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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -7.93152454634661985 \cdot 10^{153}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 2.0569776426586135 \cdot 10^{-106}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{\frac{a}{\frac{1}{2}}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -7.93152454634661985 \cdot 10^{153}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 2.0569776426586135 \cdot 10^{-106}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{\frac{a}{\frac{1}{2}}}\\

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

\end{array}

double f(double a, double b, double c) {
        double r84426 = b;
        double r84427 = -r84426;
        double r84428 = r84426 * r84426;
        double r84429 = 4.0;
        double r84430 = a;
        double r84431 = r84429 * r84430;
        double r84432 = c;
        double r84433 = r84431 * r84432;
        double r84434 = r84428 - r84433;
        double r84435 = sqrt(r84434);
        double r84436 = r84427 + r84435;
        double r84437 = 2.0;
        double r84438 = r84437 * r84430;
        double r84439 = r84436 / r84438;
        return r84439;
}

↓

double f(double a, double b, double c) {
        double r84440 = b;
        double r84441 = -7.93152454634662e+153;
        bool r84442 = r84440 <= r84441;
        double r84443 = 1.0;
        double r84444 = c;
        double r84445 = r84444 / r84440;
        double r84446 = a;
        double r84447 = r84440 / r84446;
        double r84448 = r84445 - r84447;
        double r84449 = r84443 * r84448;
        double r84450 = 2.0569776426586135e-106;
        bool r84451 = r84440 <= r84450;
        double r84452 = r84440 * r84440;
        double r84453 = 4.0;
        double r84454 = r84453 * r84446;
        double r84455 = r84454 * r84444;
        double r84456 = r84452 - r84455;
        double r84457 = sqrt(r84456);
        double r84458 = r84457 - r84440;
        double r84459 = 1.0;
        double r84460 = 2.0;
        double r84461 = r84459 / r84460;
        double r84462 = r84446 / r84461;
        double r84463 = r84458 / r84462;
        double r84464 = -1.0;
        double r84465 = r84464 * r84445;
        double r84466 = r84451 ? r84463 : r84465;
        double r84467 = r84442 ? r84449 : r84466;
        return r84467;
}

Original	33.8
Target	21.2
Herbie	9.8

Derivation

Split input into 3 regimes
if b < -7.93152454634662e+153
1. Initial program 63.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified63.8
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2}}{a}}\]
3. Taylor expanded around -inf 1.9
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified1.9
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -7.93152454634662e+153 < b < 2.0569776426586135e-106
1. Initial program 11.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified11.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num11.3
  \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2}}}}\]
5. Using strategy rm
6. Applied div-inv11.3
  \[\leadsto \frac{1}{\frac{a}{\color{blue}{\left(\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b\right) \cdot \frac{1}{2}}}}\]
7. Applied *-un-lft-identity11.3
  \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot a}}{\left(\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b\right) \cdot \frac{1}{2}}}\]
8. Applied times-frac11.4
  \[\leadsto \frac{1}{\color{blue}{\frac{1}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b} \cdot \frac{a}{\frac{1}{2}}}}\]
9. Applied associate-/r*11.3
  \[\leadsto \color{blue}{\frac{\frac{1}{\frac{1}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}}{\frac{a}{\frac{1}{2}}}}\]
10. Simplified11.2
  \[\leadsto \frac{\color{blue}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}{\frac{a}{\frac{1}{2}}}\]
if 2.0569776426586135e-106 < b
1. Initial program 52.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified52.0
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2}}{a}}\]
3. Taylor expanded around inf 10.3
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification9.8
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -7.93152454634661985 \cdot 10^{153}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 2.0569776426586135 \cdot 10^{-106}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{\frac{a}{\frac{1}{2}}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

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

Error

Try it out

Target

Derivation

`if b < -7.93152454634662e+153`

`if -7.93152454634662e+153 < b < 2.0569776426586135e-106`

`if 2.0569776426586135e-106 < b`

Reproduce

In
Out