Average Error: 33.1 → 10.3
Time: 18.5s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.1962309819144974 \cdot 10^{-65}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 5.6488521390017767 \cdot 10^{+48}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]
\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 r3072779 = b;
        double r3072780 = -r3072779;
        double r3072781 = r3072779 * r3072779;
        double r3072782 = 4.0;
        double r3072783 = a;
        double r3072784 = c;
        double r3072785 = r3072783 * r3072784;
        double r3072786 = r3072782 * r3072785;
        double r3072787 = r3072781 - r3072786;
        double r3072788 = sqrt(r3072787);
        double r3072789 = r3072780 - r3072788;
        double r3072790 = 2.0;
        double r3072791 = r3072790 * r3072783;
        double r3072792 = r3072789 / r3072791;
        return r3072792;
}
↓
double f(double a, double b, double c) {
        double r3072793 = b;
        double r3072794 = -1.1962309819144974e-65;
        bool r3072795 = r3072793 <= r3072794;
        double r3072796 = c;
        double r3072797 = r3072796 / r3072793;
        double r3072798 = -r3072797;
        double r3072799 = 5.6488521390017767e+48;
        bool r3072800 = r3072793 <= r3072799;
        double r3072801 = -r3072793;
        double r3072802 = a;
        double r3072803 = -4.0;
        double r3072804 = r3072802 * r3072803;
        double r3072805 = r3072804 * r3072796;
        double r3072806 = r3072793 * r3072793;
        double r3072807 = r3072805 + r3072806;
        double r3072808 = sqrt(r3072807);
        double r3072809 = r3072801 - r3072808;
        double r3072810 = 2.0;
        double r3072811 = r3072802 * r3072810;
        double r3072812 = r3072809 / r3072811;
        double r3072813 = r3072793 / r3072802;
        double r3072814 = r3072797 - r3072813;
        double r3072815 = r3072800 ? r3072812 : r3072814;
        double r3072816 = r3072795 ? r3072798 : r3072815;
        return r3072816;
}

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 "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)))