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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -8.55528137777049654 \cdot 10^{140}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 2.21331291805206876 \cdot 10^{-178}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{elif}\;b \le 7.05392488455172899 \cdot 10^{44}:\\ \;\;\;\;\frac{\frac{4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -8.55528137777049654 \cdot 10^{140}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 2.21331291805206876 \cdot 10^{-178}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\

\mathbf{elif}\;b \le 7.05392488455172899 \cdot 10^{44}:\\
\;\;\;\;\frac{\frac{4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r84675 = b;
        double r84676 = -r84675;
        double r84677 = r84675 * r84675;
        double r84678 = 4.0;
        double r84679 = a;
        double r84680 = c;
        double r84681 = r84679 * r84680;
        double r84682 = r84678 * r84681;
        double r84683 = r84677 - r84682;
        double r84684 = sqrt(r84683);
        double r84685 = r84676 + r84684;
        double r84686 = 2.0;
        double r84687 = r84686 * r84679;
        double r84688 = r84685 / r84687;
        return r84688;
}

↓

double f(double a, double b, double c) {
        double r84689 = b;
        double r84690 = -8.555281377770497e+140;
        bool r84691 = r84689 <= r84690;
        double r84692 = 1.0;
        double r84693 = c;
        double r84694 = r84693 / r84689;
        double r84695 = a;
        double r84696 = r84689 / r84695;
        double r84697 = r84694 - r84696;
        double r84698 = r84692 * r84697;
        double r84699 = 2.2133129180520688e-178;
        bool r84700 = r84689 <= r84699;
        double r84701 = -r84689;
        double r84702 = r84689 * r84689;
        double r84703 = 4.0;
        double r84704 = r84695 * r84693;
        double r84705 = r84703 * r84704;
        double r84706 = r84702 - r84705;
        double r84707 = sqrt(r84706);
        double r84708 = r84701 + r84707;
        double r84709 = 2.0;
        double r84710 = r84709 * r84695;
        double r84711 = r84708 / r84710;
        double r84712 = 7.053924884551729e+44;
        bool r84713 = r84689 <= r84712;
        double r84714 = r84701 - r84707;
        double r84715 = r84705 / r84714;
        double r84716 = r84715 / r84710;
        double r84717 = -1.0;
        double r84718 = r84717 * r84694;
        double r84719 = r84713 ? r84716 : r84718;
        double r84720 = r84700 ? r84711 : r84719;
        double r84721 = r84691 ? r84698 : r84720;
        return r84721;
}

Original	34.2
Target	21.1
Herbie	8.6

Derivation

Split input into 4 regimes
if b < -8.555281377770497e+140
1. Initial program 58.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around -inf 2.4
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified2.4
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -8.555281377770497e+140 < b < 2.2133129180520688e-178
1. Initial program 10.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
if 2.2133129180520688e-178 < b < 7.053924884551729e+44
1. Initial program 33.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied flip-+33.1
  \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
4. Simplified16.6
  \[\leadsto \frac{\frac{\color{blue}{0 + 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
if 7.053924884551729e+44 < b
1. Initial program 56.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around inf 3.8
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 4 regimes into one program.
Final simplification8.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -8.55528137777049654 \cdot 10^{140}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 2.21331291805206876 \cdot 10^{-178}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{elif}\;b \le 7.05392488455172899 \cdot 10^{44}:\\ \;\;\;\;\frac{\frac{4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Target

Derivation

`if b < -8.555281377770497e+140`

`if -8.555281377770497e+140 < b < 2.2133129180520688e-178`

`if 2.2133129180520688e-178 < b < 7.053924884551729e+44`

`if 7.053924884551729e+44 < b`

Reproduce

In
Out