Error

Try it out

Target

Derivation

1. Split input into 4 regimes

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

   1. Initial program 60.0

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

   3. Applied associate-/r*30.1

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

   5. Applied associate-/l*16.9

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -2.1745524547356668e-275 or -0.0 < (/ (* a1 a2) (* b1 b2)) < 2.5643756364950763e+290

   1. Initial program 0.9

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

   if -2.1745524547356668e-275 < (/ (* a1 a2) (* b1 b2)) < -0.0

   1. Initial program 14.2

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

   3. Applied times-frac3.0

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

   if 2.5643756364950763e+290 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 57.5

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

   2. Initial simplification6.5

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

4. Final simplification2.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{\frac{a1}{\frac{b1}{a2}}}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -2.1745524547356668 \cdot 10^{-275}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -0.0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 2.5643756364950763 \cdot 10^{+290}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \end{array}\]

Runtime

Time bar (total: 8.1s)Debug logProfile

herbie shell --seed 2018255 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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