Average Error: 0.9 → 0.3
Time: 1.2s
Precision: binary64
\[x - \frac{\sqrt{x}}{\frac{1}{2 \cdot \sqrt{x}}}\]
↓
\[x - \frac{2}{\frac{1}{x}}\]
x - \frac{\sqrt{x}}{\frac{1}{2 \cdot \sqrt{x}}}
↓
x - \frac{2}{\frac{1}{x}}
double code(double x) {
	return ((double) (x - ((double) (((double) sqrt(x)) / ((double) (1.0 / ((double) (2.0 * ((double) sqrt(x))))))))));
}
↓
double code(double x) {
	return ((double) (x - ((double) (2.0 / ((double) (1.0 / x))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.9

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

  2. Simplified0.3

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

  3. Final simplification0.3

    \[\leadsto x - \frac{2}{\frac{1}{x}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- x (/ (sqrt x) (/ 1 (* 2 (sqrt x)))))"
  :precision binary64
  (- x (/ (sqrt x) (/ 1.0 (* 2.0 (sqrt x))))))