Average Error: 33.1 → 10.3
Time: 18.1s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.1962309819144974 \cdot 10^{-65}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 5.6488521390017767 \cdot 10^{+48}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]
\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 -1.1962309819144974 \cdot 10^{-65}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le 5.6488521390017767 \cdot 10^{+48}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}}{a \cdot 2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r3003889 = b;
        double r3003890 = -r3003889;
        double r3003891 = r3003889 * r3003889;
        double r3003892 = 4.0;
        double r3003893 = a;
        double r3003894 = c;
        double r3003895 = r3003893 * r3003894;
        double r3003896 = r3003892 * r3003895;
        double r3003897 = r3003891 - r3003896;
        double r3003898 = sqrt(r3003897);
        double r3003899 = r3003890 - r3003898;
        double r3003900 = 2.0;
        double r3003901 = r3003900 * r3003893;
        double r3003902 = r3003899 / r3003901;
        return r3003902;
}
↓
double f(double a, double b, double c) {
        double r3003903 = b;
        double r3003904 = -1.1962309819144974e-65;
        bool r3003905 = r3003903 <= r3003904;
        double r3003906 = c;
        double r3003907 = r3003906 / r3003903;
        double r3003908 = -r3003907;
        double r3003909 = 5.6488521390017767e+48;
        bool r3003910 = r3003903 <= r3003909;
        double r3003911 = -r3003903;
        double r3003912 = a;
        double r3003913 = -4.0;
        double r3003914 = r3003912 * r3003913;
        double r3003915 = r3003914 * r3003906;
        double r3003916 = r3003903 * r3003903;
        double r3003917 = r3003915 + r3003916;
        double r3003918 = sqrt(r3003917);
        double r3003919 = r3003911 - r3003918;
        double r3003920 = 2.0;
        double r3003921 = r3003912 * r3003920;
        double r3003922 = r3003919 / r3003921;
        double r3003923 = r3003903 / r3003912;
        double r3003924 = r3003907 - r3003923;
        double r3003925 = r3003910 ? r3003922 : r3003924;
        double r3003926 = r3003905 ? r3003908 : r3003925;
        return r3003926;
}

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

Original33.1
Target20.3
Herbie10.3
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -1.1962309819144974e-65

    1. Initial program 52.3

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

    2. Taylor expanded around -inf 8.8

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

    3. Simplified8.8

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

    if -1.1962309819144974e-65 < b < 5.6488521390017767e+48

    1. Initial program 14.1

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

    3. Applied sub-neg14.1

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

    4. Simplified14.1

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

    if 5.6488521390017767e+48 < b

    1. Initial program 35.6

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

    2. Taylor expanded around inf 5.1

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

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.1962309819144974 \cdot 10^{-65}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 5.6488521390017767 \cdot 10^{+48}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (a b c)
  :name "The quadratic formula (r2)"

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

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