Error

Target

Derivation

1. Initial program 30.4

   \[\frac{1 - \cos x}{\sin x}\]
2. Using strategy rm

3. Applied flip--30.6

   \[\leadsto \frac{\color{blue}{\frac{1 \cdot 1 - \cos x \cdot \cos x}{1 + \cos x}}}{\sin x}\]

4. Applied simplify14.9

   \[\leadsto \frac{\frac{\color{blue}{\sin x \cdot \sin x}}{1 + \cos x}}{\sin x}\]
5. Using strategy rm

6. Applied add-cube-cbrt15.5

   \[\leadsto \frac{\frac{\sin x \cdot \sin x}{1 + \cos x}}{\color{blue}{\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right) \cdot \sqrt[3]{\sin x}}}\]

7. Applied add-sqr-sqrt15.5

   \[\leadsto \frac{\frac{\sin x \cdot \sin x}{\color{blue}{\sqrt{1 + \cos x} \cdot \sqrt{1 + \cos x}}}}{\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right) \cdot \sqrt[3]{\sin x}}\]

8. Applied times-frac15.6

   \[\leadsto \frac{\color{blue}{\frac{\sin x}{\sqrt{1 + \cos x}} \cdot \frac{\sin x}{\sqrt{1 + \cos x}}}}{\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right) \cdot \sqrt[3]{\sin x}}\]

9. Applied times-frac1.6

   \[\leadsto \color{blue}{\frac{\frac{\sin x}{\sqrt{1 + \cos x}}}{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}} \cdot \frac{\frac{\sin x}{\sqrt{1 + \cos x}}}{\sqrt[3]{\sin x}}}\]

Runtime

Time bar (total: 44.6s)Debug logProfile

herbie shell --seed '#(1064300848 3212030778 2049303162 3567222883 2277747821 1384278011)' 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

  :herbie-target
  (tan (/ x 2))

  (/ (- 1 (cos x)) (sin x)))