Error

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Target

Derivation

1. Split input into 4 regimes

2. if (* a1 a2) < -4.874472426675501e+191

   1. Initial program 30.3

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

   3. Applied associate-/r*30.9

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

   5. Applied associate-/l*16.7

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

   7. Applied associate-/r/16.6

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

   if -4.874472426675501e+191 < (* a1 a2) < -5.866961245433944e-207

   1. Initial program 4.8

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

   3. Applied associate-/r*4.6

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

   5. Applied div-inv4.6

      \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b1} \cdot \frac{1}{b2}}\]
   6. Using strategy rm

   7. Applied div-inv4.7

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

   8. Applied associate-*l*4.7

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

   if -5.866961245433944e-207 < (* a1 a2) < 3.2733143053841e-311 or 7.535942824848952e+88 < (* a1 a2)

   1. Initial program 18.0

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

   2. Initial simplification7.0

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

   if 3.2733143053841e-311 < (* a1 a2) < 7.535942824848952e+88

   1. Initial program 4.0

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

   3. Applied associate-/r*4.3

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

   5. Applied div-inv4.4

      \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b1} \cdot \frac{1}{b2}}\]
3. Recombined 4 regimes into one program.

4. Final simplification6.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -4.874472426675501 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{a1}{b1} \cdot a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -5.866961245433944 \cdot 10^{-207}:\\ \;\;\;\;\left(\frac{1}{b2} \cdot \frac{1}{b1}\right) \cdot \left(a1 \cdot a2\right)\\ \mathbf{elif}\;a1 \cdot a2 \le 3.2733143053841 \cdot 10^{-311}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 7.535942824848952 \cdot 10^{+88}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1} \cdot \frac{1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \end{array}\]

Reproduce

herbie shell --seed 2018365 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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

Details

Time bar (total: 3.5s)Debug log