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Target

Derivation

1. Initial program 39.8

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

2. Initial simplification0.4

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

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

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

5. Applied add-sqr-sqrt0.4

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

6. Applied times-frac0.4

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

7. Simplified0.4

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

9. Applied add-sqr-sqrt0.4

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

10. Applied associate-/l*0.4

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

11. Final simplification0.4

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

Runtime

Time bar (total: 35.7s)Debug logProfile

herbie shell --seed 2018295 +o rules:numerics
(FPCore (x)
  :name "expq2 (section 3.11)"

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

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