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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -4.3671561050226844 \cdot 10^{+101}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 5.6646816643665726 \cdot 10^{-285}:\\ \;\;\;\;\left(\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}\right) \cdot \frac{1}{a \cdot 2}\\ \mathbf{elif}\;b \le 2.8546456093447043 \cdot 10^{+107}:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{2 \cdot \left(\frac{c}{b} \cdot a - b\right)}\\ \end{array}\]

double f(double a, double b, double c) {
        double r6049172 = b;
        double r6049173 = -r6049172;
        double r6049174 = r6049172 * r6049172;
        double r6049175 = 4.0;
        double r6049176 = a;
        double r6049177 = r6049175 * r6049176;
        double r6049178 = c;
        double r6049179 = r6049177 * r6049178;
        double r6049180 = r6049174 - r6049179;
        double r6049181 = sqrt(r6049180);
        double r6049182 = r6049173 + r6049181;
        double r6049183 = 2.0;
        double r6049184 = r6049183 * r6049176;
        double r6049185 = r6049182 / r6049184;
        return r6049185;
}

↓

double f(double a, double b, double c) {
        double r6049186 = b;
        double r6049187 = -4.3671561050226844e+101;
        bool r6049188 = r6049186 <= r6049187;
        double r6049189 = c;
        double r6049190 = r6049189 / r6049186;
        double r6049191 = a;
        double r6049192 = r6049186 / r6049191;
        double r6049193 = r6049190 - r6049192;
        double r6049194 = 5.6646816643665726e-285;
        bool r6049195 = r6049186 <= r6049194;
        double r6049196 = -r6049186;
        double r6049197 = r6049186 * r6049186;
        double r6049198 = 4.0;
        double r6049199 = r6049198 * r6049191;
        double r6049200 = r6049189 * r6049199;
        double r6049201 = r6049197 - r6049200;
        double r6049202 = sqrt(r6049201);
        double r6049203 = r6049196 + r6049202;
        double r6049204 = 1.0;
        double r6049205 = 2.0;
        double r6049206 = r6049191 * r6049205;
        double r6049207 = r6049204 / r6049206;
        double r6049208 = r6049203 * r6049207;
        double r6049209 = 2.8546456093447043e+107;
        bool r6049210 = r6049186 <= r6049209;
        double r6049211 = r6049189 * r6049205;
        double r6049212 = r6049196 - r6049202;
        double r6049213 = r6049211 / r6049212;
        double r6049214 = r6049190 * r6049191;
        double r6049215 = r6049214 - r6049186;
        double r6049216 = r6049205 * r6049215;
        double r6049217 = r6049211 / r6049216;
        double r6049218 = r6049210 ? r6049213 : r6049217;
        double r6049219 = r6049195 ? r6049208 : r6049218;
        double r6049220 = r6049188 ? r6049193 : r6049219;
        return r6049220;
}

\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 -4.3671561050226844 \cdot 10^{+101}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 5.6646816643665726 \cdot 10^{-285}:\\
\;\;\;\;\left(\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}\right) \cdot \frac{1}{a \cdot 2}\\

\mathbf{elif}\;b \le 2.8546456093447043 \cdot 10^{+107}:\\
\;\;\;\;\frac{c \cdot 2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{c \cdot 2}{2 \cdot \left(\frac{c}{b} \cdot a - b\right)}\\

\end{array}

Derivation

Split input into 4 regimes
if b < -4.3671561050226844e+101
1. Initial program 44.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv44.8
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Taylor expanded around -inf 3.8
  \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]
if -4.3671561050226844e+101 < b < 5.6646816643665726e-285
1. Initial program 9.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv9.7
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
if 5.6646816643665726e-285 < b < 2.8546456093447043e+107
1. Initial program 33.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv33.5
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Using strategy rm
5. Applied flip-+33.6
  \[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}} \cdot \frac{1}{2 \cdot a}\]
6. Applied associate-*l/33.6
  \[\leadsto \color{blue}{\frac{\left(\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}\]
7. Simplified16.0
  \[\leadsto \frac{\color{blue}{-\frac{\frac{c \cdot a}{\frac{-1}{2}}}{a}}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\]
8. Taylor expanded around 0 8.7
  \[\leadsto \frac{-\color{blue}{-2 \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\]
if 2.8546456093447043e+107 < b
1. Initial program 59.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv59.5
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Using strategy rm
5. Applied flip-+59.6
  \[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}} \cdot \frac{1}{2 \cdot a}\]
6. Applied associate-*l/59.6
  \[\leadsto \color{blue}{\frac{\left(\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}\]
7. Simplified32.0
  \[\leadsto \frac{\color{blue}{-\frac{\frac{c \cdot a}{\frac{-1}{2}}}{a}}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\]
8. Taylor expanded around 0 31.4
  \[\leadsto \frac{-\color{blue}{-2 \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\]
9. Taylor expanded around inf 6.5
  \[\leadsto \frac{--2 \cdot c}{\color{blue}{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}}\]
10. Simplified2.1
  \[\leadsto \frac{--2 \cdot c}{\color{blue}{\left(\frac{c}{b} \cdot a - b\right) \cdot 2}}\]
Recombined 4 regimes into one program.
Final simplification6.7
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.3671561050226844 \cdot 10^{+101}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 5.6646816643665726 \cdot 10^{-285}:\\ \;\;\;\;\left(\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}\right) \cdot \frac{1}{a \cdot 2}\\ \mathbf{elif}\;b \le 2.8546456093447043 \cdot 10^{+107}:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{2 \cdot \left(\frac{c}{b} \cdot a - b\right)}\\ \end{array}\]

Error

Derivation

`if b < -4.3671561050226844e+101`

`if -4.3671561050226844e+101 < b < 5.6646816643665726e-285`

`if 5.6646816643665726e-285 < b < 2.8546456093447043e+107`

`if 2.8546456093447043e+107 < b`

Reproduce