Average Error: 30.1 → 0.6
Time: 15.9s
Precision: 64
$\cos \left(x + 1\right) - \cos x$
$\sqrt[3]{\left(\left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right) \cdot \left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right)\right) \cdot \left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right)}$
\cos \left(x + 1\right) - \cos x
\sqrt[3]{\left(\left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right) \cdot \left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right)\right) \cdot \left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right)}
double f(double x) {
double r42294828 = x;
double r42294829 = 1.0;
double r42294830 = r42294828 + r42294829;
double r42294831 = cos(r42294830);
double r42294832 = cos(r42294828);
double r42294833 = r42294831 - r42294832;
return r42294833;
}


double f(double x) {
double r42294834 = 1.0;
double r42294835 = cos(r42294834);
double r42294836 = x;
double r42294837 = cos(r42294836);
double r42294838 = r42294835 * r42294837;
double r42294839 = sin(r42294836);
double r42294840 = sin(r42294834);
double r42294841 = r42294839 * r42294840;
double r42294842 = r42294841 + r42294837;
double r42294843 = r42294838 - r42294842;
double r42294844 = r42294843 * r42294843;
double r42294845 = r42294844 * r42294843;
double r42294846 = cbrt(r42294845);
return r42294846;
}



Try it out

Results

 In Out
Enter valid numbers for all inputs

Derivation

1. Initial program 30.1

$\cos \left(x + 1\right) - \cos x$
2. Using strategy rm
3. Applied cos-sum0.9

$\leadsto \color{blue}{\left(\cos x \cdot \cos 1 - \sin x \cdot \sin 1\right)} - \cos x$
4. Applied associate--l-0.9

$\leadsto \color{blue}{\cos x \cdot \cos 1 - \left(\sin x \cdot \sin 1 + \cos x\right)}$
5. Using strategy rm
$\leadsto \color{blue}{\sqrt[3]{\left(\left(\cos x \cdot \cos 1 - \left(\sin x \cdot \sin 1 + \cos x\right)\right) \cdot \left(\cos x \cdot \cos 1 - \left(\sin x \cdot \sin 1 + \cos x\right)\right)\right) \cdot \left(\cos x \cdot \cos 1 - \left(\sin x \cdot \sin 1 + \cos x\right)\right)}}$
$\leadsto \sqrt[3]{\left(\left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right) \cdot \left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right)\right) \cdot \left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right)}$
herbie shell --seed 1