\[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.9387509550435187 \cdot 10^{+182}:\\ \;\;\;\;\frac{(e^{\left(a + b\right) \cdot \varepsilon} - 1)^*}{(e^{\varepsilon \cdot b} - 1)^*} \cdot (\left((\frac{1}{12} \cdot \left(a \cdot \varepsilon\right) + \frac{-1}{2})_*\right) \cdot \varepsilon + \left(\frac{1}{a}\right))_*\\ \mathbf{elif}\;b \le -1.1286820244896261 \cdot 10^{+57}:\\ \;\;\;\;\frac{\frac{\varepsilon}{(e^{a \cdot \varepsilon} - 1)^*} \cdot (e^{\left(a + b\right) \cdot \varepsilon} - 1)^*}{(e^{\varepsilon \cdot b} - 1)^*}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{b} + \frac{1}{a}\\ \end{array}\]

Original	58.6
Target	14.2
Herbie	4.4

Derivation

Split input into 3 regimes
if b < -1.9387509550435187e+182
1. Initial program 49.7
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Initial simplification16.3
  \[\leadsto \frac{(e^{\left(a + b\right) \cdot \varepsilon} - 1)^*}{(e^{\varepsilon \cdot b} - 1)^*} \cdot \frac{\varepsilon}{(e^{\varepsilon \cdot a} - 1)^*}\]
3. Taylor expanded around 0 12.8
  \[\leadsto \frac{(e^{\left(a + b\right) \cdot \varepsilon} - 1)^*}{(e^{\varepsilon \cdot b} - 1)^*} \cdot \color{blue}{\left(\left(\frac{1}{a} + \frac{1}{12} \cdot \left(a \cdot {\varepsilon}^{2}\right)\right) - \frac{1}{2} \cdot \varepsilon\right)}\]
4. Simplified12.9
  \[\leadsto \frac{(e^{\left(a + b\right) \cdot \varepsilon} - 1)^*}{(e^{\varepsilon \cdot b} - 1)^*} \cdot \color{blue}{(\left((\frac{1}{12} \cdot \left(a \cdot \varepsilon\right) + \frac{-1}{2})_*\right) \cdot \varepsilon + \left(\frac{1}{a}\right))_*}\]
if -1.9387509550435187e+182 < b < -1.1286820244896261e+57
1. Initial program 54.9
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Initial simplification17.3
  \[\leadsto \frac{(e^{\left(a + b\right) \cdot \varepsilon} - 1)^*}{(e^{\varepsilon \cdot b} - 1)^*} \cdot \frac{\varepsilon}{(e^{\varepsilon \cdot a} - 1)^*}\]
3. Using strategy rm
4. Applied associate-*l/17.3
  \[\leadsto \color{blue}{\frac{(e^{\left(a + b\right) \cdot \varepsilon} - 1)^* \cdot \frac{\varepsilon}{(e^{\varepsilon \cdot a} - 1)^*}}{(e^{\varepsilon \cdot b} - 1)^*}}\]
if -1.1286820244896261e+57 < b
1. Initial program 60.0
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Initial simplification29.1
  \[\leadsto \frac{(e^{\left(a + b\right) \cdot \varepsilon} - 1)^*}{(e^{\varepsilon \cdot b} - 1)^*} \cdot \frac{\varepsilon}{(e^{\varepsilon \cdot a} - 1)^*}\]
3. Taylor expanded around 0 2.0
  \[\leadsto \color{blue}{\frac{1}{a} + \frac{1}{b}}\]
Recombined 3 regimes into one program.
Final simplification4.4
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.9387509550435187 \cdot 10^{+182}:\\ \;\;\;\;\frac{(e^{\left(a + b\right) \cdot \varepsilon} - 1)^*}{(e^{\varepsilon \cdot b} - 1)^*} \cdot (\left((\frac{1}{12} \cdot \left(a \cdot \varepsilon\right) + \frac{-1}{2})_*\right) \cdot \varepsilon + \left(\frac{1}{a}\right))_*\\ \mathbf{elif}\;b \le -1.1286820244896261 \cdot 10^{+57}:\\ \;\;\;\;\frac{\frac{\varepsilon}{(e^{a \cdot \varepsilon} - 1)^*} \cdot (e^{\left(a + b\right) \cdot \varepsilon} - 1)^*}{(e^{\varepsilon \cdot b} - 1)^*}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{b} + \frac{1}{a}\\ \end{array}\]

Error

Target

Derivation

`if b < -1.9387509550435187e+182`

`if -1.9387509550435187e+182 < b < -1.1286820244896261e+57`

`if -1.1286820244896261e+57 < b`

Runtime