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Derivation

1. Initial program 13.2

   \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
2. Using strategy rm

3. Applied tan-sum0.2

   \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right)\]
4. Using strategy rm

5. Applied tan-quot0.2

   \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \color{blue}{\frac{\sin z}{\cos z}}} - \tan a\right)\]

6. Applied associate-*r/0.2

   \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}} - \tan a\right)\]

7. Taylor expanded around -inf 0.2

   \[\leadsto x + \color{blue}{\left(\left(\frac{\sin z}{\cos z \cdot \left(1 - \frac{\sin z \cdot \sin y}{\cos y \cdot \cos z}\right)} + \frac{\sin y}{\cos y \cdot \left(1 - \frac{\sin z \cdot \sin y}{\cos y \cdot \cos z}\right)}\right) - \frac{\sin a}{\cos a}\right)}\]

8. Final simplification0.2

   \[\leadsto x + \left(\left(\frac{\sin y}{\left(1 - \frac{\sin y \cdot \sin z}{\cos y \cdot \cos z}\right) \cdot \cos y} + \frac{\sin z}{\cos z \cdot \left(1 - \frac{\sin y \cdot \sin z}{\cos y \cdot \cos z}\right)}\right) - \frac{\sin a}{\cos a}\right)\]

Runtime

Time bar (total: 1.0m)Debug logProfile

herbie shell --seed 2018340 +o rules:numerics
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :pre (and (or (== x 0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.751224e+308)) (or (<= -1.776707e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.751224e+308)))
  (+ x (- (tan (+ y z)) (tan a))))