Average Error: 33.6 → 10.8
Time: 19.8s
Precision: 64
\[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b_2 \le -3.136683434005781 \cdot 10^{-32}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 2.0410715251838527 \cdot 10^{+49}:\\ \;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]
\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}
↓
\begin{array}{l}
\mathbf{if}\;b_2 \le -3.136683434005781 \cdot 10^{-32}:\\
\;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\

\mathbf{elif}\;b_2 \le 2.0410715251838527 \cdot 10^{+49}:\\
\;\;\;\;\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 r3192171 = b_2;
        double r3192172 = -r3192171;
        double r3192173 = r3192171 * r3192171;
        double r3192174 = a;
        double r3192175 = c;
        double r3192176 = r3192174 * r3192175;
        double r3192177 = r3192173 - r3192176;
        double r3192178 = sqrt(r3192177);
        double r3192179 = r3192172 - r3192178;
        double r3192180 = r3192179 / r3192174;
        return r3192180;
}
↓
double f(double a, double b_2, double c) {
        double r3192181 = b_2;
        double r3192182 = -3.136683434005781e-32;
        bool r3192183 = r3192181 <= r3192182;
        double r3192184 = -0.5;
        double r3192185 = c;
        double r3192186 = r3192185 / r3192181;
        double r3192187 = r3192184 * r3192186;
        double r3192188 = 2.0410715251838527e+49;
        bool r3192189 = r3192181 <= r3192188;
        double r3192190 = -r3192181;
        double r3192191 = r3192181 * r3192181;
        double r3192192 = a;
        double r3192193 = r3192192 * r3192185;
        double r3192194 = r3192191 - r3192193;
        double r3192195 = sqrt(r3192194);
        double r3192196 = r3192190 - r3192195;
        double r3192197 = r3192196 / r3192192;
        double r3192198 = 0.5;
        double r3192199 = r3192186 * r3192198;
        double r3192200 = 2.0;
        double r3192201 = r3192181 / r3192192;
        double r3192202 = r3192200 * r3192201;
        double r3192203 = r3192199 - r3192202;
        double r3192204 = r3192189 ? r3192197 : r3192203;
        double r3192205 = r3192183 ? r3192187 : r3192204;
        return r3192205;
}

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 < -3.136683434005781e-32

    1. Initial program 53.3

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

    2. Taylor expanded around -inf 7.3

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

    if -3.136683434005781e-32 < b_2 < 2.0410715251838527e+49

    1. Initial program 15.8

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

    if 2.0410715251838527e+49 < b_2

    1. Initial program 36.2

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

    2. Taylor expanded around inf 6.2

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

  4. Final simplification10.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b_2 \le -3.136683434005781 \cdot 10^{-32}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 2.0410715251838527 \cdot 10^{+49}:\\ \;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (a b_2 c)
  :name "NMSE problem 3.2.1"
  (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))