Error

Target

Derivation

1. Initial program 30.2

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

3. Applied flip--30.4

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

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 *-un-lft-identity14.9

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

7. Applied add-sqr-sqrt15.3

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

8. Applied times-frac15.2

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

9. Applied times-frac1.1

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

10. Applied simplify1.1

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

11. Applied simplify1.1

    \[\leadsto \frac{\sin x}{\sqrt{\cos x + 1}} \cdot \color{blue}{\frac{1}{\sqrt{\cos x + 1}}}\]
12. Removed slow pow expressions.

Runtime

Time bar (total: 1.9m)Debug log

herbie shell --seed '#(2094665535 3654809497 1731717781 3082199462 566033875 575777438)' 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 1

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

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