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Target

Derivation

1. Split input into 3 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0 or -5.273499225036278e-308 < (/ (* a1 a2) (* b1 b2)) < -0.0

   1. Initial program 18.9

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

   3. Applied associate-/l*10.0

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

   5. Applied associate-/r/10.0

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

   7. Applied associate-/r*5.3

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

   9. Applied associate-*l/5.0

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -5.273499225036278e-308 or -0.0 < (/ (* a1 a2) (* b1 b2)) < 7.471207601488151e+277

   1. Initial program 0.9

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

   if 7.471207601488151e+277 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 55.0

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

   3. Applied times-frac7.1

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

4. Final simplification2.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -5.273499225036278 \cdot 10^{-308}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -0.0:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 7.471207601488151 \cdot 10^{+277}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

Runtime

Time bar (total: 9.5s)Debug logProfile

herbie shell --seed 2018242 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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