Average Error: 19.0 → 6.5
Time: 31.6s
Precision: 64
\[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \end{array}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -8.582957905450698 \cdot 10^{+153}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{2 \cdot \left(a \cdot \frac{c}{b} - b\right)}\\ \end{array}\\ \mathbf{elif}\;b \le 4.466989066425707 \cdot 10^{+89}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}} \cdot \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}\\ \end{array}\\ \mathbf{elif}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot \left(a \cdot \frac{c}{b} - b\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}\\ \end{array}\]
\begin{array}{l}
\mathbf{if}\;b \ge 0:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\

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

\end{array}
↓
\begin{array}{l}
\mathbf{if}\;b \le -8.582957905450698 \cdot 10^{+153}:\\
\;\;\;\;\begin{array}{l}
\mathbf{if}\;b \ge 0:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\

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

\end{array}\\

\mathbf{elif}\;b \le 4.466989066425707 \cdot 10^{+89}:\\
\;\;\;\;\begin{array}{l}
\mathbf{if}\;b \ge 0:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}} \cdot \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\

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

\end{array}\\

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

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

\end{array}
double f(double a, double b, double c) {
        double r1183893 = b;
        double r1183894 = 0.0;
        bool r1183895 = r1183893 >= r1183894;
        double r1183896 = -r1183893;
        double r1183897 = r1183893 * r1183893;
        double r1183898 = 4.0;
        double r1183899 = a;
        double r1183900 = r1183898 * r1183899;
        double r1183901 = c;
        double r1183902 = r1183900 * r1183901;
        double r1183903 = r1183897 - r1183902;
        double r1183904 = sqrt(r1183903);
        double r1183905 = r1183896 - r1183904;
        double r1183906 = 2.0;
        double r1183907 = r1183906 * r1183899;
        double r1183908 = r1183905 / r1183907;
        double r1183909 = r1183906 * r1183901;
        double r1183910 = r1183896 + r1183904;
        double r1183911 = r1183909 / r1183910;
        double r1183912 = r1183895 ? r1183908 : r1183911;
        return r1183912;
}
↓
double f(double a, double b, double c) {
        double r1183913 = b;
        double r1183914 = -8.582957905450698e+153;
        bool r1183915 = r1183913 <= r1183914;
        double r1183916 = 0.0;
        bool r1183917 = r1183913 >= r1183916;
        double r1183918 = -r1183913;
        double r1183919 = r1183913 * r1183913;
        double r1183920 = 4.0;
        double r1183921 = a;
        double r1183922 = r1183920 * r1183921;
        double r1183923 = c;
        double r1183924 = r1183922 * r1183923;
        double r1183925 = r1183919 - r1183924;
        double r1183926 = sqrt(r1183925);
        double r1183927 = r1183918 - r1183926;
        double r1183928 = 2.0;
        double r1183929 = r1183928 * r1183921;
        double r1183930 = r1183927 / r1183929;
        double r1183931 = r1183923 * r1183928;
        double r1183932 = r1183923 / r1183913;
        double r1183933 = r1183921 * r1183932;
        double r1183934 = r1183933 - r1183913;
        double r1183935 = r1183928 * r1183934;
        double r1183936 = r1183931 / r1183935;
        double r1183937 = r1183917 ? r1183930 : r1183936;
        double r1183938 = 4.466989066425707e+89;
        bool r1183939 = r1183913 <= r1183938;
        double r1183940 = sqrt(r1183926);
        double r1183941 = r1183940 * r1183940;
        double r1183942 = r1183918 - r1183941;
        double r1183943 = r1183942 / r1183929;
        double r1183944 = r1183926 + r1183918;
        double r1183945 = r1183931 / r1183944;
        double r1183946 = r1183917 ? r1183943 : r1183945;
        double r1183947 = r1183935 / r1183929;
        double r1183948 = r1183917 ? r1183947 : r1183945;
        double r1183949 = r1183939 ? r1183946 : r1183948;
        double r1183950 = r1183915 ? r1183937 : r1183949;
        return r1183950;
}

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 < -8.582957905450698e+153

    1. Initial program 37.8

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

    2. Taylor expanded around -inf 5.4

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

    3. Simplified1.0

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

    if -8.582957905450698e+153 < b < 4.466989066425707e+89

    1. Initial program 8.4

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

    3. Applied add-sqr-sqrt8.4

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

    4. Applied sqrt-prod8.5

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

    if 4.466989066425707e+89 < b

    1. Initial program 42.0

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

    3. Applied add-sqr-sqrt42.0

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

    4. Applied sqrt-prod42.1

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

    5. Taylor expanded around inf 9.6

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

    6. Simplified4.3

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

  4. Final simplification6.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -8.582957905450698 \cdot 10^{+153}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{2 \cdot \left(a \cdot \frac{c}{b} - b\right)}\\ \end{array}\\ \mathbf{elif}\;b \le 4.466989066425707 \cdot 10^{+89}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}} \cdot \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}\\ \end{array}\\ \mathbf{elif}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot \left(a \cdot \frac{c}{b} - b\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019107 
(FPCore (a b c)
  :name "jeff quadratic root 1"
  (if (>= b 0) (/ (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)) (/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))))))