\[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

↓

\[\begin{array}{l} \mathbf{if}\;b_2 \le 0.37518310546875:\\ \;\;\;\;\frac{\frac{a \cdot c + \left(\left(-b_2\right) + b_2\right) \cdot \left(\left(-b_2\right) + \left(-b_2\right)\right)}{a}}{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\ \end{array}\]

double f(double a, double b_2, double c) {
        double r561572 = b_2;
        double r561573 = -r561572;
        double r561574 = r561572 * r561572;
        double r561575 = a;
        double r561576 = c;
        double r561577 = r561575 * r561576;
        double r561578 = r561574 - r561577;
        double r561579 = sqrt(r561578);
        double r561580 = r561573 - r561579;
        double r561581 = r561580 / r561575;
        return r561581;
}

↓

double f(double a, double b_2, double c) {
        double r561582 = b_2;
        double r561583 = 0.37518310546875;
        bool r561584 = r561582 <= r561583;
        double r561585 = a;
        double r561586 = c;
        double r561587 = r561585 * r561586;
        double r561588 = -r561582;
        double r561589 = r561588 + r561582;
        double r561590 = r561588 + r561588;
        double r561591 = r561589 * r561590;
        double r561592 = r561587 + r561591;
        double r561593 = r561592 / r561585;
        double r561594 = r561582 * r561582;
        double r561595 = r561594 - r561587;
        double r561596 = sqrt(r561595);
        double r561597 = r561588 + r561596;
        double r561598 = r561593 / r561597;
        double r561599 = r561588 - r561596;
        double r561600 = r561599 / r561585;
        double r561601 = r561584 ? r561598 : r561600;
        return r561601;
}

\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}

↓

\begin{array}{l}
\mathbf{if}\;b_2 \le 0.37518310546875:\\
\;\;\;\;\frac{\frac{a \cdot c + \left(\left(-b_2\right) + b_2\right) \cdot \left(\left(-b_2\right) + \left(-b_2\right)\right)}{a}}{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\

\end{array}

Derivation

Split input into 2 regimes
if b_2 < 0.37518310546875
1. Initial program 2.4
  \[\frac{\left(\left(-b_2\right) - \left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)\right)}{a}\]
2. Using strategy rm
3. Applied p16-flip--2.2
  \[\leadsto \frac{\color{blue}{\left(\frac{\left(\left(\left(-b_2\right) \cdot \left(-b_2\right)\right) - \left(\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right) \cdot \left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)\right)\right)}{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}\right)}}{a}\]
4. Applied associate-/l/2.3
  \[\leadsto \color{blue}{\frac{\left(\left(\left(-b_2\right) \cdot \left(-b_2\right)\right) - \left(\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right) \cdot \left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)\right)\right)}{\left(a \cdot \left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)\right)}}\]
5. Simplified0.7
  \[\leadsto \frac{\color{blue}{\left(\frac{\left(a \cdot c\right)}{\left(\left(\frac{\left(-b_2\right)}{b_2}\right) \cdot \left(\frac{\left(-b_2\right)}{\left(-b_2\right)}\right)\right)}\right)}}{\left(a \cdot \left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)\right)}\]
6. Using strategy rm
7. Applied associate-/r*0.5
  \[\leadsto \color{blue}{\frac{\left(\frac{\left(\frac{\left(a \cdot c\right)}{\left(\left(\frac{\left(-b_2\right)}{b_2}\right) \cdot \left(\frac{\left(-b_2\right)}{\left(-b_2\right)}\right)\right)}\right)}{a}\right)}{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}}\]
if 0.37518310546875 < b_2
1. Initial program 0.4
  \[\frac{\left(\left(-b_2\right) - \left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)\right)}{a}\]
Recombined 2 regimes into one program.
Final simplification0.5
\[\leadsto \begin{array}{l} \mathbf{if}\;b_2 \le 0.37518310546875:\\ \;\;\;\;\frac{\frac{a \cdot c + \left(\left(-b_2\right) + b_2\right) \cdot \left(\left(-b_2\right) + \left(-b_2\right)\right)}{a}}{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\ \end{array}\]

Error

Derivation

`if b_2 < 0.37518310546875`

`if 0.37518310546875 < b_2`

Reproduce