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Target

Derivation

1. Split input into 2 regimes

2. if (* a1 a2) < -6.525749460922175e+292 or -2.5469560807085005e-82 < (* a1 a2) < 3.160711617003064e-169 or 1.1608953560754696e+189 < (* a1 a2)

   1. Initial program 17.4

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

   2. Initial simplification6.7

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

   if -6.525749460922175e+292 < (* a1 a2) < -2.5469560807085005e-82 or 3.160711617003064e-169 < (* a1 a2) < 1.1608953560754696e+189

   1. Initial program 4.2

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

   2. Initial simplification14.5

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

   4. Applied associate-*l/10.9

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

   5. Taylor expanded around -inf 4.3

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

4. Final simplification5.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -6.525749460922175 \cdot 10^{+292}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le -2.5469560807085005 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 3.160711617003064 \cdot 10^{-169}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.1608953560754696 \cdot 10^{+189}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \end{array}\]

Runtime

Time bar (total: 9.4s)Debug logProfile

herbie shell --seed 2018263 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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