time: 1.1s
Precision: binary64
\[\sqrt{\frac{\left(x + 1\right) - i}{x + i}}\]
↓
\[\sqrt{\frac{\left(x + 1\right) - i}{x + i}}\]
\sqrt{\frac{\left(x + 1\right) - i}{x + i}}
↓
\sqrt{\frac{\left(x + 1\right) - i}{x + i}}
double code(double x, double i) {
	return ((double) sqrt(((double) (((double) (((double) (x + 1.0)) - i)) / ((double) (x + i))))));
}
↓
double code(double x, double i) {
	return ((double) sqrt(((double) (((double) (((double) (x + 1.0)) - i)) / ((double) (x + i))))));
}

Error

Bits error versus x

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

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