Average Error: 8.2 → 7.8
Time: 11.2s
Precision: 64
$\frac{\cos \left(\frac{2 \cdot \pi}{3}\right) \cdot \left(e - 2.7\right)}{\left(\pi - \sqrt{2}\right) - \sqrt{3}}$
$\frac{\cos \left(\left(\frac{2}{3} \cdot \sqrt{\pi}\right) \cdot \sqrt{\pi}\right) \cdot \left(e - 2.7\right)}{\left(\sqrt{\pi - \sqrt{2}} - \sqrt{\sqrt{3}}\right) \cdot \left(\sqrt{\pi - \sqrt{2}} + \sqrt{\sqrt{3}}\right)}$
\frac{\cos \left(\frac{2 \cdot \pi}{3}\right) \cdot \left(e - 2.7\right)}{\left(\pi - \sqrt{2}\right) - \sqrt{3}}
\frac{\cos \left(\left(\frac{2}{3} \cdot \sqrt{\pi}\right) \cdot \sqrt{\pi}\right) \cdot \left(e - 2.7\right)}{\left(\sqrt{\pi - \sqrt{2}} - \sqrt{\sqrt{3}}\right) \cdot \left(\sqrt{\pi - \sqrt{2}} + \sqrt{\sqrt{3}}\right)}
double f() {
double r42820317 = 2.0;
double r42820318 = atan2(1.0, 0.0);
double r42820319 = r42820317 * r42820318;
double r42820320 = 3.0;
double r42820321 = r42820319 / r42820320;
double r42820322 = cos(r42820321);
double r42820323 = exp(1.0);
double r42820324 = 2.7;
double r42820325 = r42820323 - r42820324;
double r42820326 = r42820322 * r42820325;
double r42820327 = sqrt(r42820317);
double r42820328 = r42820318 - r42820327;
double r42820329 = sqrt(r42820320);
double r42820330 = r42820328 - r42820329;
double r42820331 = r42820326 / r42820330;
return r42820331;
}


double f() {
double r42820332 = 0.6666666666666666;
double r42820333 = atan2(1.0, 0.0);
double r42820334 = sqrt(r42820333);
double r42820335 = r42820332 * r42820334;
double r42820336 = r42820335 * r42820334;
double r42820337 = cos(r42820336);
double r42820338 = exp(1.0);
double r42820339 = 2.7;
double r42820340 = r42820338 - r42820339;
double r42820341 = r42820337 * r42820340;
double r42820342 = 2.0;
double r42820343 = sqrt(r42820342);
double r42820344 = r42820333 - r42820343;
double r42820345 = sqrt(r42820344);
double r42820346 = 3.0;
double r42820347 = sqrt(r42820346);
double r42820348 = sqrt(r42820347);
double r42820349 = r42820345 - r42820348;
double r42820350 = r42820345 + r42820348;
double r42820351 = r42820349 * r42820350;
double r42820352 = r42820341 / r42820351;
return r42820352;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 8.2

$\frac{\cos \left(\frac{2 \cdot \pi}{3}\right) \cdot \left(e - 2.7\right)}{\left(\pi - \sqrt{2}\right) - \sqrt{3}}$
2. Simplified8.2

$\leadsto \color{blue}{\frac{\cos \left(\pi \cdot \frac{2}{3}\right) \cdot \left(e - 2.7\right)}{\left(\pi - \sqrt{2}\right) - \sqrt{3}}}$
3. Using strategy rm

$\leadsto \frac{\cos \left(\pi \cdot \frac{2}{3}\right) \cdot \left(e - 2.7\right)}{\left(\pi - \sqrt{2}\right) - \sqrt{\color{blue}{\sqrt{3} \cdot \sqrt{3}}}}$
5. Applied sqrt-prod6.9

$\leadsto \frac{\cos \left(\pi \cdot \frac{2}{3}\right) \cdot \left(e - 2.7\right)}{\left(\pi - \sqrt{2}\right) - \color{blue}{\sqrt{\sqrt{3}} \cdot \sqrt{\sqrt{3}}}}$

$\leadsto \frac{\cos \left(\pi \cdot \frac{2}{3}\right) \cdot \left(e - 2.7\right)}{\color{blue}{\sqrt{\pi - \sqrt{2}} \cdot \sqrt{\pi - \sqrt{2}}} - \sqrt{\sqrt{3}} \cdot \sqrt{\sqrt{3}}}$
7. Applied difference-of-squares7.8

$\leadsto \frac{\cos \left(\pi \cdot \frac{2}{3}\right) \cdot \left(e - 2.7\right)}{\color{blue}{\left(\sqrt{\pi - \sqrt{2}} + \sqrt{\sqrt{3}}\right) \cdot \left(\sqrt{\pi - \sqrt{2}} - \sqrt{\sqrt{3}}\right)}}$
8. Using strategy rm

$\leadsto \frac{\cos \left(\color{blue}{\left(\sqrt{\pi} \cdot \sqrt{\pi}\right)} \cdot \frac{2}{3}\right) \cdot \left(e - 2.7\right)}{\left(\sqrt{\pi - \sqrt{2}} + \sqrt{\sqrt{3}}\right) \cdot \left(\sqrt{\pi - \sqrt{2}} - \sqrt{\sqrt{3}}\right)}$
10. Applied associate-*l*7.8

$\leadsto \frac{\cos \color{blue}{\left(\sqrt{\pi} \cdot \left(\sqrt{\pi} \cdot \frac{2}{3}\right)\right)} \cdot \left(e - 2.7\right)}{\left(\sqrt{\pi - \sqrt{2}} + \sqrt{\sqrt{3}}\right) \cdot \left(\sqrt{\pi - \sqrt{2}} - \sqrt{\sqrt{3}}\right)}$
11. Final simplification7.8

$\leadsto \frac{\cos \left(\left(\frac{2}{3} \cdot \sqrt{\pi}\right) \cdot \sqrt{\pi}\right) \cdot \left(e - 2.7\right)}{\left(\sqrt{\pi - \sqrt{2}} - \sqrt{\sqrt{3}}\right) \cdot \left(\sqrt{\pi - \sqrt{2}} + \sqrt{\sqrt{3}}\right)}$

# Reproduce

herbie shell --seed 1
(FPCore ()
:name "cos(2 * PI / 3) * (E - 2.7) / (PI - sqrt(2) - sqrt(3))"
(/ (* (cos (/ (* 2 PI) 3)) (- E 2.7)) (- (- PI (sqrt 2)) (sqrt 3))))