Average Error: 19.0 → 7.1
Time: 18.9s
Precision: 64
\[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -8.715864899926357 \cdot 10^{+93}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \le 5.980436688116053 \cdot 10^{+94}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{\sqrt[3]{b \cdot b - c \cdot \left(a \cdot 4\right)} \cdot \sqrt[3]{b \cdot b - c \cdot \left(a \cdot 4\right)}} \cdot \sqrt{\sqrt[3]{b \cdot b - c \cdot \left(a \cdot 4\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} + \left(-b\right)}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b \cdot b - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} \cdot \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}}{a \cdot 2}\\ \end{array}\]
\begin{array}{l}
\mathbf{if}\;b \ge 0:\\
\;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\

\end{array}
↓
\begin{array}{l}
\mathbf{if}\;b \le -8.715864899926357 \cdot 10^{+93}:\\
\;\;\;\;\begin{array}{l}
\mathbf{if}\;b \ge 0:\\
\;\;\;\;\frac{2 \cdot c}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}{a \cdot 2}\\

\end{array}\\

\mathbf{elif}\;b \le 5.980436688116053 \cdot 10^{+94}:\\
\;\;\;\;\begin{array}{l}
\mathbf{if}\;b \ge 0:\\
\;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{\sqrt[3]{b \cdot b - c \cdot \left(a \cdot 4\right)} \cdot \sqrt[3]{b \cdot b - c \cdot \left(a \cdot 4\right)}} \cdot \sqrt{\sqrt[3]{b \cdot b - c \cdot \left(a \cdot 4\right)}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} + \left(-b\right)}{a \cdot 2}\\

\end{array}\\

\mathbf{elif}\;b \ge 0:\\
\;\;\;\;\frac{2 \cdot c}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{b \cdot b - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} \cdot \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}}{a \cdot 2}\\

\end{array}
double f(double a, double b, double c) {
        double r540015 = b;
        double r540016 = 0.0;
        bool r540017 = r540015 >= r540016;
        double r540018 = 2.0;
        double r540019 = c;
        double r540020 = r540018 * r540019;
        double r540021 = -r540015;
        double r540022 = r540015 * r540015;
        double r540023 = 4.0;
        double r540024 = a;
        double r540025 = r540023 * r540024;
        double r540026 = r540025 * r540019;
        double r540027 = r540022 - r540026;
        double r540028 = sqrt(r540027);
        double r540029 = r540021 - r540028;
        double r540030 = r540020 / r540029;
        double r540031 = r540021 + r540028;
        double r540032 = r540018 * r540024;
        double r540033 = r540031 / r540032;
        double r540034 = r540017 ? r540030 : r540033;
        return r540034;
}
↓
double f(double a, double b, double c) {
        double r540035 = b;
        double r540036 = -8.715864899926357e+93;
        bool r540037 = r540035 <= r540036;
        double r540038 = 0.0;
        bool r540039 = r540035 >= r540038;
        double r540040 = 2.0;
        double r540041 = c;
        double r540042 = r540040 * r540041;
        double r540043 = a;
        double r540044 = r540043 / r540035;
        double r540045 = r540044 * r540041;
        double r540046 = r540045 - r540035;
        double r540047 = r540040 * r540046;
        double r540048 = r540042 / r540047;
        double r540049 = r540035 / r540043;
        double r540050 = r540041 / r540049;
        double r540051 = r540050 - r540035;
        double r540052 = r540051 * r540040;
        double r540053 = r540043 * r540040;
        double r540054 = r540052 / r540053;
        double r540055 = r540039 ? r540048 : r540054;
        double r540056 = 5.980436688116053e+94;
        bool r540057 = r540035 <= r540056;
        double r540058 = -r540035;
        double r540059 = r540035 * r540035;
        double r540060 = 4.0;
        double r540061 = r540043 * r540060;
        double r540062 = r540041 * r540061;
        double r540063 = r540059 - r540062;
        double r540064 = cbrt(r540063);
        double r540065 = r540064 * r540064;
        double r540066 = sqrt(r540065);
        double r540067 = sqrt(r540064);
        double r540068 = r540066 * r540067;
        double r540069 = r540058 - r540068;
        double r540070 = r540042 / r540069;
        double r540071 = sqrt(r540063);
        double r540072 = r540071 + r540058;
        double r540073 = r540072 / r540053;
        double r540074 = r540039 ? r540070 : r540073;
        double r540075 = r540071 * r540071;
        double r540076 = r540059 - r540075;
        double r540077 = r540058 - r540071;
        double r540078 = r540076 / r540077;
        double r540079 = r540078 / r540053;
        double r540080 = r540039 ? r540048 : r540079;
        double r540081 = r540057 ? r540074 : r540080;
        double r540082 = r540037 ? r540055 : r540081;
        return r540082;
}

Error

Bits error versus a

Bits error versus b

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 < -8.715864899926357e+93

    1. Initial program 43.0

      \[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]

    2. Taylor expanded around inf 43.0

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\color{blue}{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]

    3. Simplified43.0

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\color{blue}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]

    4. Taylor expanded around -inf 10.6

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}{2 \cdot a}\\ \end{array}\]

    5. Simplified4.2

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}{2 \cdot a}\\ \end{array}\]

    if -8.715864899926357e+93 < b < 5.980436688116053e+94

    1. Initial program 9.2

      \[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt9.4

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{\color{blue}{\left(\sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]

    4. Applied sqrt-prod9.4

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \color{blue}{\sqrt{\sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c}} \cdot \sqrt{\sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]

    if 5.980436688116053e+94 < b

    1. Initial program 28.9

      \[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]

    2. Taylor expanded around inf 6.6

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\color{blue}{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]

    3. Simplified2.7

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\color{blue}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]
    4. Using strategy rm

    5. Applied flip-+2.7

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \end{array}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification7.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -8.715864899926357 \cdot 10^{+93}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \le 5.980436688116053 \cdot 10^{+94}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{\sqrt[3]{b \cdot b - c \cdot \left(a \cdot 4\right)} \cdot \sqrt[3]{b \cdot b - c \cdot \left(a \cdot 4\right)}} \cdot \sqrt{\sqrt[3]{b \cdot b - c \cdot \left(a \cdot 4\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} + \left(-b\right)}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b \cdot b - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} \cdot \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}}{a \cdot 2}\\ \end{array}\]

Reproduce

herbie shell --seed 2019133 
(FPCore (a b c)
  :name "jeff quadratic root 2"
  (if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))))