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100 # AdaptiveSimpson(_f, var_IsVariable, a_IsRationalOrNumber, b_IsRationalOrNumber, tol_IsRationalOrNumber) <-- [
Local(c, fa, fb, fc, h, q, q1, q2, stp);
c := (a + b) / 2;
fa := N(`WithValue(@var, a, f));
fc := N(`WithValue(@var, c, f));
fb := N(`WithValue(@var, b, f));
h := (b - a);
q := (b - a) / 6 * (fa + 4 * fc + fb);
stp(f, var, a, b, c, fa, fb, fc, q0, tol) := [
Local(d, e, fd, fe, q, q1, q2);
d := (a + c) / 2;
e := (c + b) / 2;
fd := N(`WithValue(@var, d, f));
fe := N(`WithValue(@var, e, f));
q1 := (c - a) / 6 * (fa + 4 * fd + fc);
q2 := (b - c) / 6 * (fc + 4 * fe + fb);
q := N(q1 + q2);
If (Abs(q - q0) > tol, [
q1 := stp (f, var, a, c, d, fa, fc, fd, q1, tol);
q2 := stp (f, var, c, b, e, fc, fb, fe, q2, tol);
q := N(q1 + q2);
]);
q;
];
stp(f, var, a, b, c, fa, fb, fc, q, tol);
];
100 # (NIntegrate(var_IsVariable, a_IsRationalOrNumber, b_IsRationalOrNumber)(_f)) <-- [
AdaptiveSimpson(f, var, a, b, 1e-8);
];
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