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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -3.396811349079212 \cdot 10^{+61}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}{a \cdot 2}\\ \mathbf{elif}\;b \le 1.3659668388152999 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{1}{2}}{a} \cdot \left(\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

\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 -3.396811349079212 \cdot 10^{+61}:\\
\;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}{a \cdot 2}\\

\mathbf{elif}\;b \le 1.3659668388152999 \cdot 10^{-67}:\\
\;\;\;\;\frac{\frac{1}{2}}{a} \cdot \left(\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b\right)\\

\mathbf{else}:\\
\;\;\;\;-\frac{c}{b}\\

\end{array}

double f(double a, double b, double c) {
        double r2387897 = b;
        double r2387898 = -r2387897;
        double r2387899 = r2387897 * r2387897;
        double r2387900 = 4.0;
        double r2387901 = a;
        double r2387902 = r2387900 * r2387901;
        double r2387903 = c;
        double r2387904 = r2387902 * r2387903;
        double r2387905 = r2387899 - r2387904;
        double r2387906 = sqrt(r2387905);
        double r2387907 = r2387898 + r2387906;
        double r2387908 = 2.0;
        double r2387909 = r2387908 * r2387901;
        double r2387910 = r2387907 / r2387909;
        return r2387910;
}

↓

double f(double a, double b, double c) {
        double r2387911 = b;
        double r2387912 = -3.396811349079212e+61;
        bool r2387913 = r2387911 <= r2387912;
        double r2387914 = c;
        double r2387915 = a;
        double r2387916 = r2387911 / r2387915;
        double r2387917 = r2387914 / r2387916;
        double r2387918 = r2387917 - r2387911;
        double r2387919 = 2.0;
        double r2387920 = r2387918 * r2387919;
        double r2387921 = r2387915 * r2387919;
        double r2387922 = r2387920 / r2387921;
        double r2387923 = 1.3659668388152999e-67;
        bool r2387924 = r2387911 <= r2387923;
        double r2387925 = 0.5;
        double r2387926 = r2387925 / r2387915;
        double r2387927 = -4.0;
        double r2387928 = r2387927 * r2387915;
        double r2387929 = r2387911 * r2387911;
        double r2387930 = fma(r2387914, r2387928, r2387929);
        double r2387931 = sqrt(r2387930);
        double r2387932 = r2387931 - r2387911;
        double r2387933 = r2387926 * r2387932;
        double r2387934 = r2387914 / r2387911;
        double r2387935 = -r2387934;
        double r2387936 = r2387924 ? r2387933 : r2387935;
        double r2387937 = r2387913 ? r2387922 : r2387936;
        return r2387937;
}

Original	33.6
Target	20.8
Herbie	9.9

Derivation

Split input into 3 regimes
if b < -3.396811349079212e+61
1. Initial program 37.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around -inf 9.6
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}}{2 \cdot a}\]
3. Simplified4.4
  \[\leadsto \frac{\color{blue}{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}}{2 \cdot a}\]
if -3.396811349079212e+61 < b < 1.3659668388152999e-67
1. Initial program 13.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified13.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied *-un-lft-identity13.9
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b}{2}}{\color{blue}{1 \cdot a}}\]
5. Applied div-inv13.9
  \[\leadsto \frac{\color{blue}{\left(\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b\right) \cdot \frac{1}{2}}}{1 \cdot a}\]
6. Applied times-frac14.0
  \[\leadsto \color{blue}{\frac{\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b}{1} \cdot \frac{\frac{1}{2}}{a}}\]
7. Simplified14.0
  \[\leadsto \color{blue}{\left(\sqrt{\mathsf{fma}\left(c, \left(a \cdot -4\right), \left(b \cdot b\right)\right)} - b\right)} \cdot \frac{\frac{1}{2}}{a}\]
8. Simplified14.0
  \[\leadsto \left(\sqrt{\mathsf{fma}\left(c, \left(a \cdot -4\right), \left(b \cdot b\right)\right)} - b\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}}\]
if 1.3659668388152999e-67 < b
1. Initial program 53.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 8.1
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
3. Simplified8.1
  \[\leadsto \color{blue}{-\frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification9.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.396811349079212 \cdot 10^{+61}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}{a \cdot 2}\\ \mathbf{elif}\;b \le 1.3659668388152999 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{1}{2}}{a} \cdot \left(\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Error

Target

Derivation

`if b < -3.396811349079212e+61`

`if -3.396811349079212e+61 < b < 1.3659668388152999e-67`

`if 1.3659668388152999e-67 < b`

Reproduce