Error

Derivation

1. Initial program 13.2

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

3. Applied tan-quot13.2

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

4. Applied tan-sum0.2

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

5. Applied frac-sub0.2

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

6. Simplified0.2

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

8. Applied flip--0.2

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

9. Applied associate-*l/0.2

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

10. Applied associate-/r/0.2

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

11. Simplified0.2

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

12. Final simplification0.2

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

Reproduce

herbie shell --seed 2019008 +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: 42.5s)Debug log