Error

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-log-exp0.2

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

4. Applied simplify0.2

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

6. Applied flip3--0.2

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

7. Applied simplify0.2

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018167 +o rules:numerics
(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))))))))))