Average Error: 0.2 → 0.2
Time: 47.8s
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{{\left(\cos delta\right)}^{3} - {\left(\sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right)\right)}\right)}^{3}}{\left(\left(\sqrt[3]{\sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right)\right)}} \cdot \left(\sqrt[3]{\sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right)\right)}}\right)\right) \cdot \cos delta + \sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right)\right)} \cdot \log \left(e^{\sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\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{{\left(\cos delta\right)}^{3} - {\left(\sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right)\right)}\right)}^{3}}{\left(\left(\sqrt[3]{\sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right)\right)}} \cdot \left(\sqrt[3]{\sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right)\right)}}\right)\right) \cdot \cos delta + \sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right)\right)} \cdot \log \left(e^{\sqrt[3]{\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\cos delta \cdot \sin \phi_1 + \sin delta \cdot \left(\cos theta \cdot \cos \phi_1\right)\right)\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 r3346191 = lambda1;
        double r3346192 = theta;
        double r3346193 = sin(r3346192);
        double r3346194 = delta;
        double r3346195 = sin(r3346194);
        double r3346196 = r3346193 * r3346195;
        double r3346197 = phi1;
        double r3346198 = cos(r3346197);
        double r3346199 = r3346196 * r3346198;
        double r3346200 = cos(r3346194);
        double r3346201 = sin(r3346197);
        double r3346202 = r3346201 * r3346200;
        double r3346203 = r3346198 * r3346195;
        double r3346204 = cos(r3346192);
        double r3346205 = r3346203 * r3346204;
        double r3346206 = r3346202 + r3346205;
        double r3346207 = asin(r3346206);
        double r3346208 = sin(r3346207);
        double r3346209 = r3346201 * r3346208;
        double r3346210 = r3346200 - r3346209;
        double r3346211 = atan2(r3346199, r3346210);
        double r3346212 = r3346191 + r3346211;
        return r3346212;
}
↓
double f(double lambda1, double phi1, double __attribute__((unused)) phi2, double delta, double theta) {
        double r3346213 = phi1;
        double r3346214 = cos(r3346213);
        double r3346215 = delta;
        double r3346216 = sin(r3346215);
        double r3346217 = theta;
        double r3346218 = sin(r3346217);
        double r3346219 = r3346216 * r3346218;
        double r3346220 = r3346214 * r3346219;
        double r3346221 = cos(r3346215);
        double r3346222 = 3.0;
        double r3346223 = pow(r3346221, r3346222);
        double r3346224 = sin(r3346213);
        double r3346225 = r3346221 * r3346224;
        double r3346226 = cos(r3346217);
        double r3346227 = r3346226 * r3346214;
        double r3346228 = r3346216 * r3346227;
        double r3346229 = r3346225 + r3346228;
        double r3346230 = asin(r3346229);
        double r3346231 = sin(r3346230);
        double r3346232 = r3346224 * r3346231;
        double r3346233 = r3346232 * r3346232;
        double r3346234 = r3346232 * r3346233;
        double r3346235 = cbrt(r3346234);
        double r3346236 = pow(r3346235, r3346222);
        double r3346237 = r3346223 - r3346236;
        double r3346238 = cbrt(r3346235);
        double r3346239 = r3346238 * r3346238;
        double r3346240 = r3346238 * r3346239;
        double r3346241 = r3346240 * r3346221;
        double r3346242 = exp(r3346235);
        double r3346243 = log(r3346242);
        double r3346244 = r3346235 * r3346243;
        double r3346245 = r3346241 + r3346244;
        double r3346246 = r3346221 * r3346221;
        double r3346247 = r3346245 + r3346246;
        double r3346248 = r3346237 / r3346247;
        double r3346249 = atan2(r3346220, r3346248);
        double r3346250 = lambda1;
        double r3346251 = r3346249 + r3346250;
        return r3346251;
}

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 add-cbrt-cube0.2

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

  4. Applied add-cbrt-cube0.2

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

  5. Applied cbrt-unprod0.2

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

  6. Simplified0.2

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

  8. 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(\sqrt[3]{\left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right) \cdot \left(\left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right) \cdot \left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right)\right)}\right)}^{3}}{\cos delta \cdot \cos delta + \left(\sqrt[3]{\left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right) \cdot \left(\left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right) \cdot \left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right)\right)} \cdot \sqrt[3]{\left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right) \cdot \left(\left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right) \cdot \left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right)\right)} + \cos delta \cdot \sqrt[3]{\left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right) \cdot \left(\left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right) \cdot \left(\sin \left(\sin^{-1} \left(\left(\cos theta \cdot \cos \phi_1\right) \cdot \sin delta + \sin \phi_1 \cdot \cos delta\right)\right) \cdot \sin \phi_1\right)\right)}\right)}}}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt0.2

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

  12. Applied add-log-exp0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 
(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))))))))))