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Target

Derivation

1. Split input into 5 regimes

2. if (/ 1 (/ a2 (* b1 b2))) < -3.070949751369445e+307

   1. Initial program 13.1

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

   2. Initial simplification6.5

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

   if -3.070949751369445e+307 < (/ 1 (/ a2 (* b1 b2))) < -4.533777763954806e-309

   1. Initial program 7.5

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

   3. Applied associate-/l*0.6

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

   5. Applied div-inv0.6

      \[\leadsto \color{blue}{a1 \cdot \frac{1}{\frac{b1 \cdot b2}{a2}}}\]

   if -4.533777763954806e-309 < (/ 1 (/ a2 (* b1 b2))) < 3.3249250654312273e-287

   1. Initial program 32.5

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

   3. Applied associate-/r*14.1

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

   if 3.3249250654312273e-287 < (/ 1 (/ a2 (* b1 b2))) < 2.0830355560044318e+242

   1. Initial program 7.1

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

   3. Applied associate-/l*0.6

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

   5. Applied clear-num0.7

      \[\leadsto \frac{a1}{\color{blue}{\frac{1}{\frac{a2}{b1 \cdot b2}}}}\]

   if 2.0830355560044318e+242 < (/ 1 (/ a2 (* b1 b2)))

   1. Initial program 12.0

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

   3. Applied times-frac6.9

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
3. Recombined 5 regimes into one program.

4. Final simplification3.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{\frac{a2}{b1 \cdot b2}} \le -3.070949751369445 \cdot 10^{+307}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;\frac{1}{\frac{a2}{b1 \cdot b2}} \le -4.533777763954806 \cdot 10^{-309}:\\ \;\;\;\;a1 \cdot \frac{1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;\frac{1}{\frac{a2}{b1 \cdot b2}} \le 3.3249250654312273 \cdot 10^{-287}:\\ \;\;\;\;\frac{\frac{a2 \cdot a1}{b1}}{b2}\\ \mathbf{elif}\;\frac{1}{\frac{a2}{b1 \cdot b2}} \le 2.0830355560044318 \cdot 10^{+242}:\\ \;\;\;\;\frac{a1}{\frac{1}{\frac{a2}{b1 \cdot b2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array}\]

Runtime

Time bar (total: 13.7s)Debug logProfile

herbie shell --seed 2018217 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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