Error

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

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

6. Applied tan-quot0.2

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

7. Applied frac-add0.2

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

8. Applied associate-/l/0.2

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

9. Simplified0.2

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

11. Applied associate-*r*0.2

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

12. Final simplification0.2

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

Reproduce

herbie shell --seed 2019004 +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))))

Details

Time bar (total: 59.3s)Debug log