Average Error: 16.0 → 16.0
Time: 2.1s
Precision: binary64
\[\sqrt{1 + {x}^{2}} + \log \left(\frac{x}{1 + \sqrt{1 + {x}^{2}}}\right)\]
↓
\[\sqrt{1 + {x}^{2}} + \log \left(\frac{x}{1 + \sqrt{1 + {x}^{2}}}\right)\]
\sqrt{1 + {x}^{2}} + \log \left(\frac{x}{1 + \sqrt{1 + {x}^{2}}}\right)
↓
\sqrt{1 + {x}^{2}} + \log \left(\frac{x}{1 + \sqrt{1 + {x}^{2}}}\right)
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) pow(x, 2.0)))))) + ((double) log(((double) (x / ((double) (1.0 + ((double) sqrt(((double) (1.0 + ((double) pow(x, 2.0))))))))))))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) pow(x, 2.0)))))) + ((double) log(((double) (x / ((double) (1.0 + ((double) sqrt(((double) (1.0 + ((double) pow(x, 2.0))))))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.0

    \[\sqrt{1 + {x}^{2}} + \log \left(\frac{x}{1 + \sqrt{1 + {x}^{2}}}\right)\]

  2. Final simplification16.0

    \[\leadsto \sqrt{1 + {x}^{2}} + \log \left(\frac{x}{1 + \sqrt{1 + {x}^{2}}}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (sqrt (+ 1 (pow x 2))) (log (/ x (+ 1 (sqrt (+ 1 (pow x 2)))))))"
  :precision binary64
  (+ (sqrt (+ 1.0 (pow x 2.0))) (log (/ x (+ 1.0 (sqrt (+ 1.0 (pow x 2.0))))))))