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Target

Derivation

1. Split input into 4 regimes

2. if (* a1 a2) < -8.817841110241764e+215

   1. Initial program 35.9

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

   2. Initial simplification9.2

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

   4. Applied div-inv9.2

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

   5. Applied associate-*l*8.5

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

   if -8.817841110241764e+215 < (* a1 a2) < -4.312723039147459e-194

   1. Initial program 4.4

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

   2. Initial simplification15.1

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

   4. Applied associate-*r/11.6

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

   5. Taylor expanded around inf 4.4

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

   if -4.312723039147459e-194 < (* a1 a2) < 2.6602715709559192e-197 or 1.1737266761683139e+247 < (* a1 a2)

   1. Initial program 18.7

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

   2. Initial simplification5.1

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

   if 2.6602715709559192e-197 < (* a1 a2) < 1.1737266761683139e+247

   1. Initial program 4.2

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

   2. Initial simplification15.0

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

   4. Applied frac-times4.2

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

4. Final simplification4.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -8.817841110241764 \cdot 10^{+215}:\\ \;\;\;\;a1 \cdot \left(\frac{a2}{b1} \cdot \frac{1}{b2}\right)\\ \mathbf{elif}\;a1 \cdot a2 \le -4.312723039147459 \cdot 10^{-194}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b2}}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.6602715709559192 \cdot 10^{-197}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.1737266761683139 \cdot 10^{+247}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array}\]

Runtime

Time bar (total: 14.8s)Debug logProfile

herbie shell --seed 2018252 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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