Average Error: 7.6 → 0.2
Time: 10.6s
Precision: 64
$3 \cdot pi + \sin \left(x + y\right)$
$\cos x \cdot \sin y + \left(3 \cdot pi + \sin x \cdot \cos y\right)$
3 \cdot pi + \sin \left(x + y\right)
\cos x \cdot \sin y + \left(3 \cdot pi + \sin x \cdot \cos y\right)
double f(double pi, double x, double y) {
double r2637723 = 3.0;
double r2637724 = pi;
double r2637725 = r2637723 * r2637724;
double r2637726 = x;
double r2637727 = y;
double r2637728 = r2637726 + r2637727;
double r2637729 = sin(r2637728);
double r2637730 = r2637725 + r2637729;
return r2637730;
}


double f(double pi, double x, double y) {
double r2637731 = x;
double r2637732 = cos(r2637731);
double r2637733 = y;
double r2637734 = sin(r2637733);
double r2637735 = r2637732 * r2637734;
double r2637736 = 3.0;
double r2637737 = pi;
double r2637738 = r2637736 * r2637737;
double r2637739 = sin(r2637731);
double r2637740 = cos(r2637733);
double r2637741 = r2637739 * r2637740;
double r2637742 = r2637738 + r2637741;
double r2637743 = r2637735 + r2637742;
return r2637743;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 7.6

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

$\leadsto 3 \cdot pi + \color{blue}{\left(\sin x \cdot \cos y + \cos x \cdot \sin y\right)}$
4. Applied associate-+r+0.2

$\leadsto \color{blue}{\left(3 \cdot pi + \sin x \cdot \cos y\right) + \cos x \cdot \sin y}$
5. Using strategy rm
6. Applied +-commutative0.2

$\leadsto \color{blue}{\cos x \cdot \sin y + \left(3 \cdot pi + \sin x \cdot \cos y\right)}$
7. Final simplification0.2

$\leadsto \cos x \cdot \sin y + \left(3 \cdot pi + \sin x \cdot \cos y\right)$

# Reproduce

herbie shell --seed 1
(FPCore (pi x y)
:name "3 * pi + sin(x + y)"
:precision binary64
(+ (* 3 pi) (sin (+ x y))))