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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -3.56950087216670373 \cdot 10^{75}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.4951704352063921 \cdot 10^{-301}:\\ \;\;\;\;\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}\\ \mathbf{elif}\;b \le 2.12540180880083329 \cdot 10^{133}:\\ \;\;\;\;\frac{\frac{\left(c \cdot 4\right) \cdot a}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -3.56950087216670373 \cdot 10^{75}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 1.4951704352063921 \cdot 10^{-301}:\\
\;\;\;\;\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}\\

\mathbf{elif}\;b \le 2.12540180880083329 \cdot 10^{133}:\\
\;\;\;\;\frac{\frac{\left(c \cdot 4\right) \cdot a}{\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 r90310 = b;
        double r90311 = -r90310;
        double r90312 = r90310 * r90310;
        double r90313 = 4.0;
        double r90314 = a;
        double r90315 = r90313 * r90314;
        double r90316 = c;
        double r90317 = r90315 * r90316;
        double r90318 = r90312 - r90317;
        double r90319 = sqrt(r90318);
        double r90320 = r90311 + r90319;
        double r90321 = 2.0;
        double r90322 = r90321 * r90314;
        double r90323 = r90320 / r90322;
        return r90323;
}

↓

double f(double a, double b, double c) {
        double r90324 = b;
        double r90325 = -3.5695008721667037e+75;
        bool r90326 = r90324 <= r90325;
        double r90327 = 1.0;
        double r90328 = c;
        double r90329 = r90328 / r90324;
        double r90330 = a;
        double r90331 = r90324 / r90330;
        double r90332 = r90329 - r90331;
        double r90333 = r90327 * r90332;
        double r90334 = 1.495170435206392e-301;
        bool r90335 = r90324 <= r90334;
        double r90336 = 1.0;
        double r90337 = 2.0;
        double r90338 = r90337 * r90330;
        double r90339 = r90324 * r90324;
        double r90340 = 4.0;
        double r90341 = r90340 * r90330;
        double r90342 = r90341 * r90328;
        double r90343 = r90339 - r90342;
        double r90344 = sqrt(r90343);
        double r90345 = r90344 - r90324;
        double r90346 = r90338 / r90345;
        double r90347 = r90336 / r90346;
        double r90348 = 2.1254018088008333e+133;
        bool r90349 = r90324 <= r90348;
        double r90350 = r90328 * r90340;
        double r90351 = r90350 * r90330;
        double r90352 = -r90324;
        double r90353 = r90352 - r90344;
        double r90354 = r90351 / r90353;
        double r90355 = r90354 / r90338;
        double r90356 = -1.0;
        double r90357 = r90356 * r90329;
        double r90358 = r90349 ? r90355 : r90357;
        double r90359 = r90335 ? r90347 : r90358;
        double r90360 = r90326 ? r90333 : r90359;
        return r90360;
}

Original	33.8
Target	21.2
Herbie	9.4

Derivation

Split input into 4 regimes
if b < -3.5695008721667037e+75
1. Initial program 42.1
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around -inf 4.0
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified4.0
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -3.5695008721667037e+75 < b < 1.495170435206392e-301
1. Initial program 9.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied clear-num9.6
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}\]
4. Simplified9.6
  \[\leadsto \frac{1}{\color{blue}{\frac{2 \cdot a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}}\]
if 1.495170435206392e-301 < b < 2.1254018088008333e+133
1. Initial program 33.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied flip-+33.6
  \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
4. Simplified16.6
  \[\leadsto \frac{\frac{\color{blue}{0 + \left(c \cdot 4\right) \cdot a}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
if 2.1254018088008333e+133 < b
1. Initial program 61.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 1.7
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 4 regimes into one program.
Final simplification9.4
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.56950087216670373 \cdot 10^{75}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.4951704352063921 \cdot 10^{-301}:\\ \;\;\;\;\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}\\ \mathbf{elif}\;b \le 2.12540180880083329 \cdot 10^{133}:\\ \;\;\;\;\frac{\frac{\left(c \cdot 4\right) \cdot a}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -3.5695008721667037e+75`

`if -3.5695008721667037e+75 < b < 1.495170435206392e-301`

`if 1.495170435206392e-301 < b < 2.1254018088008333e+133`

`if 2.1254018088008333e+133 < b`

Reproduce

In
Out