Average Error: 18.9 → 6.6
Time: 42.5s
Precision: 64
\[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \end{array}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.6509659704621613 \cdot 10^{+43}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}} \cdot \sqrt{\left|\sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c}\right| \cdot \sqrt{\sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\left(\frac{c}{b} \cdot a - b\right) \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \le 7.356079352631206 \cdot 10^{+120}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)} \cdot \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}}\\ \end{array}\\ \mathbf{elif}\;b \ge 0:\\ \;\;\;\;\frac{\left(\frac{c}{b} \cdot a - b\right) \cdot 2}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}\\ \end{array}\]
\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 -1.6509659704621613 \cdot 10^{+43}:\\
\;\;\;\;\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{\left|\sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c}\right| \cdot \sqrt{\sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}{a \cdot 2}\\

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

\end{array}\\

\mathbf{elif}\;b \le 7.356079352631206 \cdot 10^{+120}:\\
\;\;\;\;\begin{array}{l}
\mathbf{if}\;b \ge 0:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}\\

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

\end{array}\\

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

\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 r2062774 = b;
        double r2062775 = 0.0;
        bool r2062776 = r2062774 >= r2062775;
        double r2062777 = -r2062774;
        double r2062778 = r2062774 * r2062774;
        double r2062779 = 4.0;
        double r2062780 = a;
        double r2062781 = r2062779 * r2062780;
        double r2062782 = c;
        double r2062783 = r2062781 * r2062782;
        double r2062784 = r2062778 - r2062783;
        double r2062785 = sqrt(r2062784);
        double r2062786 = r2062777 - r2062785;
        double r2062787 = 2.0;
        double r2062788 = r2062787 * r2062780;
        double r2062789 = r2062786 / r2062788;
        double r2062790 = r2062787 * r2062782;
        double r2062791 = r2062777 + r2062785;
        double r2062792 = r2062790 / r2062791;
        double r2062793 = r2062776 ? r2062789 : r2062792;
        return r2062793;
}
↓
double f(double a, double b, double c) {
        double r2062794 = b;
        double r2062795 = -1.6509659704621613e+43;
        bool r2062796 = r2062794 <= r2062795;
        double r2062797 = 0.0;
        bool r2062798 = r2062794 >= r2062797;
        double r2062799 = -r2062794;
        double r2062800 = r2062794 * r2062794;
        double r2062801 = 4.0;
        double r2062802 = a;
        double r2062803 = r2062801 * r2062802;
        double r2062804 = c;
        double r2062805 = r2062803 * r2062804;
        double r2062806 = r2062800 - r2062805;
        double r2062807 = sqrt(r2062806);
        double r2062808 = sqrt(r2062807);
        double r2062809 = cbrt(r2062806);
        double r2062810 = fabs(r2062809);
        double r2062811 = sqrt(r2062809);
        double r2062812 = r2062810 * r2062811;
        double r2062813 = sqrt(r2062812);
        double r2062814 = r2062808 * r2062813;
        double r2062815 = r2062799 - r2062814;
        double r2062816 = 2.0;
        double r2062817 = r2062802 * r2062816;
        double r2062818 = r2062815 / r2062817;
        double r2062819 = r2062804 * r2062816;
        double r2062820 = r2062804 / r2062794;
        double r2062821 = r2062820 * r2062802;
        double r2062822 = r2062821 - r2062794;
        double r2062823 = r2062822 * r2062816;
        double r2062824 = r2062819 / r2062823;
        double r2062825 = r2062798 ? r2062818 : r2062824;
        double r2062826 = 7.356079352631206e+120;
        bool r2062827 = r2062794 <= r2062826;
        double r2062828 = r2062799 - r2062807;
        double r2062829 = r2062828 / r2062817;
        double r2062830 = r2062807 + r2062799;
        double r2062831 = sqrt(r2062830);
        double r2062832 = r2062831 * r2062831;
        double r2062833 = r2062819 / r2062832;
        double r2062834 = r2062798 ? r2062829 : r2062833;
        double r2062835 = r2062823 / r2062817;
        double r2062836 = r2062819 / r2062830;
        double r2062837 = r2062798 ? r2062835 : r2062836;
        double r2062838 = r2062827 ? r2062834 : r2062837;
        double r2062839 = r2062796 ? r2062825 : r2062838;
        return r2062839;
}

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 < -1.6509659704621613e+43

    1. Initial program 23.7

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

    2. Taylor expanded around -inf 6.9

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

    3. Simplified4.0

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

    5. Applied add-sqr-sqrt4.0

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

    7. Applied add-cube-cbrt4.0

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

    8. Applied sqrt-prod4.0

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

    9. Simplified4.0

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

    if -1.6509659704621613e+43 < b < 7.356079352631206e+120

    1. Initial program 8.5

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

    3. Applied add-sqr-sqrt8.7

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

    if 7.356079352631206e+120 < b

    1. Initial program 51.6

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

    2. Taylor expanded around inf 10.5

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

    3. Simplified3.6

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

  4. Final simplification6.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.6509659704621613 \cdot 10^{+43}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}} \cdot \sqrt{\left|\sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c}\right| \cdot \sqrt{\sqrt[3]{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\left(\frac{c}{b} \cdot a - b\right) \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \le 7.356079352631206 \cdot 10^{+120}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)} \cdot \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}}\\ \end{array}\\ \mathbf{elif}\;b \ge 0:\\ \;\;\;\;\frac{\left(\frac{c}{b} \cdot a - b\right) \cdot 2}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019119 
(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)))))))