Average Error: 33.6 → 11.2
Time: 25.5s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.2890050783826923 \cdot 10^{-183}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 1.9396144761399596 \cdot 10^{+100}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]
\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 -1.2890050783826923 \cdot 10^{-183}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le 1.9396144761399596 \cdot 10^{+100}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r1615837 = b;
        double r1615838 = -r1615837;
        double r1615839 = r1615837 * r1615837;
        double r1615840 = 4.0;
        double r1615841 = a;
        double r1615842 = c;
        double r1615843 = r1615841 * r1615842;
        double r1615844 = r1615840 * r1615843;
        double r1615845 = r1615839 - r1615844;
        double r1615846 = sqrt(r1615845);
        double r1615847 = r1615838 - r1615846;
        double r1615848 = 2.0;
        double r1615849 = r1615848 * r1615841;
        double r1615850 = r1615847 / r1615849;
        return r1615850;
}
↓
double f(double a, double b, double c) {
        double r1615851 = b;
        double r1615852 = -1.2890050783826923e-183;
        bool r1615853 = r1615851 <= r1615852;
        double r1615854 = c;
        double r1615855 = r1615854 / r1615851;
        double r1615856 = -r1615855;
        double r1615857 = 1.9396144761399596e+100;
        bool r1615858 = r1615851 <= r1615857;
        double r1615859 = -r1615851;
        double r1615860 = r1615851 * r1615851;
        double r1615861 = a;
        double r1615862 = r1615854 * r1615861;
        double r1615863 = 4.0;
        double r1615864 = r1615862 * r1615863;
        double r1615865 = r1615860 - r1615864;
        double r1615866 = sqrt(r1615865);
        double r1615867 = r1615859 - r1615866;
        double r1615868 = 2.0;
        double r1615869 = r1615861 * r1615868;
        double r1615870 = r1615867 / r1615869;
        double r1615871 = r1615851 / r1615861;
        double r1615872 = r1615855 - r1615871;
        double r1615873 = r1615858 ? r1615870 : r1615872;
        double r1615874 = r1615853 ? r1615856 : r1615873;
        return r1615874;
}

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

Original33.6
Target20.5
Herbie11.2
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -1.2890050783826923e-183

    1. Initial program 48.2

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

    2. Taylor expanded around -inf 14.3

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

    3. Simplified14.3

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

    if -1.2890050783826923e-183 < b < 1.9396144761399596e+100

    1. Initial program 10.5

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

    2. Taylor expanded around 0 10.5

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

    3. Simplified10.5

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

    if 1.9396144761399596e+100 < b

    1. Initial program 44.2

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

    2. Taylor expanded around 0 44.2

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

    3. Simplified44.2

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

    5. Applied div-inv44.3

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

    6. Simplified44.3

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

    7. Taylor expanded around inf 3.4

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

  4. Final simplification11.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.2890050783826923 \cdot 10^{-183}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 1.9396144761399596 \cdot 10^{+100}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019151 
(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)))