Average Error: 34.2 → 10.0
Time: 16.4s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
\[\begin{array}{l} \mathbf{if}\;b \le -2.940001550635406357572527191036557327772 \cdot 10^{93}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 2.592868408155405548302080990651854167189 \cdot 10^{-64}:\\ \;\;\;\;\left(\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b\right) \cdot \frac{1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -1\\ \end{array}\]
\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 -2.940001550635406357572527191036557327772 \cdot 10^{93}:\\
\;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\

\mathbf{elif}\;b \le 2.592868408155405548302080990651854167189 \cdot 10^{-64}:\\
\;\;\;\;\left(\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b\right) \cdot \frac{1}{a \cdot 2}\\

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

\end{array}
double f(double b, double a, double c) {
        double r23227984 = b;
        double r23227985 = -r23227984;
        double r23227986 = r23227984 * r23227984;
        double r23227987 = 4.0;
        double r23227988 = a;
        double r23227989 = r23227987 * r23227988;
        double r23227990 = c;
        double r23227991 = r23227989 * r23227990;
        double r23227992 = r23227986 - r23227991;
        double r23227993 = sqrt(r23227992);
        double r23227994 = r23227985 + r23227993;
        double r23227995 = 2.0;
        double r23227996 = r23227995 * r23227988;
        double r23227997 = r23227994 / r23227996;
        return r23227997;
}

double f(double b, double a, double c) {
        double r23227998 = b;
        double r23227999 = -2.9400015506354064e+93;
        bool r23228000 = r23227998 <= r23227999;
        double r23228001 = c;
        double r23228002 = r23228001 / r23227998;
        double r23228003 = a;
        double r23228004 = r23227998 / r23228003;
        double r23228005 = r23228002 - r23228004;
        double r23228006 = 1.0;
        double r23228007 = r23228005 * r23228006;
        double r23228008 = 2.5928684081554055e-64;
        bool r23228009 = r23227998 <= r23228008;
        double r23228010 = r23227998 * r23227998;
        double r23228011 = 4.0;
        double r23228012 = r23228001 * r23228003;
        double r23228013 = r23228011 * r23228012;
        double r23228014 = r23228010 - r23228013;
        double r23228015 = sqrt(r23228014);
        double r23228016 = r23228015 - r23227998;
        double r23228017 = 1.0;
        double r23228018 = 2.0;
        double r23228019 = r23228003 * r23228018;
        double r23228020 = r23228017 / r23228019;
        double r23228021 = r23228016 * r23228020;
        double r23228022 = -1.0;
        double r23228023 = r23228002 * r23228022;
        double r23228024 = r23228009 ? r23228021 : r23228023;
        double r23228025 = r23228000 ? r23228007 : r23228024;
        return r23228025;
}

Error

Bits error versus b

Bits error versus a

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes
  2. if b < -2.9400015506354064e+93

    1. Initial program 45.8

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
    2. Simplified45.8

      \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a \cdot 2}}\]
    3. Taylor expanded around -inf 3.3

      \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
    4. Simplified3.3

      \[\leadsto \color{blue}{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1}\]

    if -2.9400015506354064e+93 < b < 2.5928684081554055e-64

    1. Initial program 13.0

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
    2. Simplified13.0

      \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a \cdot 2}}\]
    3. Using strategy rm
    4. Applied clear-num13.1

      \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}\]
    5. Using strategy rm
    6. Applied associate-/r/13.1

      \[\leadsto \color{blue}{\frac{1}{a \cdot 2} \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b\right)}\]

    if 2.5928684081554055e-64 < b

    1. Initial program 53.6

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
    2. Simplified53.6

      \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a \cdot 2}}\]
    3. Taylor expanded around inf 9.2

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
  3. Recombined 3 regimes into one program.
  4. Final simplification10.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.940001550635406357572527191036557327772 \cdot 10^{93}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 2.592868408155405548302080990651854167189 \cdot 10^{-64}:\\ \;\;\;\;\left(\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b\right) \cdot \frac{1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -1\\ \end{array}\]

Reproduce

herbie shell --seed 1 
(FPCore (b a c)
  :name "((-b)+sqrt(b*b-4*a*c))/(2*a)"
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))