Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[\frac{\sqrt{1 + {x}^{2}}}{\sqrt{1 + {x}^{2}} \cdot \sqrt{1 - {x}^{2}}}\]
↓
\[\frac{2}{\sqrt{1 - {x}^{2}} \cdot 2}\]
\frac{\sqrt{1 + {x}^{2}}}{\sqrt{1 + {x}^{2}} \cdot \sqrt{1 - {x}^{2}}}
↓
\frac{2}{\sqrt{1 - {x}^{2}} \cdot 2}
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) pow(x, 2.0)))))) / ((double) (((double) sqrt(((double) (1.0 + ((double) pow(x, 2.0)))))) * ((double) sqrt(((double) (1.0 - ((double) pow(x, 2.0))))))))));
}
↓
double code(double x) {
	return ((double) (2.0 / ((double) (((double) sqrt(((double) (1.0 - ((double) pow(x, 2.0)))))) * 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 0.0

    \[\frac{\sqrt{1 + {x}^{2}}}{\sqrt{1 + {x}^{2}} \cdot \sqrt{1 - {x}^{2}}}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{2}{\sqrt{1 - {x}^{2}} \cdot 2}}\]

  3. Final simplification0.0

    \[\leadsto \frac{2}{\sqrt{1 - {x}^{2}} \cdot 2}\]

Reproduce

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