Average Error: 34.2 → 9.5
Time: 22.1s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -3.710887557865060611891812934492943223731 \cdot 10^{138}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 4.626043257219637986942022736183111936335 \cdot 10^{-62}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]
\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 -3.710887557865060611891812934492943223731 \cdot 10^{138}:\\
\;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\

\mathbf{elif}\;b \le 4.626043257219637986942022736183111936335 \cdot 10^{-62}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}{a \cdot 2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r2649859 = b;
        double r2649860 = -r2649859;
        double r2649861 = r2649859 * r2649859;
        double r2649862 = 4.0;
        double r2649863 = a;
        double r2649864 = r2649862 * r2649863;
        double r2649865 = c;
        double r2649866 = r2649864 * r2649865;
        double r2649867 = r2649861 - r2649866;
        double r2649868 = sqrt(r2649867);
        double r2649869 = r2649860 + r2649868;
        double r2649870 = 2.0;
        double r2649871 = r2649870 * r2649863;
        double r2649872 = r2649869 / r2649871;
        return r2649872;
}
↓
double f(double a, double b, double c) {
        double r2649873 = b;
        double r2649874 = -3.7108875578650606e+138;
        bool r2649875 = r2649873 <= r2649874;
        double r2649876 = c;
        double r2649877 = r2649876 / r2649873;
        double r2649878 = a;
        double r2649879 = r2649873 / r2649878;
        double r2649880 = r2649877 - r2649879;
        double r2649881 = 1.0;
        double r2649882 = r2649880 * r2649881;
        double r2649883 = 4.626043257219638e-62;
        bool r2649884 = r2649873 <= r2649883;
        double r2649885 = r2649873 * r2649873;
        double r2649886 = 4.0;
        double r2649887 = r2649886 * r2649878;
        double r2649888 = r2649887 * r2649876;
        double r2649889 = r2649885 - r2649888;
        double r2649890 = sqrt(r2649889);
        double r2649891 = -r2649873;
        double r2649892 = r2649890 + r2649891;
        double r2649893 = 2.0;
        double r2649894 = r2649878 * r2649893;
        double r2649895 = r2649892 / r2649894;
        double r2649896 = -1.0;
        double r2649897 = r2649896 * r2649877;
        double r2649898 = r2649884 ? r2649895 : r2649897;
        double r2649899 = r2649875 ? r2649882 : r2649898;
        return r2649899;
}

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 < -3.7108875578650606e+138

    1. Initial program 58.5

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

    2. Taylor expanded around -inf 2.0

      \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]

    3. Simplified2.0

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

    if -3.7108875578650606e+138 < b < 4.626043257219638e-62

    1. Initial program 12.3

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

    if 4.626043257219638e-62 < b

    1. Initial program 53.7

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

    2. Taylor expanded around inf 8.5

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

  4. Final simplification9.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.710887557865060611891812934492943223731 \cdot 10^{138}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 4.626043257219637986942022736183111936335 \cdot 10^{-62}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (a b c)
  :name "Quadratic roots, full range"
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))