Error

Try it out

Target

Derivation

1. Split input into 3 regimes

2. if b1 < -6.136773016984138e+103 or 3.6026389828475524e-10 < b1

   1. Initial program 9.5

      \[\frac{a1 \cdot a2}{b1 \cdot b2}\]

   2. Initial simplification10.1

      \[\leadsto \frac{a1}{b2} \cdot \frac{a2}{b1}\]
   3. Using strategy rm

   4. Applied div-inv10.1

      \[\leadsto \color{blue}{\left(a1 \cdot \frac{1}{b2}\right)} \cdot \frac{a2}{b1}\]

   5. Applied associate-*l*9.8

      \[\leadsto \color{blue}{a1 \cdot \left(\frac{1}{b2} \cdot \frac{a2}{b1}\right)}\]
   6. Using strategy rm

   7. Applied associate-*r*10.1

      \[\leadsto \color{blue}{\left(a1 \cdot \frac{1}{b2}\right) \cdot \frac{a2}{b1}}\]

   if -6.136773016984138e+103 < b1 < -1.9118140841034162e-219 or -8.133470980058762e-308 < b1 < 3.6026389828475524e-10

   1. Initial program 10.9

      \[\frac{a1 \cdot a2}{b1 \cdot b2}\]

   2. Initial simplification11.6

      \[\leadsto \frac{a1}{b2} \cdot \frac{a2}{b1}\]
   3. Using strategy rm

   4. Applied div-inv11.6

      \[\leadsto \color{blue}{\left(a1 \cdot \frac{1}{b2}\right)} \cdot \frac{a2}{b1}\]

   5. Applied associate-*l*11.8

      \[\leadsto \color{blue}{a1 \cdot \left(\frac{1}{b2} \cdot \frac{a2}{b1}\right)}\]
   6. Using strategy rm

   7. Applied pow111.8

      \[\leadsto a1 \cdot \left(\frac{1}{b2} \cdot \color{blue}{{\left(\frac{a2}{b1}\right)}^{1}}\right)\]

   8. Applied pow111.8

      \[\leadsto a1 \cdot \left(\color{blue}{{\left(\frac{1}{b2}\right)}^{1}} \cdot {\left(\frac{a2}{b1}\right)}^{1}\right)\]

   9. Applied pow-prod-down11.8

      \[\leadsto a1 \cdot \color{blue}{{\left(\frac{1}{b2} \cdot \frac{a2}{b1}\right)}^{1}}\]

   10. Simplified10.7

       \[\leadsto a1 \cdot {\color{blue}{\left(\frac{\frac{a2}{b2}}{b1}\right)}}^{1}\]
   11. Using strategy rm

   12. Applied div-inv10.7

       \[\leadsto a1 \cdot {\color{blue}{\left(\frac{a2}{b2} \cdot \frac{1}{b1}\right)}}^{1}\]

   13. Applied unpow-prod-down10.7

       \[\leadsto a1 \cdot \color{blue}{\left({\left(\frac{a2}{b2}\right)}^{1} \cdot {\left(\frac{1}{b1}\right)}^{1}\right)}\]

   14. Applied associate-*r*10.8

       \[\leadsto \color{blue}{\left(a1 \cdot {\left(\frac{a2}{b2}\right)}^{1}\right) \cdot {\left(\frac{1}{b1}\right)}^{1}}\]

   15. Simplified10.8

       \[\leadsto \left(a1 \cdot {\left(\frac{a2}{b2}\right)}^{1}\right) \cdot \color{blue}{\frac{1}{b1}}\]

   if -1.9118140841034162e-219 < b1 < -8.133470980058762e-308

   1. Initial program 17.2

      \[\frac{a1 \cdot a2}{b1 \cdot b2}\]

   2. Initial simplification20.5

      \[\leadsto \frac{a1}{b2} \cdot \frac{a2}{b1}\]
   3. Using strategy rm

   4. Applied div-inv20.6

      \[\leadsto \color{blue}{\left(a1 \cdot \frac{1}{b2}\right)} \cdot \frac{a2}{b1}\]

   5. Applied associate-*l*19.4

      \[\leadsto \color{blue}{a1 \cdot \left(\frac{1}{b2} \cdot \frac{a2}{b1}\right)}\]
   6. Using strategy rm

   7. Applied pow119.4

      \[\leadsto a1 \cdot \left(\frac{1}{b2} \cdot \color{blue}{{\left(\frac{a2}{b1}\right)}^{1}}\right)\]

   8. Applied pow119.4

      \[\leadsto a1 \cdot \left(\color{blue}{{\left(\frac{1}{b2}\right)}^{1}} \cdot {\left(\frac{a2}{b1}\right)}^{1}\right)\]

   9. Applied pow-prod-down19.4

      \[\leadsto a1 \cdot \color{blue}{{\left(\frac{1}{b2} \cdot \frac{a2}{b1}\right)}^{1}}\]

   10. Simplified18.3

       \[\leadsto a1 \cdot {\color{blue}{\left(\frac{\frac{a2}{b2}}{b1}\right)}}^{1}\]
3. Recombined 3 regimes into one program.

4. Final simplification10.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \le -6.136773016984138 \cdot 10^{+103}:\\ \;\;\;\;\frac{a2}{b1} \cdot \left(a1 \cdot \frac{1}{b2}\right)\\ \mathbf{elif}\;b1 \le -1.9118140841034162 \cdot 10^{-219}:\\ \;\;\;\;\left(\frac{a2}{b2} \cdot a1\right) \cdot \frac{1}{b1}\\ \mathbf{elif}\;b1 \le -8.133470980058762 \cdot 10^{-308}:\\ \;\;\;\;\frac{\frac{a2}{b2}}{b1} \cdot a1\\ \mathbf{elif}\;b1 \le 3.6026389828475524 \cdot 10^{-10}:\\ \;\;\;\;\left(\frac{a2}{b2} \cdot a1\right) \cdot \frac{1}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \left(a1 \cdot \frac{1}{b2}\right)\\ \end{array}\]

Runtime

Time bar (total: 8.6s)Debug logProfile

herbie shell --seed 2018296 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

  :herbie-target
  (* (/ a1 b1) (/ a2 b2))

  (/ (* a1 a2) (* b1 b2)))