Average Error: 34.5 → 10.3
Time: 15.7s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -63362873442066488610789523456:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 6.484072051994263737451444554171174935457 \cdot 10^{-107}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\begin{array}{l}
\mathbf{if}\;b \le -63362873442066488610789523456:\\
\;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\

\mathbf{elif}\;b \le 6.484072051994263737451444554171174935457 \cdot 10^{-107}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}{a \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;-1 \cdot \frac{c}{b}\\

\end{array}
double f(double a, double b, double c) {
        double r2037392 = b;
        double r2037393 = -r2037392;
        double r2037394 = r2037392 * r2037392;
        double r2037395 = 4.0;
        double r2037396 = a;
        double r2037397 = r2037395 * r2037396;
        double r2037398 = c;
        double r2037399 = r2037397 * r2037398;
        double r2037400 = r2037394 - r2037399;
        double r2037401 = sqrt(r2037400);
        double r2037402 = r2037393 + r2037401;
        double r2037403 = 2.0;
        double r2037404 = r2037403 * r2037396;
        double r2037405 = r2037402 / r2037404;
        return r2037405;
}
↓
double f(double a, double b, double c) {
        double r2037406 = b;
        double r2037407 = -6.336287344206649e+28;
        bool r2037408 = r2037406 <= r2037407;
        double r2037409 = c;
        double r2037410 = r2037409 / r2037406;
        double r2037411 = a;
        double r2037412 = r2037406 / r2037411;
        double r2037413 = r2037410 - r2037412;
        double r2037414 = 1.0;
        double r2037415 = r2037413 * r2037414;
        double r2037416 = 6.484072051994264e-107;
        bool r2037417 = r2037406 <= r2037416;
        double r2037418 = r2037406 * r2037406;
        double r2037419 = 4.0;
        double r2037420 = r2037419 * r2037411;
        double r2037421 = r2037420 * r2037409;
        double r2037422 = r2037418 - r2037421;
        double r2037423 = sqrt(r2037422);
        double r2037424 = -r2037406;
        double r2037425 = r2037423 + r2037424;
        double r2037426 = 2.0;
        double r2037427 = r2037411 * r2037426;
        double r2037428 = r2037425 / r2037427;
        double r2037429 = -1.0;
        double r2037430 = r2037429 * r2037410;
        double r2037431 = r2037417 ? r2037428 : r2037430;
        double r2037432 = r2037408 ? r2037415 : r2037431;
        return r2037432;
}

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

Derivation

  1. Split input into 3 regimes

  2. if b < -6.336287344206649e+28

    1. Initial program 34.8

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

    2. Taylor expanded around -inf 7.0

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

    3. Simplified7.0

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

    if -6.336287344206649e+28 < b < 6.484072051994264e-107

    1. Initial program 12.9

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

    if 6.484072051994264e-107 < b

    1. Initial program 52.5

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

    2. Taylor expanded around inf 9.7

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

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -63362873442066488610789523456:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 6.484072051994263737451444554171174935457 \cdot 10^{-107}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \left(-b\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (a b c)
  :name "Quadratic roots, full range"
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))