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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.297624534318876743725099723501638614139 \cdot 10^{152}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 7.752932492055353784538521387722087830871 \cdot 10^{-90}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{elif}\;b \le 683389336.59924924373626708984375:\\ \;\;\;\;\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -2.297624534318876743725099723501638614139 \cdot 10^{152}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 7.752932492055353784538521387722087830871 \cdot 10^{-90}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\

\mathbf{elif}\;b \le 683389336.59924924373626708984375:\\
\;\;\;\;\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r110168 = b;
        double r110169 = -r110168;
        double r110170 = r110168 * r110168;
        double r110171 = 4.0;
        double r110172 = a;
        double r110173 = r110171 * r110172;
        double r110174 = c;
        double r110175 = r110173 * r110174;
        double r110176 = r110170 - r110175;
        double r110177 = sqrt(r110176);
        double r110178 = r110169 + r110177;
        double r110179 = 2.0;
        double r110180 = r110179 * r110172;
        double r110181 = r110178 / r110180;
        return r110181;
}

↓

double f(double a, double b, double c) {
        double r110182 = b;
        double r110183 = -2.2976245343188767e+152;
        bool r110184 = r110182 <= r110183;
        double r110185 = 1.0;
        double r110186 = c;
        double r110187 = r110186 / r110182;
        double r110188 = a;
        double r110189 = r110182 / r110188;
        double r110190 = r110187 - r110189;
        double r110191 = r110185 * r110190;
        double r110192 = 7.752932492055354e-90;
        bool r110193 = r110182 <= r110192;
        double r110194 = -r110182;
        double r110195 = r110182 * r110182;
        double r110196 = 4.0;
        double r110197 = r110196 * r110188;
        double r110198 = r110197 * r110186;
        double r110199 = r110195 - r110198;
        double r110200 = sqrt(r110199);
        double r110201 = r110194 + r110200;
        double r110202 = 2.0;
        double r110203 = r110202 * r110188;
        double r110204 = r110201 / r110203;
        double r110205 = 683389336.5992492;
        bool r110206 = r110182 <= r110205;
        double r110207 = r110194 - r110200;
        double r110208 = r110198 / r110207;
        double r110209 = r110208 / r110203;
        double r110210 = -1.0;
        double r110211 = r110210 * r110187;
        double r110212 = r110206 ? r110209 : r110211;
        double r110213 = r110193 ? r110204 : r110212;
        double r110214 = r110184 ? r110191 : r110213;
        return r110214;
}

Original	34.4
Target	21.4
Herbie	9.1

Derivation

Split input into 4 regimes
if b < -2.2976245343188767e+152
1. Initial program 63.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around -inf 2.2
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified2.2
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -2.2976245343188767e+152 < b < 7.752932492055354e-90
1. Initial program 11.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
if 7.752932492055354e-90 < b < 683389336.5992492
1. Initial program 39.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied flip-+40.0
  \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
4. Simplified18.6
  \[\leadsto \frac{\frac{\color{blue}{0 + \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
if 683389336.5992492 < b
1. Initial program 56.1
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 5.1
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 4 regimes into one program.
Final simplification9.1
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.297624534318876743725099723501638614139 \cdot 10^{152}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 7.752932492055353784538521387722087830871 \cdot 10^{-90}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{elif}\;b \le 683389336.59924924373626708984375:\\ \;\;\;\;\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -2.2976245343188767e+152`

`if -2.2976245343188767e+152 < b < 7.752932492055354e-90`

`if 7.752932492055354e-90 < b < 683389336.5992492`

`if 683389336.5992492 < b`

Reproduce

In
Out