Average Error: 13.2 → 0.2
Time: 12.5s
Precision: 64
$cosx + \cos \left(x + 1\right)$
$cosx + \left(\cos 1 \cdot \cos x - \left(\sqrt{\sin 1} \cdot \sin x\right) \cdot \sqrt{\sin 1}\right)$
cosx + \cos \left(x + 1\right)
cosx + \left(\cos 1 \cdot \cos x - \left(\sqrt{\sin 1} \cdot \sin x\right) \cdot \sqrt{\sin 1}\right)
double f(double cosx, double x) {
double r59226640 = cosx;
double r59226641 = x;
double r59226642 = 1.0;
double r59226643 = r59226641 + r59226642;
double r59226644 = cos(r59226643);
double r59226645 = r59226640 + r59226644;
return r59226645;
}


double f(double cosx, double x) {
double r59226646 = cosx;
double r59226647 = 1.0;
double r59226648 = cos(r59226647);
double r59226649 = x;
double r59226650 = cos(r59226649);
double r59226651 = r59226648 * r59226650;
double r59226652 = sin(r59226647);
double r59226653 = sqrt(r59226652);
double r59226654 = sin(r59226649);
double r59226655 = r59226653 * r59226654;
double r59226656 = r59226655 * r59226653;
double r59226657 = r59226651 - r59226656;
double r59226658 = r59226646 + r59226657;
return r59226658;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 13.2

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

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

$\leadsto cosx + \left(\cos x \cdot \cos 1 - \sin x \cdot \color{blue}{\left(\sqrt{\sin 1} \cdot \sqrt{\sin 1}\right)}\right)$
6. Applied associate-*r*0.2

$\leadsto cosx + \left(\cos x \cdot \cos 1 - \color{blue}{\left(\sin x \cdot \sqrt{\sin 1}\right) \cdot \sqrt{\sin 1}}\right)$
7. Final simplification0.2

$\leadsto cosx + \left(\cos 1 \cdot \cos x - \left(\sqrt{\sin 1} \cdot \sin x\right) \cdot \sqrt{\sin 1}\right)$

# Reproduce

herbie shell --seed 1
(FPCore (cosx x)
:name "cosx+cos(x+1)"
(+ cosx (cos (+ x 1))))