Error

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Target

Derivation

1. Split input into 3 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0 or -2.2845054729502e-312 < (/ (* a1 a2) (* b1 b2)) < 4.506587229492748e-292

   1. Initial program 17.6

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

   3. Applied times-frac3.2

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -2.2845054729502e-312 or 4.506587229492748e-292 < (/ (* a1 a2) (* b1 b2)) < 4.736445781412451e+290

   1. Initial program 0.7

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

   2. Taylor expanded around 0 0.7

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

   if 4.736445781412451e+290 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 56.4

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

   2. Taylor expanded around 0 56.4

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

   4. Applied times-frac7.7

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

4. Final simplification2.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -2.2845054729502 \cdot 10^{-312}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 4.506587229492748 \cdot 10^{-292}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 4.736445781412451 \cdot 10^{+290}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019022 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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

Details

Time bar (total: 4.2s)Debug log