\[-1 \lt \varepsilon \land \varepsilon \lt 1\]

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

↓

\[\begin{array}{l} \mathbf{if}\;a \le 1.1199581729972231 \cdot 10^{+123}:\\ \;\;\;\;\frac{1}{b} + \frac{1}{a}\\ \mathbf{elif}\;a \le 2.335242954070617 \cdot 10^{+248}:\\ \;\;\;\;\frac{1}{\frac{\frac{\mathsf{expm1}\left(a \cdot \varepsilon\right)}{\varepsilon}}{\frac{\mathsf{expm1}\left(\mathsf{fma}\left(\varepsilon, b, a \cdot \varepsilon\right)\right)}{\mathsf{expm1}\left(b \cdot \varepsilon\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{b} + \frac{1}{a}\\ \end{array}\]

\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}\;a \le 1.1199581729972231 \cdot 10^{+123}:\\
\;\;\;\;\frac{1}{b} + \frac{1}{a}\\

\mathbf{elif}\;a \le 2.335242954070617 \cdot 10^{+248}:\\
\;\;\;\;\frac{1}{\frac{\frac{\mathsf{expm1}\left(a \cdot \varepsilon\right)}{\varepsilon}}{\frac{\mathsf{expm1}\left(\mathsf{fma}\left(\varepsilon, b, a \cdot \varepsilon\right)\right)}{\mathsf{expm1}\left(b \cdot \varepsilon\right)}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{b} + \frac{1}{a}\\

\end{array}

double f(double a, double b, double eps) {
        double r3631814 = eps;
        double r3631815 = a;
        double r3631816 = b;
        double r3631817 = r3631815 + r3631816;
        double r3631818 = r3631817 * r3631814;
        double r3631819 = exp(r3631818);
        double r3631820 = 1.0;
        double r3631821 = r3631819 - r3631820;
        double r3631822 = r3631814 * r3631821;
        double r3631823 = r3631815 * r3631814;
        double r3631824 = exp(r3631823);
        double r3631825 = r3631824 - r3631820;
        double r3631826 = r3631816 * r3631814;
        double r3631827 = exp(r3631826);
        double r3631828 = r3631827 - r3631820;
        double r3631829 = r3631825 * r3631828;
        double r3631830 = r3631822 / r3631829;
        return r3631830;
}

↓

double f(double a, double b, double eps) {
        double r3631831 = a;
        double r3631832 = 1.1199581729972231e+123;
        bool r3631833 = r3631831 <= r3631832;
        double r3631834 = 1.0;
        double r3631835 = b;
        double r3631836 = r3631834 / r3631835;
        double r3631837 = r3631834 / r3631831;
        double r3631838 = r3631836 + r3631837;
        double r3631839 = 2.335242954070617e+248;
        bool r3631840 = r3631831 <= r3631839;
        double r3631841 = eps;
        double r3631842 = r3631831 * r3631841;
        double r3631843 = expm1(r3631842);
        double r3631844 = r3631843 / r3631841;
        double r3631845 = fma(r3631841, r3631835, r3631842);
        double r3631846 = expm1(r3631845);
        double r3631847 = r3631835 * r3631841;
        double r3631848 = expm1(r3631847);
        double r3631849 = r3631846 / r3631848;
        double r3631850 = r3631844 / r3631849;
        double r3631851 = r3631834 / r3631850;
        double r3631852 = r3631840 ? r3631851 : r3631838;
        double r3631853 = r3631833 ? r3631838 : r3631852;
        return r3631853;
}

Original	58.8
Target	14.2
Herbie	3.9

Derivation

Split input into 2 regimes
if a < 1.1199581729972231e+123 or 2.335242954070617e+248 < a
1. Initial program 59.2
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Simplified27.8
  \[\leadsto \color{blue}{\frac{\frac{\varepsilon}{\mathsf{expm1}\left(\varepsilon \cdot b\right)} \cdot \mathsf{expm1}\left(\left(a + b\right) \cdot \varepsilon\right)}{\mathsf{expm1}\left(\varepsilon \cdot a\right)}}\]
3. Taylor expanded around 0 2.7
  \[\leadsto \color{blue}{\frac{1}{b} + \frac{1}{a}}\]
if 1.1199581729972231e+123 < a < 2.335242954070617e+248
1. Initial program 53.6
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Simplified16.1
  \[\leadsto \color{blue}{\frac{\frac{\varepsilon}{\mathsf{expm1}\left(\varepsilon \cdot b\right)} \cdot \mathsf{expm1}\left(\left(a + b\right) \cdot \varepsilon\right)}{\mathsf{expm1}\left(\varepsilon \cdot a\right)}}\]
3. Using strategy rm
4. Applied clear-num16.1
  \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{expm1}\left(\varepsilon \cdot a\right)}{\frac{\varepsilon}{\mathsf{expm1}\left(\varepsilon \cdot b\right)} \cdot \mathsf{expm1}\left(\left(a + b\right) \cdot \varepsilon\right)}}}\]
5. Simplified16.8
  \[\leadsto \frac{1}{\color{blue}{\frac{\frac{\mathsf{expm1}\left(a \cdot \varepsilon\right)}{\varepsilon}}{\frac{\mathsf{expm1}\left(\mathsf{fma}\left(\varepsilon, b, a \cdot \varepsilon\right)\right)}{\mathsf{expm1}\left(\varepsilon \cdot b\right)}}}}\]
Recombined 2 regimes into one program.
Final simplification3.9
\[\leadsto \begin{array}{l} \mathbf{if}\;a \le 1.1199581729972231 \cdot 10^{+123}:\\ \;\;\;\;\frac{1}{b} + \frac{1}{a}\\ \mathbf{elif}\;a \le 2.335242954070617 \cdot 10^{+248}:\\ \;\;\;\;\frac{1}{\frac{\frac{\mathsf{expm1}\left(a \cdot \varepsilon\right)}{\varepsilon}}{\frac{\mathsf{expm1}\left(\mathsf{fma}\left(\varepsilon, b, a \cdot \varepsilon\right)\right)}{\mathsf{expm1}\left(b \cdot \varepsilon\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{b} + \frac{1}{a}\\ \end{array}\]

could not determine a ground truth for program body (more)

Error

Target

Derivation

`if a < 1.1199581729972231e+123 or 2.335242954070617e+248 < a`

`if 1.1199581729972231e+123 < a < 2.335242954070617e+248`

Reproduce