Average Error: 0.2 → 0.3
Time: 1.4m
Precision: 64
\[\lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\cos delta - \sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)}\]
↓
\[\tan^{-1}_* \frac{\cos \phi_1 \cdot \left(\sin delta \cdot \sin theta\right)}{\frac{\frac{\left(\cos delta \cdot \left(1 + \cos \left(delta + delta\right)\right) - \left(\left(\left(\cos \phi_1 \cdot \cos \phi_1\right) \cdot \cos \phi_1\right) \cdot \left(\left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1\right) \cdot \left(\left(\cos theta \cdot \cos theta\right) \cdot \cos theta\right)\right)\right) \cdot \left(\sin delta \cdot \left(\sin delta \cdot \sin delta\right)\right)\right) \cdot 32 - 2 \cdot \left(2 \cdot \left(\left(\cos delta \cdot \left(1 + \cos \left(delta + delta\right)\right)\right) \cdot \left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(1 - \cos \left(\phi_1 + \phi_1\right)\right)\right)\right)\right) + \left(16 \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\cos theta \cdot \left(\cos \left(delta + delta\right) \cdot \cos \phi_1 + \cos \phi_1\right)\right)\right)}{64} - \left(\left(3 \cdot \left(\left(\sin delta \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \left(\sin delta \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right)\right)\right) \cdot \left(\left(\cos \phi_1 \cdot \cos \phi_1\right) \cdot \left(\cos delta \cdot \left(\cos theta \cdot \cos theta\right)\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot {\left(\sin \phi_1\right)}^{5}\right) \cdot \cos \phi_1\right) \cdot \cos theta\right)\right)}{\left(\cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) + \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) \cdot \left(\sin \phi_1 \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)\right) + \cos delta \cdot \cos delta}} + \lambda_1\]
\lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\cos delta - \sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)}
↓
\tan^{-1}_* \frac{\cos \phi_1 \cdot \left(\sin delta \cdot \sin theta\right)}{\frac{\frac{\left(\cos delta \cdot \left(1 + \cos \left(delta + delta\right)\right) - \left(\left(\left(\cos \phi_1 \cdot \cos \phi_1\right) \cdot \cos \phi_1\right) \cdot \left(\left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1\right) \cdot \left(\left(\cos theta \cdot \cos theta\right) \cdot \cos theta\right)\right)\right) \cdot \left(\sin delta \cdot \left(\sin delta \cdot \sin delta\right)\right)\right) \cdot 32 - 2 \cdot \left(2 \cdot \left(\left(\cos delta \cdot \left(1 + \cos \left(delta + delta\right)\right)\right) \cdot \left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(1 - \cos \left(\phi_1 + \phi_1\right)\right)\right)\right)\right) + \left(16 \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\cos theta \cdot \left(\cos \left(delta + delta\right) \cdot \cos \phi_1 + \cos \phi_1\right)\right)\right)}{64} - \left(\left(3 \cdot \left(\left(\sin delta \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \left(\sin delta \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right)\right)\right) \cdot \left(\left(\cos \phi_1 \cdot \cos \phi_1\right) \cdot \left(\cos delta \cdot \left(\cos theta \cdot \cos theta\right)\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot {\left(\sin \phi_1\right)}^{5}\right) \cdot \cos \phi_1\right) \cdot \cos theta\right)\right)}{\left(\cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) + \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) \cdot \left(\sin \phi_1 \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)\right) + \cos delta \cdot \cos delta}} + \lambda_1
double f(double lambda1, double phi1, double __attribute__((unused)) phi2, double delta, double theta) {
        double r5251964 = lambda1;
        double r5251965 = theta;
        double r5251966 = sin(r5251965);
        double r5251967 = delta;
        double r5251968 = sin(r5251967);
        double r5251969 = r5251966 * r5251968;
        double r5251970 = phi1;
        double r5251971 = cos(r5251970);
        double r5251972 = r5251969 * r5251971;
        double r5251973 = cos(r5251967);
        double r5251974 = sin(r5251970);
        double r5251975 = r5251974 * r5251973;
        double r5251976 = r5251971 * r5251968;
