Average Error: 45.7 → 45.7
Time: 2.0s
Precision: binary64
\[\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right)\]
↓
\[\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right)\]
\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right)
↓
\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right)
double code(double x) {
	return ((double) log(((double) (((double) fabs(x)) + ((double) sqrt(((double) (((double) (x * x)) + 1.0))))))));
}
↓
double code(double x) {
	return ((double) log(((double) (((double) fabs(x)) + ((double) sqrt(((double) (((double) (x * 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 45.7

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

  2. Final simplification45.7

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

Reproduce

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