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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -4.829903230896134050158793286773621805382 \cdot 10^{148}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.058331905530479345989188577279018272684 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{elif}\;b \le 400482480739649191422756162656796672:\\ \;\;\;\;\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -4.829903230896134050158793286773621805382 \cdot 10^{148}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 1.058331905530479345989188577279018272684 \cdot 10^{-144}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\

\mathbf{elif}\;b \le 400482480739649191422756162656796672:\\
\;\;\;\;\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r105628 = b;
        double r105629 = -r105628;
        double r105630 = r105628 * r105628;
        double r105631 = 4.0;
        double r105632 = a;
        double r105633 = r105631 * r105632;
        double r105634 = c;
        double r105635 = r105633 * r105634;
        double r105636 = r105630 - r105635;
        double r105637 = sqrt(r105636);
        double r105638 = r105629 + r105637;
        double r105639 = 2.0;
        double r105640 = r105639 * r105632;
        double r105641 = r105638 / r105640;
        return r105641;
}

↓

double f(double a, double b, double c) {
        double r105642 = b;
        double r105643 = -4.829903230896134e+148;
        bool r105644 = r105642 <= r105643;
        double r105645 = 1.0;
        double r105646 = c;
        double r105647 = r105646 / r105642;
        double r105648 = a;
        double r105649 = r105642 / r105648;
        double r105650 = r105647 - r105649;
        double r105651 = r105645 * r105650;
        double r105652 = 1.0583319055304793e-144;
        bool r105653 = r105642 <= r105652;
        double r105654 = -r105642;
        double r105655 = r105642 * r105642;
        double r105656 = 4.0;
        double r105657 = r105656 * r105648;
        double r105658 = r105657 * r105646;
        double r105659 = r105655 - r105658;
        double r105660 = sqrt(r105659);
        double r105661 = r105654 + r105660;
        double r105662 = 2.0;
        double r105663 = r105662 * r105648;
        double r105664 = r105661 / r105663;
        double r105665 = 4.004824807396492e+35;
        bool r105666 = r105642 <= r105665;
        double r105667 = 0.0;
        double r105668 = r105648 * r105646;
        double r105669 = r105656 * r105668;
        double r105670 = r105667 + r105669;
        double r105671 = r105654 - r105660;
        double r105672 = r105670 / r105671;
        double r105673 = r105672 / r105663;
        double r105674 = -1.0;
        double r105675 = r105674 * r105647;
        double r105676 = r105666 ? r105673 : r105675;
        double r105677 = r105653 ? r105664 : r105676;
        double r105678 = r105644 ? r105651 : r105677;
        return r105678;
}

Original	34.3
Target	20.9
Herbie	8.9

Derivation

Split input into 4 regimes
if b < -4.829903230896134e+148
1. Initial program 61.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around -inf 2.8
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified2.8
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -4.829903230896134e+148 < b < 1.0583319055304793e-144
1. Initial program 11.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
if 1.0583319055304793e-144 < b < 4.004824807396492e+35
1. Initial program 35.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied flip-+35.8
  \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
4. Simplified16.7
  \[\leadsto \frac{\frac{\color{blue}{0 + 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
if 4.004824807396492e+35 < b
1. Initial program 56.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 4.3
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 4 regimes into one program.
Final simplification8.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.829903230896134050158793286773621805382 \cdot 10^{148}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.058331905530479345989188577279018272684 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{elif}\;b \le 400482480739649191422756162656796672:\\ \;\;\;\;\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -4.829903230896134e+148`

`if -4.829903230896134e+148 < b < 1.0583319055304793e-144`

`if 1.0583319055304793e-144 < b < 4.004824807396492e+35`

`if 4.004824807396492e+35 < b`

Reproduce

In
Out