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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{1}{a} + \frac{1}{b} \le -2.5982032350689694 \cdot 10^{-18} \lor \neg \left(\frac{1}{a} + \frac{1}{b} \le 6.537931662863092 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{1}{a} + \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{(e^{\varepsilon \cdot \left(a + b\right)} - 1)^*}{(e^{(b \cdot \left(\varepsilon + \varepsilon\right) + \left(\varepsilon \cdot b\right))_*} - 1)^* \cdot \frac{(e^{a \cdot \varepsilon} - 1)^*}{\varepsilon}} \cdot \left(\left(e^{\varepsilon \cdot b} + 1\right) + e^{\varepsilon \cdot b} \cdot e^{\varepsilon \cdot b}\right)\\ \end{array}\]

Original	58.7
Target	14.7
Herbie	1.1

Derivation

Split input into 2 regimes
if (+ (/ 1 b) (/ 1 a)) < -2.5982032350689694e-18 or 6.537931662863092e-55 < (+ (/ 1 b) (/ 1 a))
1. Initial program 61.9
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Taylor expanded around 0 0.2
  \[\leadsto \color{blue}{\frac{1}{b} + \frac{1}{a}}\]
if -2.5982032350689694e-18 < (+ (/ 1 b) (/ 1 a)) < 6.537931662863092e-55
1. Initial program 42.8
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Using strategy rm
3. Applied flip3--46.9
  \[\leadsto \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \color{blue}{\frac{{\left(e^{b \cdot \varepsilon}\right)}^{3} - {1}^{3}}{e^{b \cdot \varepsilon} \cdot e^{b \cdot \varepsilon} + \left(1 \cdot 1 + e^{b \cdot \varepsilon} \cdot 1\right)}}}\]
4. Applied associate-*r/46.9
  \[\leadsto \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\color{blue}{\frac{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left({\left(e^{b \cdot \varepsilon}\right)}^{3} - {1}^{3}\right)}{e^{b \cdot \varepsilon} \cdot e^{b \cdot \varepsilon} + \left(1 \cdot 1 + e^{b \cdot \varepsilon} \cdot 1\right)}}}\]
5. Applied associate-/r/46.9
  \[\leadsto \color{blue}{\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left({\left(e^{b \cdot \varepsilon}\right)}^{3} - {1}^{3}\right)} \cdot \left(e^{b \cdot \varepsilon} \cdot e^{b \cdot \varepsilon} + \left(1 \cdot 1 + e^{b \cdot \varepsilon} \cdot 1\right)\right)}\]
6. Applied simplify5.6
  \[\leadsto \color{blue}{\frac{(e^{\left(a + b\right) \cdot \varepsilon} - 1)^*}{(e^{(b \cdot \left(\varepsilon + \varepsilon\right) + \left(\varepsilon \cdot b\right))_*} - 1)^* \cdot \frac{(e^{a \cdot \varepsilon} - 1)^*}{\varepsilon}}} \cdot \left(e^{b \cdot \varepsilon} \cdot e^{b \cdot \varepsilon} + \left(1 \cdot 1 + e^{b \cdot \varepsilon} \cdot 1\right)\right)\]
Recombined 2 regimes into one program.
Applied simplify1.1
\[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{1}{a} + \frac{1}{b} \le -2.5982032350689694 \cdot 10^{-18} \lor \neg \left(\frac{1}{a} + \frac{1}{b} \le 6.537931662863092 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{1}{a} + \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{(e^{\varepsilon \cdot \left(a + b\right)} - 1)^*}{(e^{(b \cdot \left(\varepsilon + \varepsilon\right) + \left(\varepsilon \cdot b\right))_*} - 1)^* \cdot \frac{(e^{a \cdot \varepsilon} - 1)^*}{\varepsilon}} \cdot \left(\left(e^{\varepsilon \cdot b} + 1\right) + e^{\varepsilon \cdot b} \cdot e^{\varepsilon \cdot b}\right)\\ \end{array}}\]

Error

Target

Derivation

`if (+ (/ 1 b) (/ 1 a)) < -2.5982032350689694e-18 or 6.537931662863092e-55 < (+ (/ 1 b) (/ 1 a))`

`if -2.5982032350689694e-18 < (+ (/ 1 b) (/ 1 a)) < 6.537931662863092e-55`

Runtime