Error

Target

Derivation

1. Initial program 4.0

   \[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c_n}}\]
2. Using strategy rm

3. Applied add-exp-log4.0

   \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c_p} \cdot {\color{blue}{\left(e^{\log \left(1 - \frac{1}{1 + e^{-t}}\right)}\right)}}^{c_n}}\]

4. Applied pow-exp4.0

   \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c_p} \cdot \color{blue}{e^{\log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}}\]

5. Applied add-exp-log4.0

   \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c_n}}{{\left(\frac{1}{\color{blue}{e^{\log \left(1 + e^{-t}\right)}}}\right)}^{c_p} \cdot e^{\log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}\]

6. Applied rec-exp4.0

   \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c_n}}{{\color{blue}{\left(e^{-\log \left(1 + e^{-t}\right)}\right)}}^{c_p} \cdot e^{\log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}\]

7. Applied pow-exp4.0

   \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c_n}}{\color{blue}{e^{\left(-\log \left(1 + e^{-t}\right)\right) \cdot c_p}} \cdot e^{\log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}\]

8. Applied prod-exp4.0

   \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c_n}}{\color{blue}{e^{\left(-\log \left(1 + e^{-t}\right)\right) \cdot c_p + \log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}}\]

9. Applied add-exp-log4.0

   \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot {\color{blue}{\left(e^{\log \left(1 - \frac{1}{1 + e^{-s}}\right)}\right)}}^{c_n}}{e^{\left(-\log \left(1 + e^{-t}\right)\right) \cdot c_p + \log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}\]

10. Applied pow-exp4.0

    \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot \color{blue}{e^{\log \left(1 - \frac{1}{1 + e^{-s}}\right) \cdot c_n}}}{e^{\left(-\log \left(1 + e^{-t}\right)\right) \cdot c_p + \log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}\]

11. Applied add-exp-log4.0

    \[\leadsto \frac{{\left(\frac{1}{\color{blue}{e^{\log \left(1 + e^{-s}\right)}}}\right)}^{c_p} \cdot e^{\log \left(1 - \frac{1}{1 + e^{-s}}\right) \cdot c_n}}{e^{\left(-\log \left(1 + e^{-t}\right)\right) \cdot c_p + \log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}\]

12. Applied rec-exp4.0

    \[\leadsto \frac{{\color{blue}{\left(e^{-\log \left(1 + e^{-s}\right)}\right)}}^{c_p} \cdot e^{\log \left(1 - \frac{1}{1 + e^{-s}}\right) \cdot c_n}}{e^{\left(-\log \left(1 + e^{-t}\right)\right) \cdot c_p + \log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}\]

13. Applied pow-exp4.0

    \[\leadsto \frac{\color{blue}{e^{\left(-\log \left(1 + e^{-s}\right)\right) \cdot c_p}} \cdot e^{\log \left(1 - \frac{1}{1 + e^{-s}}\right) \cdot c_n}}{e^{\left(-\log \left(1 + e^{-t}\right)\right) \cdot c_p + \log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}\]

14. Applied prod-exp4.0

    \[\leadsto \frac{\color{blue}{e^{\left(-\log \left(1 + e^{-s}\right)\right) \cdot c_p + \log \left(1 - \frac{1}{1 + e^{-s}}\right) \cdot c_n}}}{e^{\left(-\log \left(1 + e^{-t}\right)\right) \cdot c_p + \log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n}}\]

15. Applied div-exp1.7

    \[\leadsto \color{blue}{e^{\left(\left(-\log \left(1 + e^{-s}\right)\right) \cdot c_p + \log \left(1 - \frac{1}{1 + e^{-s}}\right) \cdot c_n\right) - \left(\left(-\log \left(1 + e^{-t}\right)\right) \cdot c_p + \log \left(1 - \frac{1}{1 + e^{-t}}\right) \cdot c_n\right)}}\]

16. Applied simplify1.7

    \[\leadsto e^{\color{blue}{\left(\log \left(1 + e^{-s}\right) - \log \left(e^{-t} + 1\right)\right) \cdot \left(-c_p\right) + \left(\log \left(1 - \frac{1}{1 + e^{-s}}\right) - \log \left(1 - \frac{1}{e^{-t} + 1}\right)\right) \cdot c_n}}\]
17. Using strategy rm

18. Applied diff-log1.7

    \[\leadsto e^{\left(\log \left(1 + e^{-s}\right) - \log \left(e^{-t} + 1\right)\right) \cdot \left(-c_p\right) + \color{blue}{\log \left(\frac{1 - \frac{1}{1 + e^{-s}}}{1 - \frac{1}{e^{-t} + 1}}\right)} \cdot c_n}\]
19. Using strategy rm

20. Applied add-cbrt-cube1.7

    \[\leadsto e^{\left(\log \left(1 + e^{-s}\right) - \log \left(e^{-t} + 1\right)\right) \cdot \left(-c_p\right) + \color{blue}{\sqrt[3]{\left(\log \left(\frac{1 - \frac{1}{1 + e^{-s}}}{1 - \frac{1}{e^{-t} + 1}}\right) \cdot \log \left(\frac{1 - \frac{1}{1 + e^{-s}}}{1 - \frac{1}{e^{-t} + 1}}\right)\right) \cdot \log \left(\frac{1 - \frac{1}{1 + e^{-s}}}{1 - \frac{1}{e^{-t} + 1}}\right)}} \cdot c_n}\]

21. Applied simplify1.7

    \[\leadsto e^{\left(\log \left(1 + e^{-s}\right) - \log \left(e^{-t} + 1\right)\right) \cdot \left(-c_p\right) + \sqrt[3]{\color{blue}{{\left(\log \left(\frac{1 - \frac{1}{1 + e^{-s}}}{1 - \frac{1}{e^{-t} + 1}}\right)\right)}^{3}}} \cdot c_n}\]
22. Removed slow pow expressions.

Runtime

Time bar (total: 8.0m)Debug logProfile

herbie shell --seed '#(1063027428 1192549564 1443466578 604016274 3637110559 1698629644)' 
(FPCore (c_p c_n t s)
  :name "Harley's example"
  :pre (and (< 0 c_p) (< 0 c_n))

  :herbie-target
  (* (pow (/ (+ 1 (exp (- t))) (+ 1 (exp (- s)))) c_p) (pow (/ (+ 1 (exp t)) (+ 1 (exp s))) c_n))

  (/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n))))