Average Error: 46.2 → 46.2
Time: 1.2s
Precision: binary64
\[\sqrt{\left(x - 1\right) \cdot \left(x + 1\right) + 1}\]
↓
\[\sqrt{\left(x - 1\right) \cdot \left(x + 1\right) + 1}\]
\sqrt{\left(x - 1\right) \cdot \left(x + 1\right) + 1}
↓
\sqrt{\left(x - 1\right) \cdot \left(x + 1\right) + 1}
double code(double x) {
	return ((double) sqrt(((double) (((double) (((double) (x - 1.0)) * ((double) (x + 1.0)))) + 1.0))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) (((double) (x - 1.0)) * ((double) (x + 1.0)))) + 1.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.2

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

  2. Final simplification46.2

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(sqrt (+ (* (- x 1.0) (+ x 1.0)) 1.0))"
  :precision binary64
  (sqrt (+ (* (- x 1.0) (+ x 1.0)) 1.0)))