Average Error: 26.5 → 0.4
Time: 15.0s
Precision: 64
$\sin \left(1 + 2 \cdot x\right)$
$\left(\sqrt[3]{\cos 1} \cdot \sin \left(2 \cdot x\right)\right) \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) + \sin 1 \cdot \cos \left(2 \cdot x\right)$
\sin \left(1 + 2 \cdot x\right)
\left(\sqrt[3]{\cos 1} \cdot \sin \left(2 \cdot x\right)\right) \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) + \sin 1 \cdot \cos \left(2 \cdot x\right)
double f(double x) {
double r14449700 = 1.0;
double r14449701 = 2.0;
double r14449702 = x;
double r14449703 = r14449701 * r14449702;
double r14449704 = r14449700 + r14449703;
double r14449705 = sin(r14449704);
return r14449705;
}


double f(double x) {
double r14449706 = 1.0;
double r14449707 = cos(r14449706);
double r14449708 = cbrt(r14449707);
double r14449709 = 2.0;
double r14449710 = x;
double r14449711 = r14449709 * r14449710;
double r14449712 = sin(r14449711);
double r14449713 = r14449708 * r14449712;
double r14449714 = r14449708 * r14449708;
double r14449715 = r14449713 * r14449714;
double r14449716 = sin(r14449706);
double r14449717 = cos(r14449711);
double r14449718 = r14449716 * r14449717;
double r14449719 = r14449715 + r14449718;
return r14449719;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 26.5

$\sin \left(1 + 2 \cdot x\right)$
2. Using strategy rm
3. Applied sin-sum0.4

$\leadsto \color{blue}{\sin 1 \cdot \cos \left(2 \cdot x\right) + \cos 1 \cdot \sin \left(2 \cdot x\right)}$
4. Using strategy rm

$\leadsto \sin 1 \cdot \cos \left(2 \cdot x\right) + \color{blue}{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sqrt[3]{\cos 1}\right)} \cdot \sin \left(2 \cdot x\right)$
6. Applied associate-*l*0.4

$\leadsto \sin 1 \cdot \cos \left(2 \cdot x\right) + \color{blue}{\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \left(\sqrt[3]{\cos 1} \cdot \sin \left(2 \cdot x\right)\right)}$
7. Final simplification0.4

$\leadsto \left(\sqrt[3]{\cos 1} \cdot \sin \left(2 \cdot x\right)\right) \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) + \sin 1 \cdot \cos \left(2 \cdot x\right)$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "sin(1 + 2x)"
(sin (+ 1 (* 2 x))))