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Target

Derivation

1. Split input into 4 regimes

2. if (* a1 (/ a2 b1)) < -1.7643916642203566e+269

   1. Initial program 17.8

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

   2. Initial simplification31.4

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

   4. Applied associate-*r/15.0

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

   if -1.7643916642203566e+269 < (* a1 (/ a2 b1)) < -1.0217538782175125e-230 or 3.7054397350458017e-308 < (* a1 (/ a2 b1)) < 6.479072608023693e+301

   1. Initial program 12.7

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

   2. Initial simplification7.8

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

   4. Applied associate-*l/0.6

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

   if -1.0217538782175125e-230 < (* a1 (/ a2 b1)) < 3.7054397350458017e-308

   1. Initial program 6.8

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

   2. Initial simplification10.6

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

   4. Applied associate-*r/5.7

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

   6. Applied div-inv5.8

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

   7. Applied associate-*l*4.0

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

   if 6.479072608023693e+301 < (* a1 (/ a2 b1))

   1. Initial program 15.9

      \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
3. Recombined 4 regimes into one program.

4. Final simplification3.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a2}{b1} \cdot a1 \le -1.7643916642203566 \cdot 10^{+269}:\\ \;\;\;\;\frac{\frac{a1}{b2} \cdot a2}{b1}\\ \mathbf{elif}\;\frac{a2}{b1} \cdot a1 \le -1.0217538782175125 \cdot 10^{-230}:\\ \;\;\;\;\frac{\frac{a2}{b1} \cdot a1}{b2}\\ \mathbf{elif}\;\frac{a2}{b1} \cdot a1 \le 3.7054397350458017 \cdot 10^{-308}:\\ \;\;\;\;\frac{a1 \cdot \left(\frac{1}{b2} \cdot a2\right)}{b1}\\ \mathbf{elif}\;\frac{a2}{b1} \cdot a1 \le 6.479072608023693 \cdot 10^{+301}:\\ \;\;\;\;\frac{\frac{a2}{b1} \cdot a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \end{array}\]

Runtime

Time bar (total: 24.8s)Debug logProfile

herbie shell --seed 2018216 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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