\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]

↓

\[\begin{array}{l} \mathbf{if}\;b \le -3.99906304217636 \cdot 10^{+90}:\\ \;\;\;\;\frac{1}{2} \cdot \frac{c}{b} - \frac{b}{a} \cdot \frac{2}{3}\\ \mathbf{elif}\;b \le 1.6799331677465153 \cdot 10^{-38}:\\ \;\;\;\;\frac{1}{\frac{3 \cdot a}{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b}\\ \end{array}\]

double f(double a, double b, double c, double __attribute__((unused)) d) {
        double r16084462 = b;
        double r16084463 = -r16084462;
        double r16084464 = r16084462 * r16084462;
        double r16084465 = 3.0;
        double r16084466 = a;
        double r16084467 = r16084465 * r16084466;
        double r16084468 = c;
        double r16084469 = r16084467 * r16084468;
        double r16084470 = r16084464 - r16084469;
        double r16084471 = sqrt(r16084470);
        double r16084472 = r16084463 + r16084471;
        double r16084473 = r16084472 / r16084467;
        return r16084473;
}

↓

double f(double a, double b, double c, double __attribute__((unused)) d) {
        double r16084474 = b;
        double r16084475 = -3.99906304217636e+90;
        bool r16084476 = r16084474 <= r16084475;
        double r16084477 = 0.5;
        double r16084478 = c;
        double r16084479 = r16084478 / r16084474;
        double r16084480 = r16084477 * r16084479;
        double r16084481 = a;
        double r16084482 = r16084474 / r16084481;
        double r16084483 = 0.6666666666666666;
        double r16084484 = r16084482 * r16084483;
        double r16084485 = r16084480 - r16084484;
        double r16084486 = 1.6799331677465153e-38;
        bool r16084487 = r16084474 <= r16084486;
        double r16084488 = 1.0;
        double r16084489 = 3.0;
        double r16084490 = r16084489 * r16084481;
        double r16084491 = r16084474 * r16084474;
        double r16084492 = r16084490 * r16084478;
        double r16084493 = r16084491 - r16084492;
        double r16084494 = sqrt(r16084493);
        double r16084495 = r16084494 - r16084474;
        double r16084496 = r16084490 / r16084495;
        double r16084497 = r16084488 / r16084496;
        double r16084498 = -0.5;
        double r16084499 = r16084498 * r16084479;
        double r16084500 = r16084487 ? r16084497 : r16084499;
        double r16084501 = r16084476 ? r16084485 : r16084500;
        return r16084501;
}

\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}

↓

\begin{array}{l}
\mathbf{if}\;b \le -3.99906304217636 \cdot 10^{+90}:\\
\;\;\;\;\frac{1}{2} \cdot \frac{c}{b} - \frac{b}{a} \cdot \frac{2}{3}\\

\mathbf{elif}\;b \le 1.6799331677465153 \cdot 10^{-38}:\\
\;\;\;\;\frac{1}{\frac{3 \cdot a}{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}}\\

\mathbf{else}:\\
\;\;\;\;\frac{-1}{2} \cdot \frac{c}{b}\\

\end{array}

Derivation

Split input into 3 regimes
if b < -3.99906304217636e+90
1. Initial program 44.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
2. Simplified44.2
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}{3 \cdot a}}\]
3. Using strategy rm
4. Applied *-un-lft-identity44.2
  \[\leadsto \frac{\color{blue}{1 \cdot \left(\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b\right)}}{3 \cdot a}\]
5. Applied times-frac44.2
  \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}{a}}\]
6. Simplified44.2
  \[\leadsto \color{blue}{\frac{1}{3}} \cdot \frac{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}{a}\]
7. Taylor expanded around -inf 4.4
  \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{c}{b} - \frac{2}{3} \cdot \frac{b}{a}}\]
if -3.99906304217636e+90 < b < 1.6799331677465153e-38
1. Initial program 14.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
2. Simplified14.2
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}{3 \cdot a}}\]
3. Using strategy rm
4. Applied clear-num14.3
  \[\leadsto \color{blue}{\frac{1}{\frac{3 \cdot a}{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}}}\]
if 1.6799331677465153e-38 < b
1. Initial program 53.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
2. Simplified53.4
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}{3 \cdot a}}\]
3. Using strategy rm
4. Applied *-un-lft-identity53.4
  \[\leadsto \frac{\color{blue}{1 \cdot \left(\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b\right)}}{3 \cdot a}\]
5. Applied times-frac53.4
  \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}{a}}\]
6. Simplified53.4
  \[\leadsto \color{blue}{\frac{1}{3}} \cdot \frac{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}{a}\]
7. Taylor expanded around inf 7.6
  \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.99906304217636 \cdot 10^{+90}:\\ \;\;\;\;\frac{1}{2} \cdot \frac{c}{b} - \frac{b}{a} \cdot \frac{2}{3}\\ \mathbf{elif}\;b \le 1.6799331677465153 \cdot 10^{-38}:\\ \;\;\;\;\frac{1}{\frac{3 \cdot a}{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b}\\ \end{array}\]

unused variable d

Error

Derivation

`if b < -3.99906304217636e+90`

`if -3.99906304217636e+90 < b < 1.6799331677465153e-38`

`if 1.6799331677465153e-38 < b`

Reproduce