Average Error: 33.6 → 10.8
Time: 21.7s
Precision: 64
\[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b_2 \le -3.136683434005781 \cdot 10^{-32}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 2.0410715251838527 \cdot 10^{+49}:\\ \;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]
\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 r2961420 = b_2;
        double r2961421 = -r2961420;
        double r2961422 = r2961420 * r2961420;
        double r2961423 = a;
        double r2961424 = c;
        double r2961425 = r2961423 * r2961424;
        double r2961426 = r2961422 - r2961425;
        double r2961427 = sqrt(r2961426);
        double r2961428 = r2961421 - r2961427;
        double r2961429 = r2961428 / r2961423;
        return r2961429;
}
↓
double f(double a, double b_2, double c) {
        double r2961430 = b_2;
        double r2961431 = -3.136683434005781e-32;
        bool r2961432 = r2961430 <= r2961431;
        double r2961433 = -0.5;
        double r2961434 = c;
        double r2961435 = r2961434 / r2961430;
        double r2961436 = r2961433 * r2961435;
        double r2961437 = 2.0410715251838527e+49;
        bool r2961438 = r2961430 <= r2961437;
        double r2961439 = -r2961430;
        double r2961440 = r2961430 * r2961430;
        double r2961441 = a;
        double r2961442 = r2961441 * r2961434;
        double r2961443 = r2961440 - r2961442;
        double r2961444 = sqrt(r2961443);
        double r2961445 = r2961439 - r2961444;
        double r2961446 = r2961445 / r2961441;
        double r2961447 = 0.5;
        double r2961448 = r2961435 * r2961447;
        double r2961449 = 2.0;
        double r2961450 = r2961430 / r2961441;
        double r2961451 = r2961449 * r2961450;
        double r2961452 = r2961448 - r2961451;
        double r2961453 = r2961438 ? r2961446 : r2961452;
        double r2961454 = r2961432 ? r2961436 : r2961453;
        return r2961454;
}

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))