        double r5251977 = cos(r5251965);
        double r5251978 = r5251976 * r5251977;
        double r5251979 = r5251975 + r5251978;
        double r5251980 = asin(r5251979);
        double r5251981 = sin(r5251980);
        double r5251982 = r5251974 * r5251981;
        double r5251983 = r5251973 - r5251982;
        double r5251984 = atan2(r5251972, r5251983);
        double r5251985 = r5251964 + r5251984;
        return r5251985;
}
↓
double f(double lambda1, double phi1, double __attribute__((unused)) phi2, double delta, double theta) {
        double r5251986 = phi1;
        double r5251987 = cos(r5251986);
        double r5251988 = delta;
        double r5251989 = sin(r5251988);
        double r5251990 = theta;
        double r5251991 = sin(r5251990);
        double r5251992 = r5251989 * r5251991;
        double r5251993 = r5251987 * r5251992;
        double r5251994 = cos(r5251988);
        double r5251995 = 1.0;
        double r5251996 = r5251988 + r5251988;
        double r5251997 = cos(r5251996);
        double r5251998 = r5251995 + r5251997;
        double r5251999 = r5251994 * r5251998;
        double r5252000 = r5251987 * r5251987;
        double r5252001 = r5252000 * r5251987;
        double r5252002 = r5251986 + r5251986;
        double r5252003 = cos(r5252002);
        double r5252004 = r5251995 - r5252003;
        double r5252005 = sin(r5251986);
        double r5252006 = r5252004 * r5252005;
        double r5252007 = cos(r5251990);
        double r5252008 = r5252007 * r5252007;
        double r5252009 = r5252008 * r5252007;
        double r5252010 = r5252006 * r5252009;
        double r5252011 = r5252001 * r5252010;
        double r5252012 = r5251989 * r5251989;
        double r5252013 = r5251989 * r5252012;
        double r5252014 = r5252011 * r5252013;
        double r5252015 = r5251999 - r5252014;
        double r5252016 = 32.0;
        double r5252017 = r5252015 * r5252016;
        double r5252018 = 2.0;
        double r5252019 = r5252004 * r5252004;
        double r5252020 = r5252004 * r5252019;
        double r5252021 = r5251999 * r5252020;
        double r5252022 = r5252018 * r5252021;
        double r5252023 = 16.0;
        double r5252024 = 5.0;
        double r5252025 = pow(r5252005, r5252024);
        double r5252026 = r5251989 * r5252025;
        double r5252027 = r5252023 * r5252026;
        double r5252028 = r5251997 * r5251987;
        double r5252029 = r5252028 + r5251987;
        double r5252030 = r5252007 * r5252029;
        double r5252031 = r5252027 * r5252030;
        double r5252032 = r5252022 + r5252031;
        double r5252033 = r5252018 * r5252032;
        double r5252034 = r5252017 - r5252033;
        double r5252035 = 64.0;
        double r5252036 = r5252034 / r5252035;
        double r5252037 = 3.0;
        double r5252038 = r5252005 * r5252005;
        double r5252039 = r5251989 * r5252038;
        double r5252040 = r5252039 * r5252039;
        double r5252041 = r5252037 * r5252040;
        double r5252042 = r5251994 * r5252008;
        double r5252043 = r5252000 * r5252042;
        double r5252044 = r5252041 * r5252043;
        double r5252045 = r5252018 * r5251989;
        double r5252046 = r5251994 * r5251994;
        double r5252047 = r5252046 * r5252025;
        double r5252048 = r5252047 * r5251987;
        double r5252049 = r5252048 * r5252007;
        double r5252050 = r5252045 * r5252049;
        double r5252051 = r5252044 + r5252050;
        double r5252052 = r5252036 - r5252051;
        double r5252053 = r5252005 * r5251994;
        double r5252054 = r5251987 * r5251989;
        double r5252055 = r5252054 * r5252007;
        double r5252056 = r5252053 + r5252055;
        double r5252057 = asin(r5252056);
        double r5252058 = sin(r5252057);
        double r5252059 = r5252005 * r5252058;
        double r5252060 = r5251994 * r5252059;
        double r5252061 = r5252005 * r5252059;
        double r5252062 = r5252058 * r5252061;
        double r5252063 = r5252060 + r5252062;
        double r5252064 = r5252063 + r5252046;
        double r5252065 = r5252052 / r5252064;
        double r5252066 = atan2(r5251993, r5252065);
        double r5252067 = lambda1;
        double r5252068 = r5252066 + r5252067;
        return r5252068;
}

