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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -8.260729798395838 \cdot 10^{-43}:\\ \;\;\;\;{\left(-1 \cdot \frac{c}{b}\right)}^{1}\\ \mathbf{elif}\;b \le 1.67643144401154069 \cdot 10^{104}:\\ \;\;\;\;{\left(\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \end{array}\]

\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 -8.260729798395838 \cdot 10^{-43}:\\
\;\;\;\;{\left(-1 \cdot \frac{c}{b}\right)}^{1}\\

\mathbf{elif}\;b \le 1.67643144401154069 \cdot 10^{104}:\\
\;\;\;\;{\left(\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\right)}^{1}\\

\mathbf{else}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\end{array}

double f(double a, double b, double c) {
        double r107745 = b;
        double r107746 = -r107745;
        double r107747 = r107745 * r107745;
        double r107748 = 4.0;
        double r107749 = a;
        double r107750 = c;
        double r107751 = r107749 * r107750;
        double r107752 = r107748 * r107751;
        double r107753 = r107747 - r107752;
        double r107754 = sqrt(r107753);
        double r107755 = r107746 - r107754;
        double r107756 = 2.0;
        double r107757 = r107756 * r107749;
        double r107758 = r107755 / r107757;
        return r107758;
}

↓

double f(double a, double b, double c) {
        double r107759 = b;
        double r107760 = -8.260729798395838e-43;
        bool r107761 = r107759 <= r107760;
        double r107762 = -1.0;
        double r107763 = c;
        double r107764 = r107763 / r107759;
        double r107765 = r107762 * r107764;
        double r107766 = 1.0;
        double r107767 = pow(r107765, r107766);
        double r107768 = 1.6764314440115407e+104;
        bool r107769 = r107759 <= r107768;
        double r107770 = -r107759;
        double r107771 = r107759 * r107759;
        double r107772 = 4.0;
        double r107773 = a;
        double r107774 = r107773 * r107763;
        double r107775 = r107772 * r107774;
        double r107776 = r107771 - r107775;
        double r107777 = sqrt(r107776);
        double r107778 = r107770 - r107777;
        double r107779 = 2.0;
        double r107780 = r107779 * r107773;
        double r107781 = r107778 / r107780;
        double r107782 = pow(r107781, r107766);
        double r107783 = 1.0;
        double r107784 = r107759 / r107773;
        double r107785 = r107764 - r107784;
        double r107786 = r107783 * r107785;
        double r107787 = r107769 ? r107782 : r107786;
        double r107788 = r107761 ? r107767 : r107787;
        return r107788;
}

Original	34.1
Target	21.1
Herbie	9.9

Derivation

Split input into 3 regimes
if b < -8.260729798395838e-43
1. Initial program 54.7
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv54.7
  \[\leadsto \color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Using strategy rm
5. Applied pow154.7
  \[\leadsto \left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \color{blue}{{\left(\frac{1}{2 \cdot a}\right)}^{1}}\]
6. Applied pow154.7
  \[\leadsto \color{blue}{{\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}^{1}} \cdot {\left(\frac{1}{2 \cdot a}\right)}^{1}\]
7. Applied pow-prod-down54.7
  \[\leadsto \color{blue}{{\left(\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}\right)}^{1}}\]
8. Simplified54.7
  \[\leadsto {\color{blue}{\left(\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\right)}}^{1}\]
9. Taylor expanded around -inf 7.3
  \[\leadsto {\color{blue}{\left(-1 \cdot \frac{c}{b}\right)}}^{1}\]
if -8.260729798395838e-43 < b < 1.6764314440115407e+104
1. Initial program 14.0
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv14.1
  \[\leadsto \color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Using strategy rm
5. Applied pow114.1
  \[\leadsto \left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \color{blue}{{\left(\frac{1}{2 \cdot a}\right)}^{1}}\]
6. Applied pow114.1
  \[\leadsto \color{blue}{{\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}^{1}} \cdot {\left(\frac{1}{2 \cdot a}\right)}^{1}\]
7. Applied pow-prod-down14.1
  \[\leadsto \color{blue}{{\left(\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}\right)}^{1}}\]
8. Simplified14.0
  \[\leadsto {\color{blue}{\left(\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\right)}}^{1}\]
if 1.6764314440115407e+104 < b
1. Initial program 47.9
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around inf 3.3
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified3.3
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
Recombined 3 regimes into one program.
Final simplification9.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -8.260729798395838 \cdot 10^{-43}:\\ \;\;\;\;{\left(-1 \cdot \frac{c}{b}\right)}^{1}\\ \mathbf{elif}\;b \le 1.67643144401154069 \cdot 10^{104}:\\ \;\;\;\;{\left(\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -8.260729798395838e-43`

`if -8.260729798395838e-43 < b < 1.6764314440115407e+104`

`if 1.6764314440115407e+104 < b`

Reproduce

In
Out