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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\ \;\;\;\;\frac{\frac{1}{\frac{-1}{b}}}{a}\\ \mathbf{elif}\;b \le 5.860223638943180333955717619400031865396 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{b}{c \cdot a} \cdot 1}}{a}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b \le -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\
\;\;\;\;\frac{\frac{1}{\frac{-1}{b}}}{a}\\

\mathbf{elif}\;b \le 5.860223638943180333955717619400031865396 \cdot 10^{-17}:\\
\;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}{a}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{b}{c \cdot a} \cdot 1}}{a}\\

\end{array}

double f(double a, double b, double c) {
        double r5410822 = b;
        double r5410823 = -r5410822;
        double r5410824 = r5410822 * r5410822;
        double r5410825 = 4.0;
        double r5410826 = a;
        double r5410827 = r5410825 * r5410826;
        double r5410828 = c;
        double r5410829 = r5410827 * r5410828;
        double r5410830 = r5410824 - r5410829;
        double r5410831 = sqrt(r5410830);
        double r5410832 = r5410823 + r5410831;
        double r5410833 = 2.0;
        double r5410834 = r5410833 * r5410826;
        double r5410835 = r5410832 / r5410834;
        return r5410835;
}

↓

double f(double a, double b, double c) {
        double r5410836 = b;
        double r5410837 = -1.7633154797394035e+89;
        bool r5410838 = r5410836 <= r5410837;
        double r5410839 = 1.0;
        double r5410840 = -1.0;
        double r5410841 = r5410840 / r5410836;
        double r5410842 = r5410839 / r5410841;
        double r5410843 = a;
        double r5410844 = r5410842 / r5410843;
        double r5410845 = 5.86022363894318e-17;
        bool r5410846 = r5410836 <= r5410845;
        double r5410847 = 2.0;
        double r5410848 = r5410836 * r5410836;
        double r5410849 = 4.0;
        double r5410850 = c;
        double r5410851 = r5410850 * r5410843;
        double r5410852 = r5410849 * r5410851;
        double r5410853 = r5410848 - r5410852;
        double r5410854 = sqrt(r5410853);
        double r5410855 = r5410854 - r5410836;
        double r5410856 = r5410847 / r5410855;
        double r5410857 = r5410839 / r5410856;
        double r5410858 = r5410857 / r5410843;
        double r5410859 = 1.0;
        double r5410860 = r5410859 / r5410836;
        double r5410861 = r5410836 / r5410851;
        double r5410862 = r5410861 * r5410859;
        double r5410863 = r5410860 - r5410862;
        double r5410864 = r5410839 / r5410863;
        double r5410865 = r5410864 / r5410843;
        double r5410866 = r5410846 ? r5410858 : r5410865;
        double r5410867 = r5410838 ? r5410844 : r5410866;
        return r5410867;
}

Original	34.4
Target	21.3
Herbie	14.2

Derivation

Split input into 3 regimes
if b < -1.7633154797394035e+89
1. Initial program 45.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified45.7
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num45.8
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}}{a}\]
5. Taylor expanded around -inf 4.2
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{-1}{b}}}}{a}\]
if -1.7633154797394035e+89 < b < 5.86022363894318e-17
1. Initial program 15.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified15.4
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num15.4
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}}{a}\]
if 5.86022363894318e-17 < b
1. Initial program 55.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified55.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num55.6
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}}{a}\]
5. Taylor expanded around inf 17.3
  \[\leadsto \frac{\frac{1}{\color{blue}{1 \cdot \frac{1}{b} - 1 \cdot \frac{b}{a \cdot c}}}}{a}\]
6. Simplified17.3
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{1}{b} - 1 \cdot \frac{b}{c \cdot a}}}}{a}\]
Recombined 3 regimes into one program.
Final simplification14.2
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\ \;\;\;\;\frac{\frac{1}{\frac{-1}{b}}}{a}\\ \mathbf{elif}\;b \le 5.860223638943180333955717619400031865396 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{b}{c \cdot a} \cdot 1}}{a}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.7633154797394035e+89`

`if -1.7633154797394035e+89 < b < 5.86022363894318e-17`

`if 5.86022363894318e-17 < b`

Reproduce

In
Out