Error

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Target

Derivation

1. Split input into 3 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0 or -2.3932614315738574e-232 < (/ (* a1 a2) (* b1 b2)) < -0.0

   1. Initial program 17.2

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

   3. Applied associate-/r*9.6

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

   5. Applied div-inv9.6

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

   6. Applied associate-/l*17.2

      \[\leadsto \color{blue}{\frac{a1 \cdot a2}{\frac{b2}{\frac{1}{b1}}}}\]
   7. Using strategy rm

   8. Applied associate-/r/17.2

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

   9. Applied times-frac4.4

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

   10. Simplified4.4

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -2.3932614315738574e-232 or -0.0 < (/ (* a1 a2) (* b1 b2)) < 2.689807433743198e+291

   1. Initial program 0.8

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

   if 2.689807433743198e+291 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 57.7

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

   3. Applied times-frac6.6

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

4. Final simplification2.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -2.3932614315738574 \cdot 10^{-232}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -0.0:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 2.689807433743198 \cdot 10^{+291}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 +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: 3.9s)Debug log