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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.221067196710922123169723133116561516447 \cdot 10^{149}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, \frac{c}{b}, -2 \cdot \frac{b}{a}\right)}{2}\\ \mathbf{elif}\;b \le 2.898348930695269343280527497904161468201 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

\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 -2.221067196710922123169723133116561516447 \cdot 10^{149}:\\
\;\;\;\;\frac{\mathsf{fma}\left(2, \frac{c}{b}, -2 \cdot \frac{b}{a}\right)}{2}\\

\mathbf{elif}\;b \le 2.898348930695269343280527497904161468201 \cdot 10^{-35}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)} - b}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r4510044 = b;
        double r4510045 = -r4510044;
        double r4510046 = r4510044 * r4510044;
        double r4510047 = 4.0;
        double r4510048 = a;
        double r4510049 = r4510047 * r4510048;
        double r4510050 = c;
        double r4510051 = r4510049 * r4510050;
        double r4510052 = r4510046 - r4510051;
        double r4510053 = sqrt(r4510052);
        double r4510054 = r4510045 + r4510053;
        double r4510055 = 2.0;
        double r4510056 = r4510055 * r4510048;
        double r4510057 = r4510054 / r4510056;
        return r4510057;
}

↓

double f(double a, double b, double c) {
        double r4510058 = b;
        double r4510059 = -2.221067196710922e+149;
        bool r4510060 = r4510058 <= r4510059;
        double r4510061 = 2.0;
        double r4510062 = c;
        double r4510063 = r4510062 / r4510058;
        double r4510064 = -2.0;
        double r4510065 = a;
        double r4510066 = r4510058 / r4510065;
        double r4510067 = r4510064 * r4510066;
        double r4510068 = fma(r4510061, r4510063, r4510067);
        double r4510069 = r4510068 / r4510061;
        double r4510070 = 2.8983489306952693e-35;
        bool r4510071 = r4510058 <= r4510070;
        double r4510072 = r4510058 * r4510058;
        double r4510073 = 4.0;
        double r4510074 = r4510062 * r4510073;
        double r4510075 = r4510065 * r4510074;
        double r4510076 = r4510072 - r4510075;
        double r4510077 = sqrt(r4510076);
        double r4510078 = r4510077 - r4510058;
        double r4510079 = r4510078 / r4510065;
        double r4510080 = r4510079 / r4510061;
        double r4510081 = -2.0;
        double r4510082 = r4510081 * r4510063;
        double r4510083 = r4510082 / r4510061;
        double r4510084 = r4510071 ? r4510080 : r4510083;
        double r4510085 = r4510060 ? r4510069 : r4510084;
        return r4510085;
}

Original	34.4
Target	21.5
Herbie	10.6

Derivation

Split input into 3 regimes
if b < -2.221067196710922e+149
1. Initial program 62.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified62.3
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied *-un-lft-identity62.3
  \[\leadsto \frac{\frac{\sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a} - b}{\color{blue}{1 \cdot a}}}{2}\]
5. Applied associate-/r*62.3
  \[\leadsto \frac{\color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a} - b}{1}}{a}}}{2}\]
6. Simplified62.3
  \[\leadsto \frac{\frac{\color{blue}{\sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)} - b}}{a}}{2}\]
7. Taylor expanded around -inf 2.8
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
8. Simplified2.8
  \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(2, \frac{c}{b}, -2 \cdot \frac{b}{a}\right)}}{2}\]
if -2.221067196710922e+149 < b < 2.8983489306952693e-35
1. Initial program 14.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified14.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied *-un-lft-identity14.6
  \[\leadsto \frac{\frac{\sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a} - b}{\color{blue}{1 \cdot a}}}{2}\]
5. Applied associate-/r*14.6
  \[\leadsto \frac{\color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a} - b}{1}}{a}}}{2}\]
6. Simplified14.6
  \[\leadsto \frac{\frac{\color{blue}{\sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)} - b}}{a}}{2}\]
if 2.8983489306952693e-35 < b
1. Initial program 54.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified54.4
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a} - b}{a}}{2}}\]
3. Taylor expanded around inf 7.3
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification10.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.221067196710922123169723133116561516447 \cdot 10^{149}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, \frac{c}{b}, -2 \cdot \frac{b}{a}\right)}{2}\\ \mathbf{elif}\;b \le 2.898348930695269343280527497904161468201 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -2.221067196710922e+149`

`if -2.221067196710922e+149 < b < 2.8983489306952693e-35`

`if 2.8983489306952693e-35 < b`

Reproduce