Error

Try it out

Target

Derivation

1. Split input into 4 regimes

2. if (* a1 a2) < -inf.0 or 7.901942574419375e+236 < (* a1 a2)

   1. Initial program 48.2

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

   3. Applied times-frac7.4

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

   5. Applied div-inv7.4

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

   6. Applied associate-*l*7.6

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

   if -inf.0 < (* a1 a2) < -1.5771615462003768e-77

   1. Initial program 5.4

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

   2. Taylor expanded around -inf 5.4

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

   if -1.5771615462003768e-77 < (* a1 a2) < 3.571385350498116e-179

   1. Initial program 12.3

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

   3. Applied times-frac6.1

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

   if 3.571385350498116e-179 < (* a1 a2) < 7.901942574419375e+236

   1. Initial program 4.8

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

   2. Taylor expanded around -inf 4.8

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

   4. Applied associate-/r*4.2

      \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b2}}{b1}}\]
3. Recombined 4 regimes into one program.

4. Final simplification5.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 = -\infty:\\ \;\;\;\;a1 \cdot \left(\frac{a2}{b2} \cdot \frac{1}{b1}\right)\\ \mathbf{elif}\;a1 \cdot a2 \le -1.5771615462003768 \cdot 10^{-77}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 3.571385350498116 \cdot 10^{-179}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 7.901942574419375 \cdot 10^{+236}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b2}}{b1}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \left(\frac{a2}{b2} \cdot \frac{1}{b1}\right)\\ \end{array}\]

Runtime

Time bar (total: 8.3s)Debug logProfile

herbie shell --seed 2018304 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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