Average Error: 0.0 → 0.0
Time: 16.5s
Precision: 64
${x}^{\left({x}^{2}\right)}$
${\left({x}^{\left(\sqrt{{x}^{2}}\right)}\right)}^{\left(\sqrt{{x}^{2}}\right)}$
{x}^{\left({x}^{2}\right)}
{\left({x}^{\left(\sqrt{{x}^{2}}\right)}\right)}^{\left(\sqrt{{x}^{2}}\right)}
double f(double x) {
double r233921 = x;
double r233922 = 2.0;
double r233923 = pow(r233921, r233922);
double r233924 = pow(r233921, r233923);
return r233924;
}


double f(double x) {
double r233925 = x;
double r233926 = 2.0;
double r233927 = pow(r233925, r233926);
double r233928 = sqrt(r233927);
double r233929 = pow(r233925, r233928);
double r233930 = pow(r233929, r233928);
return r233930;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

${x}^{\left({x}^{2}\right)}$
2. Using strategy rm

$\leadsto {x}^{\color{blue}{\left(\sqrt{{x}^{2}} \cdot \sqrt{{x}^{2}}\right)}}$
4. Applied pow-unpow0.0

$\leadsto \color{blue}{{\left({x}^{\left(\sqrt{{x}^{2}}\right)}\right)}^{\left(\sqrt{{x}^{2}}\right)}}$
5. Final simplification0.0

$\leadsto {\left({x}^{\left(\sqrt{{x}^{2}}\right)}\right)}^{\left(\sqrt{{x}^{2}}\right)}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "pow(x, pow(x, 2))"
:precision binary64
(pow x (pow x 2)))