Error

Derivation

1. Initial program 0.2

   \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]

2. Initial simplification0.2

   \[\leadsto \frac{1}{\sin B} - \frac{x}{\tan B}\]
3. Using strategy rm

4. Applied tan-quot0.2

   \[\leadsto \frac{1}{\sin B} - \frac{x}{\color{blue}{\frac{\sin B}{\cos B}}}\]

5. Applied associate-/r/0.2

   \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x}{\sin B} \cdot \cos B}\]

6. Applied *-un-lft-identity0.2

   \[\leadsto \color{blue}{1 \cdot \frac{1}{\sin B}} - \frac{x}{\sin B} \cdot \cos B\]

7. Applied prod-diff0.2

   \[\leadsto \color{blue}{(1 \cdot \left(\frac{1}{\sin B}\right) + \left(-\cos B \cdot \frac{x}{\sin B}\right))_* + (\left(-\cos B\right) \cdot \left(\frac{x}{\sin B}\right) + \left(\cos B \cdot \frac{x}{\sin B}\right))_*}\]

8. Simplified0.2

   \[\leadsto \color{blue}{(\left(\cos B\right) \cdot \left(\frac{-x}{\sin B}\right) + \left(\frac{1}{\sin B}\right))_*} + (\left(-\cos B\right) \cdot \left(\frac{x}{\sin B}\right) + \left(\cos B \cdot \frac{x}{\sin B}\right))_*\]

9. Simplified0.2

   \[\leadsto (\left(\cos B\right) \cdot \left(\frac{-x}{\sin B}\right) + \left(\frac{1}{\sin B}\right))_* + \color{blue}{0}\]

10. Final simplification0.2

    \[\leadsto (\left(\cos B\right) \cdot \left(\frac{-x}{\sin B}\right) + \left(\frac{1}{\sin B}\right))_*\]

Runtime

Time bar (total: 27.1s)Debug logProfile

herbie shell --seed 2018353 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))