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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.53711520045601566154780758665114619261 \cdot 10^{121}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.388070047225937856958905133202240499626 \cdot 10^{-143}:\\ \;\;\;\;\frac{\frac{1}{2}}{a} \cdot \left(\sqrt{{b}^{2} - 4 \cdot \left(a \cdot c\right)} - b\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -1.53711520045601566154780758665114619261 \cdot 10^{121}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 1.388070047225937856958905133202240499626 \cdot 10^{-143}:\\
\;\;\;\;\frac{\frac{1}{2}}{a} \cdot \left(\sqrt{{b}^{2} - 4 \cdot \left(a \cdot c\right)} - b\right)\\

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

\end{array}

double f(double a, double b, double c) {
        double r82331 = b;
        double r82332 = -r82331;
        double r82333 = r82331 * r82331;
        double r82334 = 4.0;
        double r82335 = a;
        double r82336 = c;
        double r82337 = r82335 * r82336;
        double r82338 = r82334 * r82337;
        double r82339 = r82333 - r82338;
        double r82340 = sqrt(r82339);
        double r82341 = r82332 + r82340;
        double r82342 = 2.0;
        double r82343 = r82342 * r82335;
        double r82344 = r82341 / r82343;
        return r82344;
}

↓

double f(double a, double b, double c) {
        double r82345 = b;
        double r82346 = -1.5371152004560157e+121;
        bool r82347 = r82345 <= r82346;
        double r82348 = 1.0;
        double r82349 = c;
        double r82350 = r82349 / r82345;
        double r82351 = a;
        double r82352 = r82345 / r82351;
        double r82353 = r82350 - r82352;
        double r82354 = r82348 * r82353;
        double r82355 = 1.3880700472259379e-143;
        bool r82356 = r82345 <= r82355;
        double r82357 = 1.0;
        double r82358 = 2.0;
        double r82359 = r82357 / r82358;
        double r82360 = r82359 / r82351;
        double r82361 = 2.0;
        double r82362 = pow(r82345, r82361);
        double r82363 = 4.0;
        double r82364 = r82351 * r82349;
        double r82365 = r82363 * r82364;
        double r82366 = r82362 - r82365;
        double r82367 = sqrt(r82366);
        double r82368 = r82367 - r82345;
        double r82369 = r82360 * r82368;
        double r82370 = -1.0;
        double r82371 = r82370 * r82350;
        double r82372 = r82356 ? r82369 : r82371;
        double r82373 = r82347 ? r82354 : r82372;
        return r82373;
}

Original	34.5
Target	21.5
Herbie	11.0

Derivation

Split input into 3 regimes
if b < -1.5371152004560157e+121
1. Initial program 52.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified52.3
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2 \cdot a}}\]
3. Taylor expanded around -inf 2.8
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified2.8
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -1.5371152004560157e+121 < b < 1.3880700472259379e-143
1. Initial program 11.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified11.9
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2 \cdot a}}\]
3. Using strategy rm
4. Applied clear-num12.0
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}}\]
5. Using strategy rm
6. Applied div-inv12.0
  \[\leadsto \frac{1}{\color{blue}{\left(2 \cdot a\right) \cdot \frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}}\]
7. Applied add-cube-cbrt12.0
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(2 \cdot a\right) \cdot \frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}\]
8. Applied times-frac12.0
  \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{2 \cdot a} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}}\]
9. Simplified12.0
  \[\leadsto \color{blue}{\frac{\frac{1}{2}}{a}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}\]
10. Simplified12.0
  \[\leadsto \frac{\frac{1}{2}}{a} \cdot \color{blue}{\left(\sqrt{{b}^{2} - 4 \cdot \left(a \cdot c\right)} - b\right)}\]
if 1.3880700472259379e-143 < b
1. Initial program 50.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified50.3
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2 \cdot a}}\]
3. Taylor expanded around inf 12.6
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification11.0
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.53711520045601566154780758665114619261 \cdot 10^{121}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.388070047225937856958905133202240499626 \cdot 10^{-143}:\\ \;\;\;\;\frac{\frac{1}{2}}{a} \cdot \left(\sqrt{{b}^{2} - 4 \cdot \left(a \cdot c\right)} - b\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Target

Derivation

`if b < -1.5371152004560157e+121`

`if -1.5371152004560157e+121 < b < 1.3880700472259379e-143`

`if 1.3880700472259379e-143 < b`

Reproduce

In
Out