Error

Try it out

Target

Derivation

1. Split input into 4 regimes

2. if (* a1 a2) < -1.6921838503221445e-188

   1. Initial program 9.0

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

   3. Applied associate-/r*9.5

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

   if -1.6921838503221445e-188 < (* a1 a2) < 8.705897000018843e-219

   1. Initial program 13.6

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

   3. Applied times-frac4.2

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

   5. Applied associate-*r/7.9

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

   if 8.705897000018843e-219 < (* a1 a2) < 6.654002524214254e+203

   1. Initial program 4.6

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

   3. Applied associate-/r*4.4

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

   5. Applied clear-num4.6

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

   7. Applied associate-/r/4.5

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

   8. Applied associate-/l*4.4

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

   if 6.654002524214254e+203 < (* a1 a2)

   1. Initial program 34.0

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

   3. Applied times-frac9.8

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
3. Recombined 4 regimes into one program.

4. Final simplification7.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -1.6921838503221445 \cdot 10^{-188}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 8.705897000018843 \cdot 10^{-219}:\\ \;\;\;\;\frac{\frac{a1}{b1} \cdot a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 6.654002524214254 \cdot 10^{+203}:\\ \;\;\;\;\frac{\frac{1}{b1}}{\frac{b2}{a1 \cdot a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

Reproduce

herbie shell --seed 2019002 +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: 5.3s)Debug log