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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.0697892322852844 \cdot 10^{57}:\\ \;\;\;\;\frac{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}{2 \cdot a}\\ \mathbf{elif}\;b \le 5.08229739317807349 \cdot 10^{-29}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt[3]{b} \cdot \sqrt[3]{b}, -\sqrt[3]{b}, \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{a \cdot c}{b}}{2 \cdot a}\\ \end{array}\]

\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 -2.0697892322852844 \cdot 10^{57}:\\
\;\;\;\;\frac{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}{2 \cdot a}\\

\mathbf{elif}\;b \le 5.08229739317807349 \cdot 10^{-29}:\\
\;\;\;\;\frac{\mathsf{fma}\left(\sqrt[3]{b} \cdot \sqrt[3]{b}, -\sqrt[3]{b}, \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)}{2 \cdot a}\\

\mathbf{else}:\\
\;\;\;\;\frac{-2 \cdot \frac{a \cdot c}{b}}{2 \cdot a}\\

\end{array}

double f(double a, double b, double c) {
        double r101309 = b;
        double r101310 = -r101309;
        double r101311 = r101309 * r101309;
        double r101312 = 4.0;
        double r101313 = a;
        double r101314 = r101312 * r101313;
        double r101315 = c;
        double r101316 = r101314 * r101315;
        double r101317 = r101311 - r101316;
        double r101318 = sqrt(r101317);
        double r101319 = r101310 + r101318;
        double r101320 = 2.0;
        double r101321 = r101320 * r101313;
        double r101322 = r101319 / r101321;
        return r101322;
}

↓

double f(double a, double b, double c) {
        double r101323 = b;
        double r101324 = -2.0697892322852844e+57;
        bool r101325 = r101323 <= r101324;
        double r101326 = 2.0;
        double r101327 = a;
        double r101328 = c;
        double r101329 = r101327 * r101328;
        double r101330 = r101329 / r101323;
        double r101331 = r101326 * r101330;
        double r101332 = 2.0;
        double r101333 = r101332 * r101323;
        double r101334 = r101331 - r101333;
        double r101335 = r101326 * r101327;
        double r101336 = r101334 / r101335;
        double r101337 = 5.082297393178073e-29;
        bool r101338 = r101323 <= r101337;
        double r101339 = cbrt(r101323);
        double r101340 = r101339 * r101339;
        double r101341 = -r101339;
        double r101342 = r101323 * r101323;
        double r101343 = 4.0;
        double r101344 = r101343 * r101327;
        double r101345 = r101344 * r101328;
        double r101346 = r101342 - r101345;
        double r101347 = sqrt(r101346);
        double r101348 = fma(r101340, r101341, r101347);
        double r101349 = r101348 / r101335;
        double r101350 = -2.0;
        double r101351 = r101350 * r101330;
        double r101352 = r101351 / r101335;
        double r101353 = r101338 ? r101349 : r101352;
        double r101354 = r101325 ? r101336 : r101353;
        return r101354;
}

Original	34.2
Target	21.1
Herbie	15.4

Derivation

Split input into 3 regimes
if b < -2.0697892322852844e+57
1. Initial program 39.1
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied add-cube-cbrt39.2
  \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot \color{blue}{\left(\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \sqrt[3]{c}\right)}}}{2 \cdot a}\]
4. Applied associate-*r*39.2
  \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \color{blue}{\left(\left(4 \cdot a\right) \cdot \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right)\right) \cdot \sqrt[3]{c}}}}{2 \cdot a}\]
5. Using strategy rm
6. Applied add-cube-cbrt39.2
  \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(\left(4 \cdot a\right) \cdot \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right)\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)}}}{2 \cdot a}\]
7. Taylor expanded around -inf 10.0
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}}{2 \cdot a}\]
if -2.0697892322852844e+57 < b < 5.082297393178073e-29
1. Initial program 16.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied add-cube-cbrt16.2
  \[\leadsto \frac{\left(-\color{blue}{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}}\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
4. Applied distribute-rgt-neg-in16.2
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(-\sqrt[3]{b}\right)} + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
5. Applied fma-def16.2
  \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt[3]{b} \cdot \sqrt[3]{b}, -\sqrt[3]{b}, \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)}}{2 \cdot a}\]
if 5.082297393178073e-29 < b
1. Initial program 54.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 17.5
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{a \cdot c}{b}}}{2 \cdot a}\]
Recombined 3 regimes into one program.
Final simplification15.4
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.0697892322852844 \cdot 10^{57}:\\ \;\;\;\;\frac{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}{2 \cdot a}\\ \mathbf{elif}\;b \le 5.08229739317807349 \cdot 10^{-29}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt[3]{b} \cdot \sqrt[3]{b}, -\sqrt[3]{b}, \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{a \cdot c}{b}}{2 \cdot a}\\ \end{array}\]

Error

Target

Derivation

`if b < -2.0697892322852844e+57`

`if -2.0697892322852844e+57 < b < 5.082297393178073e-29`

`if 5.082297393178073e-29 < b`

Reproduce