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

↓

\[\begin{array}{l} \mathbf{if}\;a2 \le -3.0479637035265785 \cdot 10^{+207}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;a2 \le -7.20153105055616 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{a1}{b1 \cdot b2}}{\frac{1}{a2}}\\ \mathbf{if}\;a2 \le -1.5416890105866388 \cdot 10^{-97}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\ \mathbf{if}\;a2 \le -2.1538731346239785 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{if}\;a2 \le 5.701154346137465 \cdot 10^{-243}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;a2 \le 7.219968817692392 \cdot 10^{-103}:\\ \;\;\;\;\left(a1 \cdot \frac{1}{b1 \cdot b2}\right) \cdot a2\\ \mathbf{if}\;a2 \le 1.7037602706608895 \cdot 10^{+94}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;a2 \le 3.2705679617905636 \cdot 10^{+171}:\\ \;\;\;\;\frac{\frac{a1}{b1 \cdot b2}}{\frac{1}{a2}}\\ \mathbf{if}\;a2 \le 9.309401273607693 \cdot 10^{+249}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b1 \cdot b2}}{\frac{1}{a2}}\\ \end{array}\]

Original	10.9
Target	11.4
Herbie	11.0

Derivation

Split input into 6 regimes
if a2 < -3.0479637035265785e+207 or -2.1538731346239785e-256 < a2 < 5.701154346137465e-243
1. Initial program 14.0
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac14.4
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
if -3.0479637035265785e+207 < a2 < -7.20153105055616e+66 or 1.7037602706608895e+94 < a2 < 3.2705679617905636e+171 or 9.309401273607693e+249 < a2
1. Initial program 13.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*13.6
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied div-inv13.7
  \[\leadsto \frac{a1}{\color{blue}{\left(b1 \cdot b2\right) \cdot \frac{1}{a2}}}\]
6. Applied associate-/r*12.9
  \[\leadsto \color{blue}{\frac{\frac{a1}{b1 \cdot b2}}{\frac{1}{a2}}}\]
if -7.20153105055616e+66 < a2 < -1.5416890105866388e-97
1. Initial program 7.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*7.5
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied div-inv7.7
  \[\leadsto \color{blue}{a1 \cdot \frac{1}{\frac{b1 \cdot b2}{a2}}}\]
6. Applied simplify8.1
  \[\leadsto a1 \cdot \color{blue}{\frac{\frac{a2}{b1}}{b2}}\]
if -1.5416890105866388e-97 < a2 < -2.1538731346239785e-256
1. Initial program 9.6
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*9.4
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
if 5.701154346137465e-243 < a2 < 7.219968817692392e-103
1. Initial program 9.7
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*9.1
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied associate-/r/10.1
  \[\leadsto \color{blue}{\frac{a1}{b1 \cdot b2} \cdot a2}\]
6. Using strategy rm
7. Applied div-inv10.2
  \[\leadsto \color{blue}{\left(a1 \cdot \frac{1}{b1 \cdot b2}\right)} \cdot a2\]
if 7.219968817692392e-103 < a2 < 1.7037602706608895e+94 or 3.2705679617905636e+171 < a2 < 9.309401273607693e+249
1. Initial program 9.3
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac10.0
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
Recombined 6 regimes into one program.
Removed slow pow expressions.

Error

Target

Derivation

`if a2 < -3.0479637035265785e+207 or -2.1538731346239785e-256 < a2 < 5.701154346137465e-243`

`if -3.0479637035265785e+207 < a2 < -7.20153105055616e+66 or 1.7037602706608895e+94 < a2 < 3.2705679617905636e+171 or 9.309401273607693e+249 < a2`

`if -7.20153105055616e+66 < a2 < -1.5416890105866388e-97`

`if -1.5416890105866388e-97 < a2 < -2.1538731346239785e-256`

`if 5.701154346137465e-243 < a2 < 7.219968817692392e-103`

`if 7.219968817692392e-103 < a2 < 1.7037602706608895e+94 or 3.2705679617905636e+171 < a2 < 9.309401273607693e+249`

Runtime