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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\ \;\;\;\;\frac{\frac{1}{\frac{-1}{b}}}{a}\\ \mathbf{elif}\;b \le 5.860223638943180333955717619400031865396 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{b}{c \cdot a} \cdot 1}}{a}\\ \end{array}\]

\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 -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\
\;\;\;\;\frac{\frac{1}{\frac{-1}{b}}}{a}\\

\mathbf{elif}\;b \le 5.860223638943180333955717619400031865396 \cdot 10^{-17}:\\
\;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r3352437 = b;
        double r3352438 = -r3352437;
        double r3352439 = r3352437 * r3352437;
        double r3352440 = 4.0;
        double r3352441 = a;
        double r3352442 = r3352440 * r3352441;
        double r3352443 = c;
        double r3352444 = r3352442 * r3352443;
        double r3352445 = r3352439 - r3352444;
        double r3352446 = sqrt(r3352445);
        double r3352447 = r3352438 + r3352446;
        double r3352448 = 2.0;
        double r3352449 = r3352448 * r3352441;
        double r3352450 = r3352447 / r3352449;
        return r3352450;
}

↓

double f(double a, double b, double c) {
        double r3352451 = b;
        double r3352452 = -1.7633154797394035e+89;
        bool r3352453 = r3352451 <= r3352452;
        double r3352454 = 1.0;
        double r3352455 = -1.0;
        double r3352456 = r3352455 / r3352451;
        double r3352457 = r3352454 / r3352456;
        double r3352458 = a;
        double r3352459 = r3352457 / r3352458;
        double r3352460 = 5.86022363894318e-17;
        bool r3352461 = r3352451 <= r3352460;
        double r3352462 = 2.0;
        double r3352463 = r3352451 * r3352451;
        double r3352464 = 4.0;
        double r3352465 = c;
        double r3352466 = r3352465 * r3352458;
        double r3352467 = r3352464 * r3352466;
        double r3352468 = r3352463 - r3352467;
        double r3352469 = sqrt(r3352468);
        double r3352470 = r3352469 - r3352451;
        double r3352471 = r3352462 / r3352470;
        double r3352472 = r3352454 / r3352471;
        double r3352473 = r3352472 / r3352458;
        double r3352474 = 1.0;
        double r3352475 = r3352474 / r3352451;
        double r3352476 = r3352451 / r3352466;
        double r3352477 = r3352476 * r3352474;
        double r3352478 = r3352475 - r3352477;
        double r3352479 = r3352454 / r3352478;
        double r3352480 = r3352479 / r3352458;
        double r3352481 = r3352461 ? r3352473 : r3352480;
        double r3352482 = r3352453 ? r3352459 : r3352481;
        return r3352482;
}

Original	34.4
Target	21.3
Herbie	14.2

Derivation

Split input into 3 regimes
if b < -1.7633154797394035e+89
1. Initial program 45.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified45.7
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num45.8
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}}{a}\]
5. Taylor expanded around -inf 4.2
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{-1}{b}}}}{a}\]
if -1.7633154797394035e+89 < b < 5.86022363894318e-17
1. Initial program 15.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified15.4
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num15.4
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}}{a}\]
if 5.86022363894318e-17 < b
1. Initial program 55.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified55.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num55.6
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}}{a}\]
5. Taylor expanded around inf 17.3
  \[\leadsto \frac{\frac{1}{\color{blue}{1 \cdot \frac{1}{b} - 1 \cdot \frac{b}{a \cdot c}}}}{a}\]
6. Simplified17.3
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{1}{b} - 1 \cdot \frac{b}{c \cdot a}}}}{a}\]
Recombined 3 regimes into one program.
Final simplification14.2
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\ \;\;\;\;\frac{\frac{1}{\frac{-1}{b}}}{a}\\ \mathbf{elif}\;b \le 5.860223638943180333955717619400031865396 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{b}{c \cdot a} \cdot 1}}{a}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.7633154797394035e+89`

`if -1.7633154797394035e+89 < b < 5.86022363894318e-17`

`if 5.86022363894318e-17 < b`

Reproduce

In
Out