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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -5.148407540792454 \cdot 10^{+110}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 2.326372645943808 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - \frac{b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c}{b} \cdot -2}{2}\\ \end{array}\]

\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 -5.148407540792454 \cdot 10^{+110}:\\
\;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\

\mathbf{elif}\;b \le 2.326372645943808 \cdot 10^{-74}:\\
\;\;\;\;\frac{\frac{1}{a} \cdot \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - \frac{b}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r1640919 = b;
        double r1640920 = -r1640919;
        double r1640921 = r1640919 * r1640919;
        double r1640922 = 4.0;
        double r1640923 = a;
        double r1640924 = r1640922 * r1640923;
        double r1640925 = c;
        double r1640926 = r1640924 * r1640925;
        double r1640927 = r1640921 - r1640926;
        double r1640928 = sqrt(r1640927);
        double r1640929 = r1640920 + r1640928;
        double r1640930 = 2.0;
        double r1640931 = r1640930 * r1640923;
        double r1640932 = r1640929 / r1640931;
        return r1640932;
}

↓

double f(double a, double b, double c) {
        double r1640933 = b;
        double r1640934 = -5.148407540792454e+110;
        bool r1640935 = r1640933 <= r1640934;
        double r1640936 = c;
        double r1640937 = r1640936 / r1640933;
        double r1640938 = a;
        double r1640939 = r1640933 / r1640938;
        double r1640940 = r1640937 - r1640939;
        double r1640941 = 2.0;
        double r1640942 = r1640940 * r1640941;
        double r1640943 = r1640942 / r1640941;
        double r1640944 = 2.326372645943808e-74;
        bool r1640945 = r1640933 <= r1640944;
        double r1640946 = 1.0;
        double r1640947 = r1640946 / r1640938;
        double r1640948 = r1640933 * r1640933;
        double r1640949 = 4.0;
        double r1640950 = r1640936 * r1640938;
        double r1640951 = r1640949 * r1640950;
        double r1640952 = r1640948 - r1640951;
        double r1640953 = sqrt(r1640952);
        double r1640954 = r1640947 * r1640953;
        double r1640955 = r1640954 - r1640939;
        double r1640956 = r1640955 / r1640941;
        double r1640957 = -2.0;
        double r1640958 = r1640937 * r1640957;
        double r1640959 = r1640958 / r1640941;
        double r1640960 = r1640945 ? r1640956 : r1640959;
        double r1640961 = r1640935 ? r1640943 : r1640960;
        return r1640961;
}

Original	33.4
Target	20.3
Herbie	9.9

Derivation

Split input into 3 regimes
if b < -5.148407540792454e+110
1. Initial program 46.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified46.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied div-sub46.9
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a} - \frac{b}{a}}}{2}\]
5. Taylor expanded around -inf 3.6
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
6. Simplified3.6
  \[\leadsto \frac{\color{blue}{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}}{2}\]
if -5.148407540792454e+110 < b < 2.326372645943808e-74
1. Initial program 12.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified12.7
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied div-sub12.7
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a} - \frac{b}{a}}}{2}\]
5. Using strategy rm
6. Applied div-inv12.8
  \[\leadsto \frac{\color{blue}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} \cdot \frac{1}{a}} - \frac{b}{a}}{2}\]
if 2.326372645943808e-74 < b
1. Initial program 52.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified52.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied div-sub53.2
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a} - \frac{b}{a}}}{2}\]
5. Using strategy rm
6. Applied div-inv54.1
  \[\leadsto \frac{\color{blue}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} \cdot \frac{1}{a}} - \frac{b}{a}}{2}\]
7. Taylor expanded around inf 8.8
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification9.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -5.148407540792454 \cdot 10^{+110}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 2.326372645943808 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - \frac{b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c}{b} \cdot -2}{2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -5.148407540792454e+110`

`if -5.148407540792454e+110 < b < 2.326372645943808e-74`

`if 2.326372645943808e-74 < b`

Reproduce

In
Out