Average Error: 0.2 → 0.2
Time: 6.2s
Precision: 64
$\frac{x}{\sqrt{2}} + 5$
$\frac{1}{\sqrt[3]{\sqrt[3]{\sqrt{2}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{2}}}} \cdot \frac{\frac{x}{\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}}}{\sqrt[3]{\sqrt[3]{\sqrt{2}}}} + 5$
\frac{x}{\sqrt{2}} + 5
\frac{1}{\sqrt[3]{\sqrt[3]{\sqrt{2}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{2}}}} \cdot \frac{\frac{x}{\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}}}{\sqrt[3]{\sqrt[3]{\sqrt{2}}}} + 5
double f(double x) {
double r172300 = x;
double r172301 = 2.0;
double r172302 = sqrt(r172301);
double r172303 = r172300 / r172302;
double r172304 = 5.0;
double r172305 = r172303 + r172304;
return r172305;
}


double f(double x) {
double r172306 = 1.0;
double r172307 = 2.0;
double r172308 = sqrt(r172307);
double r172309 = cbrt(r172308);
double r172310 = cbrt(r172309);
double r172311 = r172310 * r172310;
double r172312 = r172306 / r172311;
double r172313 = x;
double r172314 = r172309 * r172309;
double r172315 = r172313 / r172314;
double r172316 = r172315 / r172310;
double r172317 = r172312 * r172316;
double r172318 = 5.0;
double r172319 = r172317 + r172318;
return r172319;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.2

$\frac{x}{\sqrt{2}} + 5$
2. Using strategy rm

$\leadsto \frac{x}{\color{blue}{\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \sqrt[3]{\sqrt{2}}}} + 5$
4. Applied associate-/r*0.2

$\leadsto \color{blue}{\frac{\frac{x}{\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}}}{\sqrt[3]{\sqrt{2}}}} + 5$
5. Using strategy rm

$\leadsto \frac{\frac{x}{\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}}}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{\sqrt{2}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{2}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt{2}}}}} + 5$
7. Applied *-un-lft-identity0.2

$\leadsto \frac{\color{blue}{1 \cdot \frac{x}{\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}}}}{\left(\sqrt[3]{\sqrt[3]{\sqrt{2}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{2}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt{2}}}} + 5$
8. Applied times-frac0.2

$\leadsto \color{blue}{\frac{1}{\sqrt[3]{\sqrt[3]{\sqrt{2}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{2}}}} \cdot \frac{\frac{x}{\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}}}{\sqrt[3]{\sqrt[3]{\sqrt{2}}}}} + 5$
9. Final simplification0.2

$\leadsto \frac{1}{\sqrt[3]{\sqrt[3]{\sqrt{2}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{2}}}} \cdot \frac{\frac{x}{\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}}}{\sqrt[3]{\sqrt[3]{\sqrt{2}}}} + 5$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "x/sqrt(2)+5"
(+ (/ x (sqrt 2.0)) 5.0))