Error

Try it out

Target

Derivation

1. Split input into 2 regimes

2. if (* a1 a2) < -3.881499779096344e+241 or -3.6891869219375896e-239 < (* a1 a2) < 6.648346854945822e-243 or 1.0906941155259606e+230 < (* a1 a2)

   1. Initial program 24.1

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

   2. Initial simplification5.0

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

   if -3.881499779096344e+241 < (* a1 a2) < -3.6891869219375896e-239 or 6.648346854945822e-243 < (* a1 a2) < 1.0906941155259606e+230

   1. Initial program 4.9

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

   2. Initial simplification14.1

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

   4. Applied div-inv14.2

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

   5. Applied associate-*r*11.3

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

   6. Taylor expanded around -inf 4.9

      \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b2 \cdot b1}}\]
3. Recombined 2 regimes into one program.

4. Final simplification4.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -3.881499779096344 \cdot 10^{+241}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le -3.6891869219375896 \cdot 10^{-239}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 6.648346854945822 \cdot 10^{-243}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.0906941155259606 \cdot 10^{+230}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \end{array}\]

Runtime

Time bar (total: 11.7s)Debug logProfile

herbie shell --seed 2018340 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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