Average Error: 0.4 → 0.1
Time: 6.3s
Precision: 64
$\frac{1}{x \cdot x - 1}$
$\frac{\frac{1}{x + \sqrt{1}}}{x - \sqrt{1}}$
\frac{1}{x \cdot x - 1}
\frac{\frac{1}{x + \sqrt{1}}}{x - \sqrt{1}}
double f(double x) {
double r1515261 = 1.0;
double r1515262 = x;
double r1515263 = r1515262 * r1515262;
double r1515264 = r1515263 - r1515261;
double r1515265 = r1515261 / r1515264;
return r1515265;
}


double f(double x) {
double r1515266 = 1.0;
double r1515267 = x;
double r1515268 = sqrt(r1515266);
double r1515269 = r1515267 + r1515268;
double r1515270 = r1515266 / r1515269;
double r1515271 = r1515267 - r1515268;
double r1515272 = r1515270 / r1515271;
return r1515272;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.4

$\frac{1}{x \cdot x - 1}$
2. Using strategy rm

$\leadsto \frac{1}{x \cdot x - \color{blue}{\sqrt{1} \cdot \sqrt{1}}}$
4. Applied difference-of-squares0.4

$\leadsto \frac{1}{\color{blue}{\left(x + \sqrt{1}\right) \cdot \left(x - \sqrt{1}\right)}}$
5. Applied associate-/r*0.1

$\leadsto \color{blue}{\frac{\frac{1}{x + \sqrt{1}}}{x - \sqrt{1}}}$
6. Final simplification0.1

$\leadsto \frac{\frac{1}{x + \sqrt{1}}}{x - \sqrt{1}}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "1/(x*x-1)"
:precision binary64
(/ 1 (- (* x x) 1)))