Average Error: 26.4 → 0.3
Time: 9.0s
Precision: 64
$\sin \left(x + 1\right)$
$\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sin x\right) \cdot \sqrt[3]{\cos 1} + \cos x \cdot \sin 1$
\sin \left(x + 1\right)
\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sin x\right) \cdot \sqrt[3]{\cos 1} + \cos x \cdot \sin 1
double f(double x) {
double r1060687 = x;
double r1060688 = 1.0;
double r1060689 = r1060687 + r1060688;
double r1060690 = sin(r1060689);
return r1060690;
}


double f(double x) {
double r1060691 = 1.0;
double r1060692 = cos(r1060691);
double r1060693 = cbrt(r1060692);
double r1060694 = r1060693 * r1060693;
double r1060695 = x;
double r1060696 = sin(r1060695);
double r1060697 = r1060694 * r1060696;
double r1060698 = r1060697 * r1060693;
double r1060699 = cos(r1060695);
double r1060700 = sin(r1060691);
double r1060701 = r1060699 * r1060700;
double r1060702 = r1060698 + r1060701;
return r1060702;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 26.4

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

$\leadsto \color{blue}{\sin x \cdot \cos 1 + \cos x \cdot \sin 1}$
4. Using strategy rm

$\leadsto \sin x \cdot \color{blue}{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sqrt[3]{\cos 1}\right)} + \cos x \cdot \sin 1$
6. Applied associate-*r*0.3

$\leadsto \color{blue}{\left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1}} + \cos x \cdot \sin 1$
7. Simplified0.3

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

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

# Reproduce

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