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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -4.12310353364421125 \cdot 10^{95}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 3.446447862996811 \cdot 10^{-75}:\\ \;\;\;\;\left(\sqrt{\mathsf{fma}\left(b, b, -\left(a \cdot c\right) \cdot 4\right)} - b\right) \cdot \frac{\frac{1}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -4.12310353364421125 \cdot 10^{95}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 3.446447862996811 \cdot 10^{-75}:\\
\;\;\;\;\left(\sqrt{\mathsf{fma}\left(b, b, -\left(a \cdot c\right) \cdot 4\right)} - b\right) \cdot \frac{\frac{1}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r96331 = b;
        double r96332 = -r96331;
        double r96333 = r96331 * r96331;
        double r96334 = 4.0;
        double r96335 = a;
        double r96336 = c;
        double r96337 = r96335 * r96336;
        double r96338 = r96334 * r96337;
        double r96339 = r96333 - r96338;
        double r96340 = sqrt(r96339);
        double r96341 = r96332 + r96340;
        double r96342 = 2.0;
        double r96343 = r96342 * r96335;
        double r96344 = r96341 / r96343;
        return r96344;
}

↓

double f(double a, double b, double c) {
        double r96345 = b;
        double r96346 = -4.123103533644211e+95;
        bool r96347 = r96345 <= r96346;
        double r96348 = 1.0;
        double r96349 = c;
        double r96350 = r96349 / r96345;
        double r96351 = a;
        double r96352 = r96345 / r96351;
        double r96353 = r96350 - r96352;
        double r96354 = r96348 * r96353;
        double r96355 = 3.446447862996811e-75;
        bool r96356 = r96345 <= r96355;
        double r96357 = r96351 * r96349;
        double r96358 = 4.0;
        double r96359 = r96357 * r96358;
        double r96360 = -r96359;
        double r96361 = fma(r96345, r96345, r96360);
        double r96362 = sqrt(r96361);
        double r96363 = r96362 - r96345;
        double r96364 = 1.0;
        double r96365 = r96364 / r96351;
        double r96366 = 2.0;
        double r96367 = r96365 / r96366;
        double r96368 = r96363 * r96367;
        double r96369 = -1.0;
        double r96370 = r96369 * r96350;
        double r96371 = r96356 ? r96368 : r96370;
        double r96372 = r96347 ? r96354 : r96371;
        return r96372;
}

Original	34.2
Target	21.1
Herbie	10.4

Derivation

Split input into 3 regimes
if b < -4.123103533644211e+95
1. Initial program 47.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified47.3
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Taylor expanded around -inf 3.8
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified3.8
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -4.123103533644211e+95 < b < 3.446447862996811e-75
1. Initial program 13.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified13.3
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num13.4
  \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}}\]
5. Using strategy rm
6. Applied div-inv13.4
  \[\leadsto \frac{1}{\frac{a}{\color{blue}{\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right) \cdot \frac{1}{2}}}}\]
7. Applied *-un-lft-identity13.4
  \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot a}}{\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right) \cdot \frac{1}{2}}}\]
8. Applied times-frac13.5
  \[\leadsto \frac{1}{\color{blue}{\frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b} \cdot \frac{a}{\frac{1}{2}}}}\]
9. Applied add-cube-cbrt13.5
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b} \cdot \frac{a}{\frac{1}{2}}}\]
10. Applied times-frac13.5
  \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\frac{1}{2}}}}\]
11. Simplified13.4
  \[\leadsto \color{blue}{\left(\sqrt{\mathsf{fma}\left(b, b, -\left(a \cdot c\right) \cdot 4\right)} - b\right)} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\frac{1}{2}}}\]
12. Simplified13.4
  \[\leadsto \left(\sqrt{\mathsf{fma}\left(b, b, -\left(a \cdot c\right) \cdot 4\right)} - b\right) \cdot \color{blue}{\frac{\frac{1}{a}}{2}}\]
if 3.446447862996811e-75 < b
1. Initial program 52.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified52.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Taylor expanded around inf 9.7
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.4
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.12310353364421125 \cdot 10^{95}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 3.446447862996811 \cdot 10^{-75}:\\ \;\;\;\;\left(\sqrt{\mathsf{fma}\left(b, b, -\left(a \cdot c\right) \cdot 4\right)} - b\right) \cdot \frac{\frac{1}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

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

Error

Target

Derivation

`if b < -4.123103533644211e+95`

`if -4.123103533644211e+95 < b < 3.446447862996811e-75`

`if 3.446447862996811e-75 < b`

Reproduce