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 *-un-lft-identity0.2

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

6. Applied div-inv0.2

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

7. Applied prod-diff0.2

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

8. Applied associate-+r+0.2

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

9. Simplified0.2

   \[\leadsto \left(x + (\left(\tan y + \tan z\right) \cdot \left(\frac{1}{1 - \tan y \cdot \tan z}\right) + \left(-\tan a \cdot 1\right))_*\right) + \color{blue}{\tan a \cdot 0}\]

10. Final simplification0.2

    \[\leadsto 0 \cdot \tan a + \left((\left(\tan y + \tan z\right) \cdot \left(\frac{1}{1 - \tan z \cdot \tan y}\right) + \left(-\tan a\right))_* + x\right)\]

Reproduce

herbie shell --seed 2019090 +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))))