Error

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Derivation

1. Initial program 13.1

   \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
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 flip--0.2

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

7. Applied tan-quot0.2

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

8. Applied associate-*r/0.2

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

10. Applied add-log-exp0.3

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

11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019005 +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: 42.9s)Debug log