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 add-sqr-sqrt30.9

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

6. Applied flip--30.9

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

7. Applied associate-/r/30.9

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

8. Applied prod-diff30.9

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

9. Simplified30.9

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

10. Simplified0.2

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

12. Applied tan-quot0.2

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

13. Applied associate-*l/0.2

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

14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019016 +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: 45.8s)Debug log