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Target

Derivation

1. Initial program 40.1

   \[\frac{e^{x}}{e^{x} - 1}\]

2. Initial simplification0.4

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

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

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

5. Applied associate-/l*0.4

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

7. Applied div-inv0.4

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

8. Applied associate-/r*0.4

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

9. Simplified0.4

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

10. Final simplification0.4

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

Runtime

Time bar (total: 11.8s)Debug logProfile

herbie shell --seed 2018354 +o rules:numerics
(FPCore (x)
  :name "expq2 (section 3.11)"

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

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