Average Error: 28.9 → 0.1
Time: 8.8s
Precision: 64
$\left(\left(1 + x\right) - x\right) + \sqrt{\frac{1}{x}}$
$\sqrt{\frac{1}{x}} + 1$
\left(\left(1 + x\right) - x\right) + \sqrt{\frac{1}{x}}
\sqrt{\frac{1}{x}} + 1
double f(double x) {
double r3468310 = 1.0;
double r3468311 = x;
double r3468312 = r3468310 + r3468311;
double r3468313 = r3468312 - r3468311;
double r3468314 = r3468310 / r3468311;
double r3468315 = sqrt(r3468314);
double r3468316 = r3468313 + r3468315;
return r3468316;
}


double f(double x) {
double r3468317 = 1.0;
double r3468318 = x;
double r3468319 = r3468317 / r3468318;
double r3468320 = sqrt(r3468319);
double r3468321 = r3468320 + r3468317;
return r3468321;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 28.9

$\left(\left(1 + x\right) - x\right) + \sqrt{\frac{1}{x}}$
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 1
(FPCore (x)
:name "(1+x) - x + sqrt(1/x)"
:precision binary64
(+ (- (+ 1 x) x) (sqrt (/ 1 x))))