Error

Bits error versus lambda1

Bits error versus phi1

Bits error versus phi2

Bits error versus delta

Bits error versus theta

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\cos delta - \sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)}\]
  2. Using strategy rm

  3. Applied flip3--0.2

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\color{blue}{\frac{{\left(\cos delta\right)}^{3} - {\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)}^{3}}{\cos delta \cdot \cos delta + \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}}\]

  4. Taylor expanded around inf 0.2

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\color{blue}{{\left(\cos delta\right)}^{3} - \left({\left(\cos \phi_1\right)}^{3} \cdot \left({\left(\sin delta\right)}^{3} \cdot \left({\left(\cos theta\right)}^{3} \cdot {\left(\sin \phi_1\right)}^{3}\right)\right) + \left({\left(\sin \phi_1\right)}^{6} \cdot {\left(\cos delta\right)}^{3} + \left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\sin delta \cdot \left(\cos theta \cdot {\left(\cos delta\right)}^{2}\right)\right)\right) + \left(2 \cdot \left(\sin delta \cdot \left(\cos \phi_1 \cdot \left(\cos theta \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot {\left(\cos delta\right)}^{2}\right)\right)\right)\right) + 3 \cdot \left({\left(\sin delta\right)}^{2} \cdot \left({\left(\sin \phi_1\right)}^{4} \cdot \left({\left(\cos theta\right)}^{2} \cdot \left({\left(\cos \phi_1\right)}^{2} \cdot \cos delta\right)\right)\right)\right)\right)\right)\right)\right)}}{\cos delta \cdot \cos delta + \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  5. Simplified0.2

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\color{blue}{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta\right)\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}}{\cos delta \cdot \cos delta + \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]
  6. Using strategy rm

  7. Applied associate-*r*0.2

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta\right)\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\color{blue}{\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)} + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]
  8. Using strategy rm

  9. Applied cos-mult0.2

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \left(\color{blue}{\frac{\cos \left(delta + delta\right) + \cos \left(delta - delta\right)}{2}} \cdot \cos delta\right)\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  10. Applied associate-*l/0.2

