Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[\log \left(x + \sqrt{x - 1} \cdot \sqrt{x + 1}\right)\]
↓
\[\log \left(x + \sqrt{x - 1} \cdot \sqrt{x + 1}\right)\]
\log \left(x + \sqrt{x - 1} \cdot \sqrt{x + 1}\right)
↓
\log \left(x + \sqrt{x - 1} \cdot \sqrt{x + 1}\right)
double code(double x) {
	return ((double) log(((double) (x + ((double) (((double) sqrt(((double) (x - 1.0)))) * ((double) sqrt(((double) (x + 1.0))))))))));
}
↓
double code(double x) {
	return ((double) log(((double) (x + ((double) (((double) sqrt(((double) (x - 1.0)))) * ((double) sqrt(((double) (x + 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 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(log (+ x (* (sqrt (- x 1)) (sqrt (+ x 1)))))"
  :precision binary64
  (log (+ x (* (sqrt (- x 1.0)) (sqrt (+ x 1.0))))))