Average Error: 32.5 → 10.2
Time: 28.7s
Precision: 64
\[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b_2 \le -1.2963906698702263 \cdot 10^{-56}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 9.735084379330809 \cdot 10^{+35}:\\ \;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]
\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}
↓
\begin{array}{l}
\mathbf{if}\;b_2 \le -1.2963906698702263 \cdot 10^{-56}:\\
\;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\

\mathbf{elif}\;b_2 \le 9.735084379330809 \cdot 10^{+35}:\\
\;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\

\mathbf{else}:\\
\;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\

\end{array}
double f(double a, double b_2, double c) {
        double r3852015 = b_2;
        double r3852016 = -r3852015;
        double r3852017 = r3852015 * r3852015;
        double r3852018 = a;
        double r3852019 = c;
        double r3852020 = r3852018 * r3852019;
        double r3852021 = r3852017 - r3852020;
        double r3852022 = sqrt(r3852021);
        double r3852023 = r3852016 - r3852022;
        double r3852024 = r3852023 / r3852018;
        return r3852024;
}
↓
double f(double a, double b_2, double c) {
        double r3852025 = b_2;
        double r3852026 = -1.2963906698702263e-56;
        bool r3852027 = r3852025 <= r3852026;
        double r3852028 = -0.5;
        double r3852029 = c;
        double r3852030 = r3852029 / r3852025;
        double r3852031 = r3852028 * r3852030;
        double r3852032 = 9.735084379330809e+35;
        bool r3852033 = r3852025 <= r3852032;
        double r3852034 = -r3852025;
        double r3852035 = r3852025 * r3852025;
        double r3852036 = a;
        double r3852037 = r3852036 * r3852029;
        double r3852038 = r3852035 - r3852037;
        double r3852039 = sqrt(r3852038);
        double r3852040 = r3852034 - r3852039;
        double r3852041 = r3852040 / r3852036;
        double r3852042 = 0.5;
        double r3852043 = r3852030 * r3852042;
        double r3852044 = 2.0;
        double r3852045 = r3852025 / r3852036;
        double r3852046 = r3852044 * r3852045;
        double r3852047 = r3852043 - r3852046;
        double r3852048 = r3852033 ? r3852041 : r3852047;
        double r3852049 = r3852027 ? r3852031 : r3852048;
        return r3852049;
}

Error

Bits error versus a

Bits error versus b_2

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if b_2 < -1.2963906698702263e-56

    1. Initial program 52.5

      \[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

    2. Taylor expanded around -inf 8.3

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{c}{b_2}}\]

    if -1.2963906698702263e-56 < b_2 < 9.735084379330809e+35

    1. Initial program 13.8

      \[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

    if 9.735084379330809e+35 < b_2

    1. Initial program 33.0

      \[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

    2. Taylor expanded around inf 6.6

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{c}{b_2} - 2 \cdot \frac{b_2}{a}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;b_2 \le -1.2963906698702263 \cdot 10^{-56}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 9.735084379330809 \cdot 10^{+35}:\\ \;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019149 
(FPCore (a b_2 c)
  :name "NMSE problem 3.2.1"
  (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))