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Target

Derivation

1. Split input into 2 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0 or -4.877016002976535e-305 < (/ (* a1 a2) (* b1 b2)) < 7.783309181859375e-256 or 2.9378956593072405e+307 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 24.2

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

   2. Initial simplification4.4

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

   4. Applied associate-*r/6.8

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

   6. Applied associate-/l*4.6

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -4.877016002976535e-305 or 7.783309181859375e-256 < (/ (* a1 a2) (* b1 b2)) < 2.9378956593072405e+307

   1. Initial program 0.9

      \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
3. Recombined 2 regimes into one program.

4. Final simplification2.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -4.877016002976535 \cdot 10^{-305}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 7.783309181859375 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 2.9378956593072405 \cdot 10^{+307}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \end{array}\]

Runtime

Time bar (total: 6.6s)Debug logProfile

herbie shell --seed 2018297 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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