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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -9.348931433494438 \cdot 10^{+39}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 1.3353078790738604 \cdot 10^{-121}:\\ \;\;\;\;\frac{\sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b} - b}{\frac{a}{\frac{1}{2}}}\\ \mathbf{elif}\;b \le 1.6168702840263923 \cdot 10^{-79}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \le 1.546013236023957 \cdot 10^{-67}:\\ \;\;\;\;\frac{\sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b} - b}{\frac{a}{\frac{1}{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array}\]

\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 -9.348931433494438 \cdot 10^{+39}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 1.3353078790738604 \cdot 10^{-121}:\\
\;\;\;\;\frac{\sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b} - b}{\frac{a}{\frac{1}{2}}}\\

\mathbf{elif}\;b \le 1.6168702840263923 \cdot 10^{-79}:\\
\;\;\;\;\frac{-c}{b}\\

\mathbf{elif}\;b \le 1.546013236023957 \cdot 10^{-67}:\\
\;\;\;\;\frac{\sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b} - b}{\frac{a}{\frac{1}{2}}}\\

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

\end{array}

double f(double a, double b, double c) {
        double r6658960 = b;
        double r6658961 = -r6658960;
        double r6658962 = r6658960 * r6658960;
        double r6658963 = 4.0;
        double r6658964 = a;
        double r6658965 = r6658963 * r6658964;
        double r6658966 = c;
        double r6658967 = r6658965 * r6658966;
        double r6658968 = r6658962 - r6658967;
        double r6658969 = sqrt(r6658968);
        double r6658970 = r6658961 + r6658969;
        double r6658971 = 2.0;
        double r6658972 = r6658971 * r6658964;
        double r6658973 = r6658970 / r6658972;
        return r6658973;
}

↓

double f(double a, double b, double c) {
        double r6658974 = b;
        double r6658975 = -9.348931433494438e+39;
        bool r6658976 = r6658974 <= r6658975;
        double r6658977 = c;
        double r6658978 = r6658977 / r6658974;
        double r6658979 = a;
        double r6658980 = r6658974 / r6658979;
        double r6658981 = r6658978 - r6658980;
        double r6658982 = 1.3353078790738604e-121;
        bool r6658983 = r6658974 <= r6658982;
        double r6658984 = -4.0;
        double r6658985 = r6658979 * r6658984;
        double r6658986 = r6658985 * r6658977;
        double r6658987 = r6658974 * r6658974;
        double r6658988 = r6658986 + r6658987;
        double r6658989 = sqrt(r6658988);
        double r6658990 = r6658989 - r6658974;
        double r6658991 = 0.5;
        double r6658992 = r6658979 / r6658991;
        double r6658993 = r6658990 / r6658992;
        double r6658994 = 1.6168702840263923e-79;
        bool r6658995 = r6658974 <= r6658994;
        double r6658996 = -r6658977;
        double r6658997 = r6658996 / r6658974;
        double r6658998 = 1.546013236023957e-67;
        bool r6658999 = r6658974 <= r6658998;
        double r6659000 = r6658999 ? r6658993 : r6658997;
        double r6659001 = r6658995 ? r6658997 : r6659000;
        double r6659002 = r6658983 ? r6658993 : r6659001;
        double r6659003 = r6658976 ? r6658981 : r6659002;
        return r6659003;
}

Original	33.0
Target	20.1
Herbie	10.8

Derivation

Split input into 3 regimes
if b < -9.348931433494438e+39
1. Initial program 34.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around -inf 6.2
  \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]
if -9.348931433494438e+39 < b < 1.3353078790738604e-121 or 1.6168702840263923e-79 < b < 1.546013236023957e-67
1. Initial program 12.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv13.0
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Simplified13.0
  \[\leadsto \left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}}\]
5. Using strategy rm
6. Applied clear-num13.0
  \[\leadsto \left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \color{blue}{\frac{1}{\frac{a}{\frac{1}{2}}}}\]
7. Applied associate-*r/12.9
  \[\leadsto \color{blue}{\frac{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot 1}{\frac{a}{\frac{1}{2}}}}\]
8. Simplified12.9
  \[\leadsto \frac{\color{blue}{\sqrt{b \cdot b + \left(-4 \cdot a\right) \cdot c} - b}}{\frac{a}{\frac{1}{2}}}\]
if 1.3353078790738604e-121 < b < 1.6168702840263923e-79 or 1.546013236023957e-67 < b
1. Initial program 50.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 11.2
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
3. Simplified11.2
  \[\leadsto \color{blue}{\frac{-c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.8
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -9.348931433494438 \cdot 10^{+39}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 1.3353078790738604 \cdot 10^{-121}:\\ \;\;\;\;\frac{\sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b} - b}{\frac{a}{\frac{1}{2}}}\\ \mathbf{elif}\;b \le 1.6168702840263923 \cdot 10^{-79}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \le 1.546013236023957 \cdot 10^{-67}:\\ \;\;\;\;\frac{\sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b} - b}{\frac{a}{\frac{1}{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -9.348931433494438e+39`

`if -9.348931433494438e+39 < b < 1.3353078790738604e-121 or 1.6168702840263923e-79 < b < 1.546013236023957e-67`

`if 1.3353078790738604e-121 < b < 1.6168702840263923e-79 or 1.546013236023957e-67 < b`

Reproduce

In
Out