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Target

Derivation

1. Split input into 3 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0 or 4.158377208669037e+275 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 56.2

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

   2. Initial simplification8.6

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -1.1950997256574e-314 or 6.148252691079469e-273 < (/ (* a1 a2) (* b1 b2)) < 4.158377208669037e+275

   1. Initial program 0.9

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

   if -1.1950997256574e-314 < (/ (* a1 a2) (* b1 b2)) < 6.148252691079469e-273

   1. Initial program 12.2

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

   2. Initial simplification3.3

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

   4. Applied associate-*r/4.1

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

4. Final simplification2.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -1.1950997256574 \cdot 10^{-314}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 6.148252691079469 \cdot 10^{-273}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b2}}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 4.158377208669037 \cdot 10^{+275}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \end{array}\]

Runtime

Time bar (total: 7.0s)Debug logProfile

herbie shell --seed 2018219 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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