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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.6844644503075447 \cdot 10^{+144}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.739098950628615 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a} - \frac{b}{a}}{2}\\ \mathbf{elif}\;b \le 1.8656332031849816 \cdot 10^{-25}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \mathbf{elif}\;b \le 5.297236684235463 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a} - \frac{b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

\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 -1.6844644503075447 \cdot 10^{+144}:\\
\;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\

\mathbf{elif}\;b \le 1.739098950628615 \cdot 10^{-79}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a} - \frac{b}{a}}{2}\\

\mathbf{elif}\;b \le 1.8656332031849816 \cdot 10^{-25}:\\
\;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\

\mathbf{elif}\;b \le 5.297236684235463 \cdot 10^{-16}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a} - \frac{b}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r1597793 = b;
        double r1597794 = -r1597793;
        double r1597795 = r1597793 * r1597793;
        double r1597796 = 4.0;
        double r1597797 = a;
        double r1597798 = c;
        double r1597799 = r1597797 * r1597798;
        double r1597800 = r1597796 * r1597799;
        double r1597801 = r1597795 - r1597800;
        double r1597802 = sqrt(r1597801);
        double r1597803 = r1597794 + r1597802;
        double r1597804 = 2.0;
        double r1597805 = r1597804 * r1597797;
        double r1597806 = r1597803 / r1597805;
        return r1597806;
}

↓

double f(double a, double b, double c) {
        double r1597807 = b;
        double r1597808 = -1.6844644503075447e+144;
        bool r1597809 = r1597807 <= r1597808;
        double r1597810 = c;
        double r1597811 = r1597810 / r1597807;
        double r1597812 = a;
        double r1597813 = r1597807 / r1597812;
        double r1597814 = r1597811 - r1597813;
        double r1597815 = 2.0;
        double r1597816 = r1597814 * r1597815;
        double r1597817 = r1597816 / r1597815;
        double r1597818 = 1.739098950628615e-79;
        bool r1597819 = r1597807 <= r1597818;
        double r1597820 = r1597807 * r1597807;
        double r1597821 = 4.0;
        double r1597822 = r1597821 * r1597812;
        double r1597823 = r1597810 * r1597822;
        double r1597824 = r1597820 - r1597823;
        double r1597825 = sqrt(r1597824);
        double r1597826 = r1597825 / r1597812;
        double r1597827 = r1597826 - r1597813;
        double r1597828 = r1597827 / r1597815;
        double r1597829 = 1.8656332031849816e-25;
        bool r1597830 = r1597807 <= r1597829;
        double r1597831 = -2.0;
        double r1597832 = r1597831 * r1597811;
        double r1597833 = r1597832 / r1597815;
        double r1597834 = 5.297236684235463e-16;
        bool r1597835 = r1597807 <= r1597834;
        double r1597836 = r1597835 ? r1597828 : r1597833;
        double r1597837 = r1597830 ? r1597833 : r1597836;
        double r1597838 = r1597819 ? r1597828 : r1597837;
        double r1597839 = r1597809 ? r1597817 : r1597838;
        return r1597839;
}

Original	33.8
Target	20.3
Herbie	9.6

Derivation

Split input into 3 regimes
if b < -1.6844644503075447e+144
1. Initial program 58.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified58.0
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Taylor expanded around -inf 2.5
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
4. Simplified2.5
  \[\leadsto \frac{\color{blue}{2 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}}{2}\]
if -1.6844644503075447e+144 < b < 1.739098950628615e-79 or 1.8656332031849816e-25 < b < 5.297236684235463e-16
1. Initial program 12.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified12.3
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied div-sub12.3
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a} - \frac{b}{a}}}{2}\]
if 1.739098950628615e-79 < b < 1.8656332031849816e-25 or 5.297236684235463e-16 < b
1. Initial program 53.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified53.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Taylor expanded around inf 8.2
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification9.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.6844644503075447 \cdot 10^{+144}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.739098950628615 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a} - \frac{b}{a}}{2}\\ \mathbf{elif}\;b \le 1.8656332031849816 \cdot 10^{-25}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \mathbf{elif}\;b \le 5.297236684235463 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a} - \frac{b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.6844644503075447e+144`

`if -1.6844644503075447e+144 < b < 1.739098950628615e-79 or 1.8656332031849816e-25 < b < 5.297236684235463e-16`

`if 1.739098950628615e-79 < b < 1.8656332031849816e-25 or 5.297236684235463e-16 < b`

Reproduce

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