Average Error: 15.1 → 0.3
Time: 9.5s
Precision: 64
$\sin \left(x + y\right)$
$\sin x \cdot \cos y + \left(\sqrt[3]{\cos x} \cdot \sqrt[3]{\cos x}\right) \cdot \left(\sqrt[3]{\cos x} \cdot \sin y\right)$
\sin \left(x + y\right)
\sin x \cdot \cos y + \left(\sqrt[3]{\cos x} \cdot \sqrt[3]{\cos x}\right) \cdot \left(\sqrt[3]{\cos x} \cdot \sin y\right)
double f(double x, double y) {
double r2502298 = x;
double r2502299 = y;
double r2502300 = r2502298 + r2502299;
double r2502301 = sin(r2502300);
return r2502301;
}


double f(double x, double y) {
double r2502302 = x;
double r2502303 = sin(r2502302);
double r2502304 = y;
double r2502305 = cos(r2502304);
double r2502306 = r2502303 * r2502305;
double r2502307 = cos(r2502302);
double r2502308 = cbrt(r2502307);
double r2502309 = r2502308 * r2502308;
double r2502310 = sin(r2502304);
double r2502311 = r2502308 * r2502310;
double r2502312 = r2502309 * r2502311;
double r2502313 = r2502306 + r2502312;
return r2502313;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 15.1

$\sin \left(x + y\right)$
2. Using strategy rm
3. Applied sin-sum0.2

$\leadsto \color{blue}{\sin x \cdot \cos y + \cos x \cdot \sin y}$
4. Using strategy rm

$\leadsto \sin x \cdot \cos y + \color{blue}{\left(\left(\sqrt[3]{\cos x} \cdot \sqrt[3]{\cos x}\right) \cdot \sqrt[3]{\cos x}\right)} \cdot \sin y$
6. Applied associate-*l*0.3

$\leadsto \sin x \cdot \cos y + \color{blue}{\left(\sqrt[3]{\cos x} \cdot \sqrt[3]{\cos x}\right) \cdot \left(\sqrt[3]{\cos x} \cdot \sin y\right)}$
7. Final simplification0.3

$\leadsto \sin x \cdot \cos y + \left(\sqrt[3]{\cos x} \cdot \sqrt[3]{\cos x}\right) \cdot \left(\sqrt[3]{\cos x} \cdot \sin y\right)$

# Reproduce

herbie shell --seed 1
(FPCore (x y)
:name "sin(x+y)"
:precision binary64
(sin (+ x y)))