Average Error: 18.4 → 18.5
Time: 10.6s
Precision: 64
$\cos \left(3 \cdot x\right) + \cos \left(4 \cdot x\right)$
$\frac{{\left(\cos \left(3 \cdot x\right)\right)}^{3} + {\left(\cos \left(4 \cdot x\right)\right)}^{3}}{\cos \left(4 \cdot x\right) \cdot \left(\cos \left(4 \cdot x\right) - \cos \left(3 \cdot x\right)\right) + \cos \left(3 \cdot x\right) \cdot \cos \left(3 \cdot x\right)}$
\cos \left(3 \cdot x\right) + \cos \left(4 \cdot x\right)
\frac{{\left(\cos \left(3 \cdot x\right)\right)}^{3} + {\left(\cos \left(4 \cdot x\right)\right)}^{3}}{\cos \left(4 \cdot x\right) \cdot \left(\cos \left(4 \cdot x\right) - \cos \left(3 \cdot x\right)\right) + \cos \left(3 \cdot x\right) \cdot \cos \left(3 \cdot x\right)}
double f(double x) {
double r3415427 = 3.0;
double r3415428 = x;
double r3415429 = r3415427 * r3415428;
double r3415430 = cos(r3415429);
double r3415431 = 4.0;
double r3415432 = r3415431 * r3415428;
double r3415433 = cos(r3415432);
double r3415434 = r3415430 + r3415433;
return r3415434;
}


double f(double x) {
double r3415435 = 3.0;
double r3415436 = x;
double r3415437 = r3415435 * r3415436;
double r3415438 = cos(r3415437);
double r3415439 = 3.0;
double r3415440 = pow(r3415438, r3415439);
double r3415441 = 4.0;
double r3415442 = r3415441 * r3415436;
double r3415443 = cos(r3415442);
double r3415444 = pow(r3415443, r3415439);
double r3415445 = r3415440 + r3415444;
double r3415446 = r3415443 - r3415438;
double r3415447 = r3415443 * r3415446;
double r3415448 = r3415438 * r3415438;
double r3415449 = r3415447 + r3415448;
double r3415450 = r3415445 / r3415449;
return r3415450;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 18.4

$\cos \left(3 \cdot x\right) + \cos \left(4 \cdot x\right)$
2. Using strategy rm
3. Applied flip3-+18.5

$\leadsto \color{blue}{\frac{{\left(\cos \left(3 \cdot x\right)\right)}^{3} + {\left(\cos \left(4 \cdot x\right)\right)}^{3}}{\cos \left(3 \cdot x\right) \cdot \cos \left(3 \cdot x\right) + \left(\cos \left(4 \cdot x\right) \cdot \cos \left(4 \cdot x\right) - \cos \left(3 \cdot x\right) \cdot \cos \left(4 \cdot x\right)\right)}}$
4. Simplified18.5

$\leadsto \frac{{\left(\cos \left(3 \cdot x\right)\right)}^{3} + {\left(\cos \left(4 \cdot x\right)\right)}^{3}}{\color{blue}{\cos \left(4 \cdot x\right) \cdot \left(\cos \left(4 \cdot x\right) - \cos \left(3 \cdot x\right)\right) + \cos \left(3 \cdot x\right) \cdot \cos \left(3 \cdot x\right)}}$
5. Final simplification18.5

$\leadsto \frac{{\left(\cos \left(3 \cdot x\right)\right)}^{3} + {\left(\cos \left(4 \cdot x\right)\right)}^{3}}{\cos \left(4 \cdot x\right) \cdot \left(\cos \left(4 \cdot x\right) - \cos \left(3 \cdot x\right)\right) + \cos \left(3 \cdot x\right) \cdot \cos \left(3 \cdot x\right)}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "cos(3*x)+cos(4*x)"
:precision binary64
(+ (cos (* 3 x)) (cos (* 4 x))))