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Target

Derivation

1. Split input into 5 regimes

2. if (/ (* b1 b2) a2) < -7.425788847764119e+304

   1. Initial program 13.0

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

   2. Initial simplification6.5

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

   if -7.425788847764119e+304 < (/ (* b1 b2) a2) < -9.715238065617437e-309

   1. Initial program 7.6

      \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
   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 -9.715238065617437e-309 < (/ (* b1 b2) a2) < 3.259654195747313e-296

   1. Initial program 33.1

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

   3. Applied associate-/r*14.2

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

   if 3.259654195747313e-296 < (/ (* b1 b2) a2) < 1.6631962846554361e+243

   1. Initial program 7.0

      \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
   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 1.6631962846554361e+243 < (/ (* b1 b2) a2)

   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

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b1 \cdot b2}{a2} \le -7.425788847764119 \cdot 10^{+304}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;\frac{b1 \cdot b2}{a2} \le -9.715238065617437 \cdot 10^{-309}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a2}} \cdot a1\\ \mathbf{elif}\;\frac{b1 \cdot b2}{a2} \le 3.259654195747313 \cdot 10^{-296}:\\ \;\;\;\;\frac{\frac{a2 \cdot a1}{b1}}{b2}\\ \mathbf{elif}\;\frac{b1 \cdot b2}{a2} \le 1.6631962846554361 \cdot 10^{+243}:\\ \;\;\;\;\frac{a1}{\frac{1}{\frac{a2}{b1 \cdot b2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array}\]

Runtime

Time bar (total: 13.0s)Debug logProfile

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

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

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