Average Error: 33.2 → 10.4
Time: 23.4s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -5.571206846913461 \cdot 10^{+106}:\\ \;\;\;\;\frac{\left(2 \cdot \frac{c}{b} - \frac{b}{a}\right) - \frac{b}{a}}{2}\\ \mathbf{elif}\;b \le 3.821014310434392 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a} - \frac{b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}
↓
\begin{array}{l}
\mathbf{if}\;b \le -5.571206846913461 \cdot 10^{+106}:\\
\;\;\;\;\frac{\left(2 \cdot \frac{c}{b} - \frac{b}{a}\right) - \frac{b}{a}}{2}\\

\mathbf{elif}\;b \le 3.821014310434392 \cdot 10^{-21}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a} - \frac{b}{a}}{2}\\

\mathbf{else}:\\
\;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\

\end{array}
double f(double a, double b, double c) {
        double r2302879 = b;
        double r2302880 = -r2302879;
        double r2302881 = r2302879 * r2302879;
        double r2302882 = 4.0;
        double r2302883 = a;
        double r2302884 = c;
        double r2302885 = r2302883 * r2302884;
        double r2302886 = r2302882 * r2302885;
        double r2302887 = r2302881 - r2302886;
        double r2302888 = sqrt(r2302887);
        double r2302889 = r2302880 + r2302888;
        double r2302890 = 2.0;
        double r2302891 = r2302890 * r2302883;
        double r2302892 = r2302889 / r2302891;
        return r2302892;
}
↓
double f(double a, double b, double c) {
        double r2302893 = b;
        double r2302894 = -5.571206846913461e+106;
        bool r2302895 = r2302893 <= r2302894;
        double r2302896 = 2.0;
        double r2302897 = c;
        double r2302898 = r2302897 / r2302893;
        double r2302899 = r2302896 * r2302898;
        double r2302900 = a;
        double r2302901 = r2302893 / r2302900;
        double r2302902 = r2302899 - r2302901;
        double r2302903 = r2302902 - r2302901;
        double r2302904 = r2302903 / r2302896;
        double r2302905 = 3.821014310434392e-21;
        bool r2302906 = r2302893 <= r2302905;
        double r2302907 = r2302893 * r2302893;
        double r2302908 = 4.0;
        double r2302909 = r2302908 * r2302900;
        double r2302910 = r2302909 * r2302897;
        double r2302911 = r2302907 - r2302910;
        double r2302912 = sqrt(r2302911);
        double r2302913 = r2302912 / r2302900;
        double r2302914 = r2302913 - r2302901;
        double r2302915 = r2302914 / r2302896;
        double r2302916 = -2.0;
        double r2302917 = r2302916 * r2302898;
        double r2302918 = r2302917 / r2302896;
        double r2302919 = r2302906 ? r2302915 : r2302918;
        double r2302920 = r2302895 ? r2302904 : r2302919;
        return r2302920;
}

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

Target

Original33.2
Target20.4
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -5.571206846913461e+106

    1. Initial program 46.5

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

    2. Simplified46.5

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

    4. Applied div-sub46.5

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

    5. Taylor expanded around -inf 3.5

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

    if -5.571206846913461e+106 < b < 3.821014310434392e-21

    1. Initial program 14.8

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

    2. Simplified14.8

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

    4. Applied div-sub14.8

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

    if 3.821014310434392e-21 < b

    1. Initial program 54.7

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

    2. Simplified54.7

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

    4. Applied div-sub55.4

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

    5. Taylor expanded around inf 6.8

      \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -5.571206846913461 \cdot 10^{+106}:\\ \;\;\;\;\frac{\left(2 \cdot \frac{c}{b} - \frac{b}{a}\right) - \frac{b}{a}}{2}\\ \mathbf{elif}\;b \le 3.821014310434392 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a} - \frac{b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Reproduce

herbie shell --seed 2019149 
(FPCore (a b c)
  :name "quadp (p42, positive)"

  :herbie-target
  (if (< b 0) (/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)) (/ c (* a (/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))))

  (/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))