Error

Target

Derivation

1. Split input into 2 regimes

2. if (* a1 a2) < -5.411611453885197e+243 or -6.976155388654356e-270 < (* a1 a2) < 5.9641687086964e-311

   1. Initial program 24.7

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

   3. Applied times-frac4.7

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

   if -5.411611453885197e+243 < (* a1 a2) < -6.976155388654356e-270 or 5.9641687086964e-311 < (* a1 a2)

   1. Initial program 7.5

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

   3. Applied clear-num7.8

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

   5. Applied associate-/l*8.0

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

   7. Applied associate-/r/7.7

      \[\leadsto \color{blue}{\frac{1}{b1} \cdot \frac{a1 \cdot a2}{b2}}\]
3. Recombined 2 regimes into one program.

4. Final simplification7.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -5.411611453885197 \cdot 10^{+243}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -6.976155388654356 \cdot 10^{-270}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2} \cdot \frac{1}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 5.9641687086964 \cdot 10^{-311}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2} \cdot \frac{1}{b1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019093 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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