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Target

Derivation

1. Split input into 4 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0

   1. Initial program 59.9

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

   2. Initial simplification10.4

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

   4. Applied associate-*r/16.2

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

   6. Applied div-inv16.3

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

   7. Applied associate-*l*17.2

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -8.349989479786357e-276 or -0.0 < (/ (* a1 a2) (* b1 b2)) < 5.22467364138413e+269

   1. Initial program 0.8

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

   if -8.349989479786357e-276 < (/ (* a1 a2) (* b1 b2)) < -0.0

   1. Initial program 11.9

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

   2. Initial simplification2.7

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

   if 5.22467364138413e+269 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 52.6

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

   2. Initial simplification9.0

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

   4. Applied associate-*r/14.6

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

   6. Applied div-inv14.6

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

   7. Applied associate-*l*14.1

      \[\leadsto \frac{\color{blue}{a1 \cdot \left(\frac{1}{b2} \cdot a2\right)}}{b1}\]
   8. Using strategy rm

   9. Applied associate-/l*12.6

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

4. Final simplification2.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{\left(\frac{1}{b2} \cdot a2\right) \cdot a1}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -8.349989479786357 \cdot 10^{-276}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -0.0:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 5.22467364138413 \cdot 10^{+269}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b1}{\frac{1}{b2} \cdot a2}}\\ \end{array}\]

Runtime

Time bar (total: 8.5s)Debug logProfile

herbie shell --seed 2018225 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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