Error

Target

Derivation

1. Initial program 40.2

   \[\frac{e^{x}}{e^{x} - 1}\]
2. Using strategy rm

3. Applied expm1-def0.4

   \[\leadsto \frac{e^{x}}{\color{blue}{(e^{x} - 1)^*}}\]
4. Using strategy rm

5. Applied *-un-lft-identity0.4

   \[\leadsto \frac{\color{blue}{1 \cdot e^{x}}}{(e^{x} - 1)^*}\]

6. Applied associate-/l*0.4

   \[\leadsto \color{blue}{\frac{1}{\frac{(e^{x} - 1)^*}{e^{x}}}}\]
7. Using strategy rm

8. Applied div-inv0.4

   \[\leadsto \frac{1}{\color{blue}{(e^{x} - 1)^* \cdot \frac{1}{e^{x}}}}\]

9. Applied associate-/r*0.4

   \[\leadsto \color{blue}{\frac{\frac{1}{(e^{x} - 1)^*}}{\frac{1}{e^{x}}}}\]

10. Final simplification0.4

    \[\leadsto \frac{\frac{1}{(e^{x} - 1)^*}}{\frac{1}{e^{x}}}\]

Reproduce

herbie shell --seed 2019068 +o rules:numerics
(FPCore (x)
  :name "expq2 (section 3.11)"

  :herbie-target
  (/ 1 (- 1 (exp (- x))))

  (/ (exp x) (- (exp x) 1)))