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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.006124725233072906597672755451758607334 \cdot 10^{153}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 5.668416736491797065158030167390678793472 \cdot 10^{-35}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2} - \frac{b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -1\\ \end{array}\]

\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 -1.006124725233072906597672755451758607334 \cdot 10^{153}:\\
\;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\

\mathbf{elif}\;b \le 5.668416736491797065158030167390678793472 \cdot 10^{-35}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2} - \frac{b}{a \cdot 2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r6107739 = b;
        double r6107740 = -r6107739;
        double r6107741 = r6107739 * r6107739;
        double r6107742 = 4.0;
        double r6107743 = a;
        double r6107744 = r6107742 * r6107743;
        double r6107745 = c;
        double r6107746 = r6107744 * r6107745;
        double r6107747 = r6107741 - r6107746;
        double r6107748 = sqrt(r6107747);
        double r6107749 = r6107740 + r6107748;
        double r6107750 = 2.0;
        double r6107751 = r6107750 * r6107743;
        double r6107752 = r6107749 / r6107751;
        return r6107752;
}

↓

double f(double a, double b, double c) {
        double r6107753 = b;
        double r6107754 = -1.0061247252330729e+153;
        bool r6107755 = r6107753 <= r6107754;
        double r6107756 = c;
        double r6107757 = r6107756 / r6107753;
        double r6107758 = a;
        double r6107759 = r6107753 / r6107758;
        double r6107760 = r6107757 - r6107759;
        double r6107761 = 1.0;
        double r6107762 = r6107760 * r6107761;
        double r6107763 = 5.668416736491797e-35;
        bool r6107764 = r6107753 <= r6107763;
        double r6107765 = r6107753 * r6107753;
        double r6107766 = 4.0;
        double r6107767 = r6107758 * r6107756;
        double r6107768 = r6107766 * r6107767;
        double r6107769 = r6107765 - r6107768;
        double r6107770 = sqrt(r6107769);
        double r6107771 = 2.0;
        double r6107772 = r6107758 * r6107771;
        double r6107773 = r6107770 / r6107772;
        double r6107774 = r6107753 / r6107772;
        double r6107775 = r6107773 - r6107774;
        double r6107776 = -1.0;
        double r6107777 = r6107757 * r6107776;
        double r6107778 = r6107764 ? r6107775 : r6107777;
        double r6107779 = r6107755 ? r6107762 : r6107778;
        return r6107779;
}

Original	34.0
Target	21.1
Herbie	10.2

Derivation

Split input into 3 regimes
if b < -1.0061247252330729e+153
1. Initial program 63.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv63.7
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Taylor expanded around -inf 2.0
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
5. Simplified2.0
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -1.0061247252330729e+153 < b < 5.668416736491797e-35
1. Initial program 13.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied clear-num14.1
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}\]
4. Simplified14.1
  \[\leadsto \frac{1}{\color{blue}{\frac{a \cdot 2}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}}}\]
5. Using strategy rm
6. Applied *-un-lft-identity14.1
  \[\leadsto \frac{1}{\color{blue}{1 \cdot \frac{a \cdot 2}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}}}\]
7. Applied add-cube-cbrt14.1
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{1 \cdot \frac{a \cdot 2}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}}\]
8. Applied times-frac14.1
  \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\sqrt[3]{1}}{\frac{a \cdot 2}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}}}\]
9. Simplified14.1
  \[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{a \cdot 2}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}}\]
10. Simplified13.9
  \[\leadsto 1 \cdot \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a \cdot 2}}\]
11. Using strategy rm
12. Applied div-sub14.0
  \[\leadsto 1 \cdot \color{blue}{\left(\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2} - \frac{b}{a \cdot 2}\right)}\]
if 5.668416736491797e-35 < b
1. Initial program 54.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 7.2
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.2
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.006124725233072906597672755451758607334 \cdot 10^{153}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 5.668416736491797065158030167390678793472 \cdot 10^{-35}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2} - \frac{b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -1\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.0061247252330729e+153`

`if -1.0061247252330729e+153 < b < 5.668416736491797e-35`

`if 5.668416736491797e-35 < b`

Reproduce

In
Out