Average Error: 33.3 → 10.4
Time: 17.1s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -5.961198324014865 \cdot 10^{-88}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \le 6.384705165981893 \cdot 10^{+101}:\\ \;\;\;\;\frac{1}{\frac{2 \cdot a}{\left(-b\right) - \sqrt{b \cdot b + \left(-4 \cdot a\right) \cdot c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]
\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 -5.961198324014865 \cdot 10^{-88}:\\
\;\;\;\;\frac{-c}{b}\\

\mathbf{elif}\;b \le 6.384705165981893 \cdot 10^{+101}:\\
\;\;\;\;\frac{1}{\frac{2 \cdot a}{\left(-b\right) - \sqrt{b \cdot b + \left(-4 \cdot a\right) \cdot c}}}\\

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

\end{array}
double f(double a, double b, double c) {
        double r1451891 = b;
        double r1451892 = -r1451891;
        double r1451893 = r1451891 * r1451891;
        double r1451894 = 4.0;
        double r1451895 = a;
        double r1451896 = c;
        double r1451897 = r1451895 * r1451896;
        double r1451898 = r1451894 * r1451897;
        double r1451899 = r1451893 - r1451898;
        double r1451900 = sqrt(r1451899);
        double r1451901 = r1451892 - r1451900;
        double r1451902 = 2.0;
        double r1451903 = r1451902 * r1451895;
        double r1451904 = r1451901 / r1451903;
        return r1451904;
}
↓
double f(double a, double b, double c) {
        double r1451905 = b;
        double r1451906 = -5.961198324014865e-88;
        bool r1451907 = r1451905 <= r1451906;
        double r1451908 = c;
        double r1451909 = -r1451908;
        double r1451910 = r1451909 / r1451905;
        double r1451911 = 6.384705165981893e+101;
        bool r1451912 = r1451905 <= r1451911;
        double r1451913 = 1.0;
        double r1451914 = 2.0;
        double r1451915 = a;
        double r1451916 = r1451914 * r1451915;
        double r1451917 = -r1451905;
        double r1451918 = r1451905 * r1451905;
        double r1451919 = -4.0;
        double r1451920 = r1451919 * r1451915;
        double r1451921 = r1451920 * r1451908;
        double r1451922 = r1451918 + r1451921;
        double r1451923 = sqrt(r1451922);
        double r1451924 = r1451917 - r1451923;
        double r1451925 = r1451916 / r1451924;
        double r1451926 = r1451913 / r1451925;
        double r1451927 = r1451908 / r1451905;
        double r1451928 = r1451905 / r1451915;
        double r1451929 = r1451927 - r1451928;
        double r1451930 = r1451912 ? r1451926 : r1451929;
        double r1451931 = r1451907 ? r1451910 : r1451930;
        return r1451931;
}

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

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

Derivation

  1. Split input into 3 regimes

  2. if b < -5.961198324014865e-88

    1. Initial program 51.4

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

    2. Taylor expanded around -inf 9.8

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

    3. Simplified9.8

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

    if -5.961198324014865e-88 < b < 6.384705165981893e+101

    1. Initial program 13.1

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

    3. Applied clear-num13.3

      \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}\]
    4. Using strategy rm

    5. Applied sub-neg13.3

      \[\leadsto \frac{1}{\frac{2 \cdot a}{\left(-b\right) - \sqrt{\color{blue}{b \cdot b + \left(-4 \cdot \left(a \cdot c\right)\right)}}}}\]

    6. Simplified13.3

      \[\leadsto \frac{1}{\frac{2 \cdot a}{\left(-b\right) - \sqrt{b \cdot b + \color{blue}{\left(-4 \cdot a\right) \cdot c}}}}\]

    if 6.384705165981893e+101 < b

    1. Initial program 43.9

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

    2. Taylor expanded around inf 3.7

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

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -5.961198324014865 \cdot 10^{-88}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \le 6.384705165981893 \cdot 10^{+101}:\\ \;\;\;\;\frac{1}{\frac{2 \cdot a}{\left(-b\right) - \sqrt{b \cdot b + \left(-4 \cdot a\right) \cdot c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019154 
(FPCore (a b c)
  :name "quadm (p42, negative)"

  :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)))