\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.8774910265390396 \cdot 10^{-73}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \mathbf{elif}\;b \le 2.5703497435733685 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(a \cdot -4, c, b \cdot b\right)}}{a}}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \end{array}\]

\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}

↓

\begin{array}{l}
\mathbf{if}\;b \le -1.8774910265390396 \cdot 10^{-73}:\\
\;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\

\mathbf{elif}\;b \le 2.5703497435733685 \cdot 10^{+102}:\\
\;\;\;\;\frac{\frac{1}{\frac{1}{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(a \cdot -4, c, b \cdot b\right)}}{a}}}}{2}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\

\end{array}

double f(double a, double b, double c) {
        double r1331801 = b;
        double r1331802 = -r1331801;
        double r1331803 = r1331801 * r1331801;
        double r1331804 = 4.0;
        double r1331805 = a;
        double r1331806 = c;
        double r1331807 = r1331805 * r1331806;
        double r1331808 = r1331804 * r1331807;
        double r1331809 = r1331803 - r1331808;
        double r1331810 = sqrt(r1331809);
        double r1331811 = r1331802 - r1331810;
        double r1331812 = 2.0;
        double r1331813 = r1331812 * r1331805;
        double r1331814 = r1331811 / r1331813;
        return r1331814;
}

↓

double f(double a, double b, double c) {
        double r1331815 = b;
        double r1331816 = -1.8774910265390396e-73;
        bool r1331817 = r1331815 <= r1331816;
        double r1331818 = -2.0;
        double r1331819 = c;
        double r1331820 = r1331819 / r1331815;
        double r1331821 = r1331818 * r1331820;
        double r1331822 = 2.0;
        double r1331823 = r1331821 / r1331822;
        double r1331824 = 2.5703497435733685e+102;
        bool r1331825 = r1331815 <= r1331824;
        double r1331826 = 1.0;
        double r1331827 = -r1331815;
        double r1331828 = a;
        double r1331829 = -4.0;
        double r1331830 = r1331828 * r1331829;
        double r1331831 = r1331815 * r1331815;
        double r1331832 = fma(r1331830, r1331819, r1331831);
        double r1331833 = sqrt(r1331832);
        double r1331834 = r1331827 - r1331833;
        double r1331835 = r1331834 / r1331828;
        double r1331836 = r1331826 / r1331835;
        double r1331837 = r1331826 / r1331836;
        double r1331838 = r1331837 / r1331822;
        double r1331839 = r1331815 / r1331828;
        double r1331840 = r1331820 - r1331839;
        double r1331841 = r1331840 * r1331822;
        double r1331842 = r1331841 / r1331822;
        double r1331843 = r1331825 ? r1331838 : r1331842;
        double r1331844 = r1331817 ? r1331823 : r1331843;
        return r1331844;
}

Original	33.2
Target	20.4
Herbie	9.9

Derivation

Split input into 3 regimes
if b < -1.8774910265390396e-73
1. Initial program 52.5
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified52.5
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}{2}}\]
3. Taylor expanded around -inf 8.6
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
if -1.8774910265390396e-73 < b < 2.5703497435733685e+102
1. Initial program 13.1
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified13.1
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}{2}}\]
3. Using strategy rm
4. Applied clear-num13.2
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}}}}{2}\]
5. Using strategy rm
6. Applied clear-num13.2
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{1}{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}}}}{2}\]
if 2.5703497435733685e+102 < b
1. Initial program 43.9
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified43.9
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}{2}}\]
3. Using strategy rm
4. Applied clear-num43.9
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}}}}{2}\]
5. Using strategy rm
6. Applied clear-num43.9
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{1}{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}}}}{2}\]
7. Taylor expanded around inf 3.0
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
8. Simplified3.0
  \[\leadsto \frac{\color{blue}{2 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}}{2}\]
Recombined 3 regimes into one program.
Final simplification9.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.8774910265390396 \cdot 10^{-73}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \mathbf{elif}\;b \le 2.5703497435733685 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(a \cdot -4, c, b \cdot b\right)}}{a}}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -1.8774910265390396e-73`

`if -1.8774910265390396e-73 < b < 2.5703497435733685e+102`

`if 2.5703497435733685e+102 < b`

Reproduce