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \color{blue}{\frac{\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta}{2}}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  11. Applied sin-mult0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \color{blue}{\frac{\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)}{2}}\right) \cdot \frac{\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta}{2}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  12. Applied sin-mult0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \color{blue}{\frac{\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)}{2}}\right) \cdot \frac{\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)}{2}\right) \cdot \frac{\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta}{2}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  13. Applied sin-mult0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \left(\left(\color{blue}{\frac{\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)}{2}} \cdot \frac{\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)}{2}\right) \cdot \frac{\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)}{2}\right) \cdot \frac{\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta}{2}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  14. Applied frac-times0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \left(\color{blue}{\frac{\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)}{2 \cdot 2}} \cdot \frac{\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)}{2}\right) \cdot \frac{\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta}{2}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  15. Applied frac-times0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \color{blue}{\frac{\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)}{\left(2 \cdot 2\right) \cdot 2}} \cdot \frac{\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta}{2}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  16. Applied frac-times0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \color{blue}{\frac{\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)}{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2}}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  17. Applied cos-mult0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \color{blue}{\frac{\cos \left(delta + delta\right) + \cos \left(delta - delta\right)}{2}}\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \frac{\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)}{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  18. Applied associate-*r/0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\left(\cos theta \cdot \color{blue}{\frac{\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)}{2}}\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \frac{\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)}{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  19. Applied associate-*r/0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\color{blue}{\frac{\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)}{2}} \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) + \frac{\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)}{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  20. Applied associate-*l/0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \left(\color{blue}{\frac{\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)}{2}} + \frac{\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)}{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2}\right)\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  21. Applied frac-add0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \color{blue}{\frac{\left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right) + 2 \cdot \left(\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)\right)}{2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)}}\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  22. Applied sin-mult0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\color{blue}{\frac{\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)}{2}} \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \frac{\left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right) + 2 \cdot \left(\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)\right)}{2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)}\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  23. Applied associate-*l/0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \color{blue}{\frac{\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1}{2}}\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \frac{\left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right) + 2 \cdot \left(\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)\right)}{2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)}\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  24. Applied associate-*r/0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \color{blue}{\frac{\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1\right)}{2}}\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \frac{\left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right) + 2 \cdot \left(\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)\right)}{2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)}\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  25. Applied associate-*r/0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \color{blue}{\frac{\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1\right)\right)}{2}} \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) - \frac{\left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right) + 2 \cdot \left(\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)\right)}{2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)}\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  26. Applied associate-*l/0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot \cos delta - \color{blue}{\frac{\left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)}{2}}\right) - \frac{\left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right) + 2 \cdot \left(\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)\right)}{2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)}\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  27. Applied cos-mult0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\color{blue}{\frac{\cos \left(delta + delta\right) + \cos \left(delta - delta\right)}{2}} \cdot \cos delta - \frac{\left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)}{2}\right) - \frac{\left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right) + 2 \cdot \left(\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)\right)}{2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)}\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  28. Applied associate-*l/0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\left(\color{blue}{\frac{\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta}{2}} - \frac{\left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)}{2}\right) - \frac{\left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right) + 2 \cdot \left(\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)\right)}{2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)}\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  29. Applied sub-div0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\left(\color{blue}{\frac{\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)}{2}} - \frac{\left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right) + 2 \cdot \left(\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)\right)}{2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)}\right) - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  30. Applied frac-sub0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\color{blue}{\frac{\left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta - \left(\left(\left(\sin delta \cdot \sin delta\right) \cdot \sin delta\right) \cdot \left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right) \cdot \left(2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)\right) - 2 \cdot \left(\left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right)\right)\right) \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right) + 2 \cdot \left(\left(\left(\left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\cos \left(\phi_1 - \phi_1\right) - \cos \left(\phi_1 + \phi_1\right)\right)\right) \cdot \left(\left(\cos \left(delta + delta\right) + \cos \left(delta - delta\right)\right) \cdot \cos delta\right)\right)\right)}{2 \cdot \left(2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)\right)}} - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  31. Simplified0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\frac{\color{blue}{\left(\cos delta \cdot \left(\cos \left(delta + delta\right) + 1\right) - \left(\sin delta \cdot \left(\sin delta \cdot \sin delta\right)\right) \cdot \left(\left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\sin \phi_1 \cdot \left(1 - \cos \left(\phi_1 + \phi_1\right)\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right)\right) \cdot 32 - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \cos \left(delta + delta\right) + \cos \phi_1\right)\right) \cdot \left(\left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) \cdot 16\right) + 2 \cdot \left(\left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(1 - \cos \left(\phi_1 + \phi_1\right)\right)\right)\right) \cdot \left(\cos delta \cdot \left(\cos \left(delta + delta\right) + 1\right)\right)\right)\right) \cdot 2}}{2 \cdot \left(2 \cdot \left(\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot 2\right)\right)} - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  32. Simplified0.3

