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Target

Derivation

1. Split input into 3 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0

   1. Initial program 60.0

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

   2. Initial simplification8.0

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

   4. Applied associate-*r/14.6

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

   6. Applied div-inv14.7

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

   7. Applied associate-*l*16.2

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -1.671324024065761e-306 or 0.0 < (/ (* a1 a2) (* b1 b2)) < 2.5703034890500252e+300

   1. Initial program 0.8

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

   2. Initial simplification16.3

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

   4. Applied associate-*r/14.4

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

   6. Applied associate-*l/7.7

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

   7. Applied associate-/l/0.8

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

   if -1.671324024065761e-306 < (/ (* a1 a2) (* b1 b2)) < 0.0 or 2.5703034890500252e+300 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 21.4

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

   2. Initial simplification3.0

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

4. Final simplification2.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{\left(\frac{1}{b2} \cdot a2\right) \cdot a1}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -1.671324024065761 \cdot 10^{-306}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 0.0:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 2.5703034890500252 \cdot 10^{+300}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \end{array}\]

Runtime

Time bar (total: 8.2s)Debug logProfile

herbie shell --seed 2018354 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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