Error

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Target

Derivation

1. Split input into 3 regimes

2. if (* a1 a2) < -1.80032910927971e+260 or 1.2457885067808956e+138 < (* a1 a2)

   1. Initial program 31.7

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

   2. Initial simplification11.5

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

   4. Applied div-inv11.5

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

   5. Applied associate-*l*11.6

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

   7. Applied associate-*r/11.4

      \[\leadsto a1 \cdot \color{blue}{\frac{\frac{1}{b2} \cdot a2}{b1}}\]

   if -1.80032910927971e+260 < (* a1 a2) < -9.386666746135581e-144 or 2.133718381578429e-211 < (* a1 a2) < 1.2457885067808956e+138

   1. Initial program 4.1

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

   2. Initial simplification14.6

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

   3. Taylor expanded around inf 4.1

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

   if -9.386666746135581e-144 < (* a1 a2) < 2.133718381578429e-211

   1. Initial program 13.0

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

   2. Initial simplification4.8

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

4. Final simplification5.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -1.80032910927971 \cdot 10^{+260}:\\ \;\;\;\;a1 \cdot \frac{a2 \cdot \frac{1}{b2}}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le -9.386666746135581 \cdot 10^{-144}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.133718381578429 \cdot 10^{-211}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.2457885067808956 \cdot 10^{+138}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2 \cdot \frac{1}{b2}}{b1}\\ \end{array}\]

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(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