Average Error: 33.3 → 8.6
Time: 24.4s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -4.82289647433212 \cdot 10^{+153}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 3.1232170674377175 \cdot 10^{-242}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a \cdot 2}\\ \mathbf{elif}\;b \le 1.3233344071163898 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{\left(b \cdot b - b \cdot b\right) + c \cdot \left(4 \cdot a\right)}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]
\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 -4.82289647433212 \cdot 10^{+153}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 3.1232170674377175 \cdot 10^{-242}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a \cdot 2}\\

\mathbf{elif}\;b \le 1.3233344071163898 \cdot 10^{+19}:\\
\;\;\;\;\frac{\frac{\left(b \cdot b - b \cdot b\right) + c \cdot \left(4 \cdot a\right)}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}}{a \cdot 2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r1684933 = b;
        double r1684934 = -r1684933;
        double r1684935 = r1684933 * r1684933;
        double r1684936 = 4.0;
        double r1684937 = a;
        double r1684938 = r1684936 * r1684937;
        double r1684939 = c;
        double r1684940 = r1684938 * r1684939;
        double r1684941 = r1684935 - r1684940;
        double r1684942 = sqrt(r1684941);
        double r1684943 = r1684934 + r1684942;
        double r1684944 = 2.0;
        double r1684945 = r1684944 * r1684937;
        double r1684946 = r1684943 / r1684945;
        return r1684946;
}
↓
double f(double a, double b, double c) {
        double r1684947 = b;
        double r1684948 = -4.82289647433212e+153;
        bool r1684949 = r1684947 <= r1684948;
        double r1684950 = c;
        double r1684951 = r1684950 / r1684947;
        double r1684952 = a;
        double r1684953 = r1684947 / r1684952;
        double r1684954 = r1684951 - r1684953;
        double r1684955 = 3.1232170674377175e-242;
        bool r1684956 = r1684947 <= r1684955;
        double r1684957 = -r1684947;
        double r1684958 = r1684947 * r1684947;
        double r1684959 = 4.0;
        double r1684960 = r1684959 * r1684952;
        double r1684961 = r1684950 * r1684960;
        double r1684962 = r1684958 - r1684961;
        double r1684963 = sqrt(r1684962);
        double r1684964 = r1684957 + r1684963;
        double r1684965 = 2.0;
        double r1684966 = r1684952 * r1684965;
        double r1684967 = r1684964 / r1684966;
        double r1684968 = 1.3233344071163898e+19;
        bool r1684969 = r1684947 <= r1684968;
        double r1684970 = r1684958 - r1684958;
        double r1684971 = r1684970 + r1684961;
        double r1684972 = r1684957 - r1684963;
        double r1684973 = r1684971 / r1684972;
        double r1684974 = r1684973 / r1684966;
        double r1684975 = -r1684951;
        double r1684976 = r1684969 ? r1684974 : r1684975;
        double r1684977 = r1684956 ? r1684967 : r1684976;
        double r1684978 = r1684949 ? r1684954 : r1684977;
        return r1684978;
}

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 4 regimes

  2. if b < -4.82289647433212e+153

    1. Initial program 60.9

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

    2. Taylor expanded around -inf 2.3

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

    if -4.82289647433212e+153 < b < 3.1232170674377175e-242

    1. Initial program 9.2

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

    if 3.1232170674377175e-242 < b < 1.3233344071163898e+19

    1. Initial program 28.7

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

    3. Applied flip-+28.9

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

    4. Simplified17.4

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

    if 1.3233344071163898e+19 < b

    1. Initial program 55.3

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

    2. Taylor expanded around inf 4.8

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

    3. Simplified4.8

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

  4. Final simplification8.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.82289647433212 \cdot 10^{+153}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 3.1232170674377175 \cdot 10^{-242}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a \cdot 2}\\ \mathbf{elif}\;b \le 1.3233344071163898 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{\left(b \cdot b - b \cdot b\right) + c \cdot \left(4 \cdot a\right)}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019142 
(FPCore (a b c)
  :name "Quadratic roots, full range"
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))