Error

Try it out

Target

Derivation

1. Split input into 3 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0 or 5.21624264135564e+298 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 59.3

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

   3. Applied times-frac8.5

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -1.4730004851386487e-292 or -0.0 < (/ (* a1 a2) (* b1 b2)) < 5.21624264135564e+298

   1. Initial program 0.8

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

   if -1.4730004851386487e-292 < (/ (* a1 a2) (* b1 b2)) < -0.0

   1. Initial program 13.1

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

   3. Applied div-inv13.2

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

   5. Applied associate-/r*12.5

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

   7. Applied pow112.5

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

   8. Applied pow112.5

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

   9. Applied pow-prod-down12.5

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

   10. Simplified2.5

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

   12. Applied associate-*l/3.6

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

4. Final simplification2.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -1.4730004851386487 \cdot 10^{-292}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -0.0:\\ \;\;\;\;\frac{a1 \cdot \frac{a2}{b1}}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 5.21624264135564 \cdot 10^{+298}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

Reproduce

herbie shell --seed 2019026 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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