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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.0027271082217074 \cdot 10^{+110}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 2.326372645943808 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c}{b} \cdot -2}{2}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b \le -1.0027271082217074 \cdot 10^{+110}:\\
\;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\

\mathbf{elif}\;b \le 2.326372645943808 \cdot 10^{-74}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r1555770 = b;
        double r1555771 = -r1555770;
        double r1555772 = r1555770 * r1555770;
        double r1555773 = 4.0;
        double r1555774 = a;
        double r1555775 = c;
        double r1555776 = r1555774 * r1555775;
        double r1555777 = r1555773 * r1555776;
        double r1555778 = r1555772 - r1555777;
        double r1555779 = sqrt(r1555778);
        double r1555780 = r1555771 + r1555779;
        double r1555781 = 2.0;
        double r1555782 = r1555781 * r1555774;
        double r1555783 = r1555780 / r1555782;
        return r1555783;
}

↓

double f(double a, double b, double c) {
        double r1555784 = b;
        double r1555785 = -1.0027271082217074e+110;
        bool r1555786 = r1555784 <= r1555785;
        double r1555787 = c;
        double r1555788 = r1555787 / r1555784;
        double r1555789 = a;
        double r1555790 = r1555784 / r1555789;
        double r1555791 = r1555788 - r1555790;
        double r1555792 = 2.0;
        double r1555793 = r1555791 * r1555792;
        double r1555794 = r1555793 / r1555792;
        double r1555795 = 2.326372645943808e-74;
        bool r1555796 = r1555784 <= r1555795;
        double r1555797 = r1555784 * r1555784;
        double r1555798 = 4.0;
        double r1555799 = r1555798 * r1555789;
        double r1555800 = r1555799 * r1555787;
        double r1555801 = r1555797 - r1555800;
        double r1555802 = sqrt(r1555801);
        double r1555803 = r1555802 - r1555784;
        double r1555804 = r1555803 / r1555789;
        double r1555805 = r1555804 / r1555792;
        double r1555806 = -2.0;
        double r1555807 = r1555788 * r1555806;
        double r1555808 = r1555807 / r1555792;
        double r1555809 = r1555796 ? r1555805 : r1555808;
        double r1555810 = r1555786 ? r1555794 : r1555809;
        return r1555810;
}

Original	33.4
Target	20.3
Herbie	9.9

Derivation

Split input into 3 regimes
if b < -1.0027271082217074e+110
1. Initial program 46.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified46.7
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied div-sub46.7
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a} - \frac{b}{a}}}{2}\]
5. Using strategy rm
6. Applied div-inv46.8
  \[\leadsto \frac{\color{blue}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \frac{1}{a}} - \frac{b}{a}}{2}\]
7. Taylor expanded around -inf 3.6
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
8. Simplified3.6
  \[\leadsto \frac{\color{blue}{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}}{2}\]
if -1.0027271082217074e+110 < b < 2.326372645943808e-74
1. Initial program 12.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified12.8
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied div-sub12.8
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a} - \frac{b}{a}}}{2}\]
5. Using strategy rm
6. Applied sub-div12.8
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}}{2}\]
if 2.326372645943808e-74 < b
1. Initial program 52.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified52.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied div-sub53.2
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a} - \frac{b}{a}}}{2}\]
5. Using strategy rm
6. Applied sub-div52.5
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}}{2}\]
7. Taylor expanded around inf 8.8
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification9.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.0027271082217074 \cdot 10^{+110}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 2.326372645943808 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c}{b} \cdot -2}{2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.0027271082217074e+110`

`if -1.0027271082217074e+110 < b < 2.326372645943808e-74`

`if 2.326372645943808e-74 < b`

Reproduce

In
Out