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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -9.088000531423294 \cdot 10^{+152}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 9.354082991670835 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a}}{2} - \frac{\frac{b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

\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 -9.088000531423294 \cdot 10^{+152}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 9.354082991670835 \cdot 10^{-125}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a}}{2} - \frac{\frac{b}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r1647009 = b;
        double r1647010 = -r1647009;
        double r1647011 = r1647009 * r1647009;
        double r1647012 = 4.0;
        double r1647013 = a;
        double r1647014 = r1647012 * r1647013;
        double r1647015 = c;
        double r1647016 = r1647014 * r1647015;
        double r1647017 = r1647011 - r1647016;
        double r1647018 = sqrt(r1647017);
        double r1647019 = r1647010 + r1647018;
        double r1647020 = 2.0;
        double r1647021 = r1647020 * r1647013;
        double r1647022 = r1647019 / r1647021;
        return r1647022;
}

↓

double f(double a, double b, double c) {
        double r1647023 = b;
        double r1647024 = -9.088000531423294e+152;
        bool r1647025 = r1647023 <= r1647024;
        double r1647026 = c;
        double r1647027 = r1647026 / r1647023;
        double r1647028 = a;
        double r1647029 = r1647023 / r1647028;
        double r1647030 = r1647027 - r1647029;
        double r1647031 = 9.354082991670835e-125;
        bool r1647032 = r1647023 <= r1647031;
        double r1647033 = r1647023 * r1647023;
        double r1647034 = r1647026 * r1647028;
        double r1647035 = 4.0;
        double r1647036 = r1647034 * r1647035;
        double r1647037 = r1647033 - r1647036;
        double r1647038 = sqrt(r1647037);
        double r1647039 = r1647038 / r1647028;
        double r1647040 = 2.0;
        double r1647041 = r1647039 / r1647040;
        double r1647042 = r1647029 / r1647040;
        double r1647043 = r1647041 - r1647042;
        double r1647044 = -r1647027;
        double r1647045 = r1647032 ? r1647043 : r1647044;
        double r1647046 = r1647025 ? r1647030 : r1647045;
        return r1647046;
}

Original	32.9
Target	20.3
Herbie	10.3

Derivation

Split input into 3 regimes
if b < -9.088000531423294e+152
1. Initial program 60.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified60.4
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied *-un-lft-identity60.4
  \[\leadsto \frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a}}{\color{blue}{1 \cdot 2}}\]
5. Applied div-inv60.4
  \[\leadsto \frac{\color{blue}{\left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b\right) \cdot \frac{1}{a}}}{1 \cdot 2}\]
6. Applied times-frac60.4
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{1} \cdot \frac{\frac{1}{a}}{2}}\]
7. Simplified60.4
  \[\leadsto \color{blue}{\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right)} \cdot \frac{\frac{1}{a}}{2}\]
8. Taylor expanded around -inf 1.5
  \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]
if -9.088000531423294e+152 < b < 9.354082991670835e-125
1. Initial program 10.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified10.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied div-sub10.9
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a} - \frac{b}{a}}}{2}\]
5. Applied div-sub10.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a}}{2} - \frac{\frac{b}{a}}{2}}\]
if 9.354082991670835e-125 < b
1. Initial program 49.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified49.8
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied *-un-lft-identity49.8
  \[\leadsto \frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a}}{\color{blue}{1 \cdot 2}}\]
5. Applied div-inv49.8
  \[\leadsto \frac{\color{blue}{\left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b\right) \cdot \frac{1}{a}}}{1 \cdot 2}\]
6. Applied times-frac49.8
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{1} \cdot \frac{\frac{1}{a}}{2}}\]
7. Simplified49.8
  \[\leadsto \color{blue}{\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right)} \cdot \frac{\frac{1}{a}}{2}\]
8. Taylor expanded around inf 11.9
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
9. Simplified11.9
  \[\leadsto \color{blue}{-\frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -9.088000531423294 \cdot 10^{+152}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 9.354082991670835 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a}}{2} - \frac{\frac{b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -9.088000531423294e+152`

`if -9.088000531423294e+152 < b < 9.354082991670835e-125`

`if 9.354082991670835e-125 < b`

Reproduce

In
Out