    \[\leadsto \lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\frac{\frac{\left(\cos delta \cdot \left(\cos \left(delta + delta\right) + 1\right) - \left(\sin delta \cdot \left(\sin delta \cdot \sin delta\right)\right) \cdot \left(\left(\left(\cos theta \cdot \left(\cos theta \cdot \cos theta\right)\right) \cdot \left(\sin \phi_1 \cdot \left(1 - \cos \left(\phi_1 + \phi_1\right)\right)\right)\right) \cdot \left(\cos \phi_1 \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right)\right)\right) \cdot 32 - \left(\left(\cos theta \cdot \left(\cos \phi_1 \cdot \cos \left(delta + delta\right) + \cos \phi_1\right)\right) \cdot \left(\left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right) \cdot 16\right) + 2 \cdot \left(\left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(1 - \cos \left(\phi_1 + \phi_1\right)\right)\right)\right) \cdot \left(\cos delta \cdot \left(\cos \left(delta + delta\right) + 1\right)\right)\right)\right) \cdot 2}{\color{blue}{64}} - \left(\left(3 \cdot \left(\left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \phi_1\right) \cdot \sin delta\right)\right)\right) \cdot \left(\left(\left(\cos theta \cdot \cos theta\right) \cdot \cos delta\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_1\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\cos \phi_1 \cdot \left({\left(\sin \phi_1\right)}^{5} \cdot \left(\cos delta \cdot \cos delta\right)\right)\right) \cdot \cos theta\right)\right)}{\cos delta \cdot \cos delta + \left(\left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) \cdot \sin \phi_1\right) \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) + \cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)}}\]

  33. Final simplification0.3

    \[\leadsto \tan^{-1}_* \frac{\cos \phi_1 \cdot \left(\sin delta \cdot \sin theta\right)}{\frac{\frac{\left(\cos delta \cdot \left(1 + \cos \left(delta + delta\right)\right) - \left(\left(\left(\cos \phi_1 \cdot \cos \phi_1\right) \cdot \cos \phi_1\right) \cdot \left(\left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \sin \phi_1\right) \cdot \left(\left(\cos theta \cdot \cos theta\right) \cdot \cos theta\right)\right)\right) \cdot \left(\sin delta \cdot \left(\sin delta \cdot \sin delta\right)\right)\right) \cdot 32 - 2 \cdot \left(2 \cdot \left(\left(\cos delta \cdot \left(1 + \cos \left(delta + delta\right)\right)\right) \cdot \left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(\left(1 - \cos \left(\phi_1 + \phi_1\right)\right) \cdot \left(1 - \cos \left(\phi_1 + \phi_1\right)\right)\right)\right)\right) + \left(16 \cdot \left(\sin delta \cdot {\left(\sin \phi_1\right)}^{5}\right)\right) \cdot \left(\cos theta \cdot \left(\cos \left(delta + delta\right) \cdot \cos \phi_1 + \cos \phi_1\right)\right)\right)}{64} - \left(\left(3 \cdot \left(\left(\sin delta \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right) \cdot \left(\sin delta \cdot \left(\sin \phi_1 \cdot \sin \phi_1\right)\right)\right)\right) \cdot \left(\left(\cos \phi_1 \cdot \cos \phi_1\right) \cdot \left(\cos delta \cdot \left(\cos theta \cdot \cos theta\right)\right)\right) + \left(2 \cdot \sin delta\right) \cdot \left(\left(\left(\left(\cos delta \cdot \cos delta\right) \cdot {\left(\sin \phi_1\right)}^{5}\right) \cdot \cos \phi_1\right) \cdot \cos theta\right)\right)}{\left(\cos delta \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right) + \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right) \cdot \left(\sin \phi_1 \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)\right)\right)\right) + \cos delta \cdot \cos delta}} + \lambda_1\]

Reproduce

herbie shell --seed 2019164 
(FPCore (lambda1 phi1 phi2 delta theta)
  :name "Destination given bearing on a great circle"
  (+ lambda1 (atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))