Error

Try it out

Target

Derivation

1. Split input into 4 regimes

2. if (* b1 b2) < -2.519628138410373e+192

   1. Initial program 14.8

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

   3. Applied associate-/r*8.1

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

   5. Applied associate-/l*5.2

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

   7. Applied associate-/r/4.4

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

   8. Applied associate-/l*4.3

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

   if -2.519628138410373e+192 < (* b1 b2) < -9.768489324541237e-137 or 6.034183376454478e-220 < (* b1 b2) < 2.236418586449766e+137

   1. Initial program 3.9

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

   3. Applied div-inv3.9

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

   if -9.768489324541237e-137 < (* b1 b2) < 6.034183376454478e-220

   1. Initial program 28.1

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

   3. Applied times-frac10.7

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

   if 2.236418586449766e+137 < (* b1 b2)

   1. Initial program 14.7

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

   2. Initial simplification5.5

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

4. Final simplification5.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -2.519628138410373 \cdot 10^{+192}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le -9.768489324541237 \cdot 10^{-137}:\\ \;\;\;\;\left(a2 \cdot a1\right) \cdot \frac{1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 6.034183376454478 \cdot 10^{-220}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.236418586449766 \cdot 10^{+137}:\\ \;\;\;\;\left(a2 \cdot a1\right) \cdot \frac{1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array}\]

Runtime

Time bar (total: 8.7s)Debug logProfile

herbie shell --seed 2018248 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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