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Target

Derivation

1. Split input into 2 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0 or -1.5446318367563974e-299 < (/ (* a1 a2) (* b1 b2)) < 0.0 or 6.997852254995738e+280 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 24.6

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

   2. Initial simplification3.8

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -1.5446318367563974e-299 or 0.0 < (/ (* a1 a2) (* b1 b2)) < 6.997852254995738e+280

   1. Initial program 0.8

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

4. Final simplification2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -1.5446318367563974 \cdot 10^{-299}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 0.0:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 6.997852254995738 \cdot 10^{+280}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \end{array}\]

Runtime

Time bar (total: 7.6s)Debug logProfile

herbie shell --seed 2018221 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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