Average Error: 26.6 → 26.6
Time: 32.1s
Precision: 64
$\sin \left(\cos \left(\tan \left(\sqrt{x}\right)\right)\right)$
$\sin \left(\cos \left(\sqrt[3]{{\left(\sqrt[3]{{\left(\tan \left(\sqrt{x}\right)\right)}^{2}} \cdot \sqrt[3]{\tan \left(\sqrt{x}\right)}\right)}^{3}}\right)\right)$
\sin \left(\cos \left(\tan \left(\sqrt{x}\right)\right)\right)
\sin \left(\cos \left(\sqrt[3]{{\left(\sqrt[3]{{\left(\tan \left(\sqrt{x}\right)\right)}^{2}} \cdot \sqrt[3]{\tan \left(\sqrt{x}\right)}\right)}^{3}}\right)\right)
double f(double x) {
double r1587428 = x;
double r1587429 = sqrt(r1587428);
double r1587430 = tan(r1587429);
double r1587431 = cos(r1587430);
double r1587432 = sin(r1587431);
return r1587432;
}


double f(double x) {
double r1587433 = x;
double r1587434 = sqrt(r1587433);
double r1587435 = tan(r1587434);
double r1587436 = 2.0;
double r1587437 = pow(r1587435, r1587436);
double r1587438 = cbrt(r1587437);
double r1587439 = cbrt(r1587435);
double r1587440 = r1587438 * r1587439;
double r1587441 = 3.0;
double r1587442 = pow(r1587440, r1587441);
double r1587443 = cbrt(r1587442);
double r1587444 = cos(r1587443);
double r1587445 = sin(r1587444);
return r1587445;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 26.6

$\sin \left(\cos \left(\tan \left(\sqrt{x}\right)\right)\right)$
2. Using strategy rm

$\leadsto \sin \left(\cos \color{blue}{\left(\sqrt[3]{\left(\tan \left(\sqrt{x}\right) \cdot \tan \left(\sqrt{x}\right)\right) \cdot \tan \left(\sqrt{x}\right)}\right)}\right)$
4. Simplified26.6

$\leadsto \sin \left(\cos \left(\sqrt[3]{\color{blue}{{\left(\tan \left(\sqrt{x}\right)\right)}^{3}}}\right)\right)$
5. Using strategy rm

$\leadsto \sin \left(\cos \left(\sqrt[3]{{\color{blue}{\left(\left(\sqrt[3]{\tan \left(\sqrt{x}\right)} \cdot \sqrt[3]{\tan \left(\sqrt{x}\right)}\right) \cdot \sqrt[3]{\tan \left(\sqrt{x}\right)}\right)}}^{3}}\right)\right)$
7. Simplified26.6

$\leadsto \sin \left(\cos \left(\sqrt[3]{{\left(\color{blue}{\sqrt[3]{{\left(\tan \left(\sqrt{x}\right)\right)}^{2}}} \cdot \sqrt[3]{\tan \left(\sqrt{x}\right)}\right)}^{3}}\right)\right)$
8. Final simplification26.6

$\leadsto \sin \left(\cos \left(\sqrt[3]{{\left(\sqrt[3]{{\left(\tan \left(\sqrt{x}\right)\right)}^{2}} \cdot \sqrt[3]{\tan \left(\sqrt{x}\right)}\right)}^{3}}\right)\right)$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "sin(cos(tan(sqrt(x))))"
:precision binary64
(sin (cos (tan (sqrt x)))))