Average Error: 33.2 → 9.9
Time: 16.8s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -4.600306435637794 \cdot 10^{+151}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 5.930445637544082 \cdot 10^{-86}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]
\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 -4.600306435637794 \cdot 10^{+151}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 5.930445637544082 \cdot 10^{-86}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r3492891 = b;
        double r3492892 = -r3492891;
        double r3492893 = r3492891 * r3492891;
        double r3492894 = 4.0;
        double r3492895 = a;
        double r3492896 = c;
        double r3492897 = r3492895 * r3492896;
        double r3492898 = r3492894 * r3492897;
        double r3492899 = r3492893 - r3492898;
        double r3492900 = sqrt(r3492899);
        double r3492901 = r3492892 + r3492900;
        double r3492902 = 2.0;
        double r3492903 = r3492902 * r3492895;
        double r3492904 = r3492901 / r3492903;
        return r3492904;
}
↓
double f(double a, double b, double c) {
        double r3492905 = b;
        double r3492906 = -4.600306435637794e+151;
        bool r3492907 = r3492905 <= r3492906;
        double r3492908 = c;
        double r3492909 = r3492908 / r3492905;
        double r3492910 = a;
        double r3492911 = r3492905 / r3492910;
        double r3492912 = r3492909 - r3492911;
        double r3492913 = 5.930445637544082e-86;
        bool r3492914 = r3492905 <= r3492913;
        double r3492915 = -r3492905;
        double r3492916 = r3492905 * r3492905;
        double r3492917 = r3492908 * r3492910;
        double r3492918 = 4.0;
        double r3492919 = r3492917 * r3492918;
        double r3492920 = r3492916 - r3492919;
        double r3492921 = sqrt(r3492920);
        double r3492922 = r3492915 + r3492921;
        double r3492923 = 2.0;
        double r3492924 = r3492910 * r3492923;
        double r3492925 = r3492922 / r3492924;
        double r3492926 = -r3492909;
        double r3492927 = r3492914 ? r3492925 : r3492926;
        double r3492928 = r3492907 ? r3492912 : r3492927;
        return r3492928;
}

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
Target20.6
Herbie9.9
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -4.600306435637794e+151

    1. Initial program 59.7

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

    2. Taylor expanded around -inf 2.2

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

    if -4.600306435637794e+151 < b < 5.930445637544082e-86

    1. Initial program 11.6

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

    if 5.930445637544082e-86 < b

    1. Initial program 52.2

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

    2. Taylor expanded around inf 9.9

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

    3. Simplified9.9

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

  4. Final simplification9.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.600306435637794 \cdot 10^{+151}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 5.930445637544082 \cdot 10^{-86}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(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)))