Average Error: 28.5 → 0.1
Time: 1.3s
Precision: binary64
\[\left(\left(1 + x\right) - x\right) + \sqrt{\frac{1}{x}}\]
↓
\[\sqrt{\frac{1}{x}} + 1\]
\left(\left(1 + x\right) - x\right) + \sqrt{\frac{1}{x}}
↓
\sqrt{\frac{1}{x}} + 1
double code(double x) {
	return ((double) (((double) (((double) (1.0 + x)) - x)) + ((double) sqrt(((double) (1.0 / x))))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 / 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 28.5

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\sqrt{\frac{1}{x}} + 1}\]

  3. Final simplification0.1

    \[\leadsto \sqrt{\frac{1}{x}} + 1\]

Reproduce

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