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Target

Derivation

1. Split input into 3 regimes

2. if (* a1 a2) < -2.944484643285243e+184 or -4.326764193848891e-248 < (* a1 a2) < 3.0547059436491664e-254

   1. Initial program 21.1

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

   3. Applied times-frac4.9

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

   if -2.944484643285243e+184 < (* a1 a2) < -4.326764193848891e-248 or 3.0547059436491664e-254 < (* a1 a2) < 6.198738995740791e+263

   1. Initial program 5.1

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

   3. Applied associate-/r*5.1

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

   if 6.198738995740791e+263 < (* a1 a2)

   1. Initial program 46.6

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

   2. Initial simplification9.4

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

4. Final simplification5.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -2.944484643285243 \cdot 10^{+184}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -4.326764193848891 \cdot 10^{-248}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 3.0547059436491664 \cdot 10^{-254}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 6.198738995740791 \cdot 10^{+263}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \end{array}\]

Runtime

Time bar (total: 7.0s)Debug logProfile

herbie shell --seed 2018348 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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