Error

Target

Derivation

1. Initial program 30.3

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

3. Applied flip--30.5

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

4. Applied simplify15.1

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

6. Applied *-un-lft-identity15.1

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

7. Applied *-un-lft-identity15.1

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

8. Applied times-frac15.0

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

9. Applied times-frac0.5

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

10. Applied simplify0.5

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

11. Applied simplify0.5

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

Runtime

Time bar (total: 28.7s)Debug logProfile

herbie shell --seed '#(1064269945 2896236262 301053905 1701069080 1701464310 1614783279)' +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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