- Split input into 4 regimes
if (* (* a1 a2) (/ 1 (* b1 b2))) < -1.4971996319998483e+307
Initial program 56.5
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
- Using strategy
rm Applied times-frac12.5
\[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
if -1.4971996319998483e+307 < (* (* a1 a2) (/ 1 (* b1 b2))) < -4.9406564584125e-324 or 1.8670147877566e-318 < (* (* a1 a2) (/ 1 (* b1 b2))) < 4.667883831678636e+289
Initial program 0.6
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
- Using strategy
rm Applied div-inv0.7
\[\leadsto \color{blue}{\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}}\]
if -4.9406564584125e-324 < (* (* a1 a2) (/ 1 (* b1 b2))) < 1.8670147877566e-318
Initial program 13.5
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
- Using strategy
rm Applied div-inv13.5
\[\leadsto \color{blue}{\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}}\]
- Using strategy
rm Applied log1p-expm1-u13.5
\[\leadsto \color{blue}{\log_* (1 + (e^{\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}} - 1)^*)}\]
Applied simplify2.6
\[\leadsto \log_* (1 + \color{blue}{(e^{\frac{a1}{b2} \cdot \frac{a2}{b1}} - 1)^*})\]
if 4.667883831678636e+289 < (* (* a1 a2) (/ 1 (* b1 b2)))
Initial program 56.8
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
- Using strategy
rm Applied clear-num56.8
\[\leadsto \color{blue}{\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}}\]
- Using strategy
rm Applied div-inv56.8
\[\leadsto \color{blue}{1 \cdot \frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}}\]
Applied simplify5.7
\[\leadsto 1 \cdot \color{blue}{\frac{\frac{a1}{b1}}{\frac{b2}{a2}}}\]
- Recombined 4 regimes into one program.
Applied simplify2.2
\[\leadsto \color{blue}{\begin{array}{l}
\mathbf{if}\;\frac{1}{b2 \cdot b1} \cdot \left(a2 \cdot a1\right) \le -1.4971996319998483 \cdot 10^{+307}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\
\mathbf{if}\;\frac{1}{b2 \cdot b1} \cdot \left(a2 \cdot a1\right) \le -4.9406564584125 \cdot 10^{-324}:\\
\;\;\;\;\frac{1}{b2 \cdot b1} \cdot \left(a2 \cdot a1\right)\\
\mathbf{if}\;\frac{1}{b2 \cdot b1} \cdot \left(a2 \cdot a1\right) \le 1.8670147877566 \cdot 10^{-318}:\\
\;\;\;\;\log_* (1 + (e^{\frac{a2}{b1} \cdot \frac{a1}{b2}} - 1)^*)\\
\mathbf{if}\;\frac{1}{b2 \cdot b1} \cdot \left(a2 \cdot a1\right) \le 4.667883831678636 \cdot 10^{+289}:\\
\;\;\;\;\frac{1}{b2 \cdot b1} \cdot \left(a2 \cdot a1\right)\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\
\end{array}}\]