Average Error: 19.9 → 6.9
Time: 4.5s
Precision: binary64
\[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \end{array}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -4.6093372929168977 \cdot 10^{+136}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) + \left(2 \cdot \left(c \cdot \frac{a}{b}\right) - b\right)}\\ \end{array}\\ \mathbf{elif}\;b \le 2.26281686210341 \cdot 10^{+69}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{2}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}\\ \end{array}\\ \mathbf{elif}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot \left(c \cdot \frac{a}{b}\right) + b \cdot -2}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \end{array}\]
\begin{array}{l}
\mathbf{if}\;b \ge 0:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\

\mathbf{else}:\\
\;\;\;\;\frac{2 \cdot c}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\

\end{array}
↓
\begin{array}{l}
\mathbf{if}\;b \le -4.6093372929168977 \cdot 10^{+136}:\\
\;\;\;\;\begin{array}{l}
\mathbf{if}\;b \ge 0:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;\frac{c \cdot 2}{\left(-b\right) + \left(2 \cdot \left(c \cdot \frac{a}{b}\right) - b\right)}\\

\end{array}\\

\mathbf{elif}\;b \le 2.26281686210341 \cdot 10^{+69}:\\
\;\;\;\;\begin{array}{l}
\mathbf{if}\;b \ge 0:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;c \cdot \frac{2}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}\\

\end{array}\\

\mathbf{elif}\;b \ge 0:\\
\;\;\;\;\frac{2 \cdot \left(c \cdot \frac{a}{b}\right) + b \cdot -2}{a \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;\frac{c \cdot 2}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\

\end{array}
double code(double a, double b, double c) {
	double VAR;
	if ((b >= 0.0)) {
		VAR = ((double) (((double) (((double) -(b)) - ((double) sqrt(((double) (((double) (b * b)) - ((double) (((double) (4.0 * a)) * c)))))))) / ((double) (2.0 * a))));
	} else {
		VAR = ((double) (((double) (2.0 * c)) / ((double) (((double) -(b)) + ((double) sqrt(((double) (((double) (b * b)) - ((double) (((double) (4.0 * a)) * c))))))))));
	}
	return VAR;
}
↓
double code(double a, double b, double c) {
	double VAR;
	if ((b <= -4.6093372929168977e+136)) {
		double VAR_1;
		if ((b >= 0.0)) {
			VAR_1 = ((double) (((double) (((double) -(b)) - ((double) sqrt(((double) (((double) (b * b)) - ((double) (((double) (4.0 * a)) * c)))))))) / ((double) (a * 2.0))));
		} else {
			VAR_1 = ((double) (((double) (c * 2.0)) / ((double) (((double) -(b)) + ((double) (((double) (2.0 * ((double) (c * ((double) (a / b)))))) - b))))));
		}
		VAR = VAR_1;
	} else {
		double VAR_2;
		if ((b <= 2.26281686210341e+69)) {
			double VAR_3;
			if ((b >= 0.0)) {
				VAR_3 = ((double) (((double) (((double) -(b)) - ((double) sqrt(((double) (((double) (b * b)) - ((double) (4.0 * ((double) (a * c)))))))))) / ((double) (a * 2.0))));
			} else {
				VAR_3 = ((double) (c * ((double) (2.0 / ((double) (((double) sqrt(((double) (((double) (b * b)) - ((double) (4.0 * ((double) (a * c)))))))) - b))))));
			}
			VAR_2 = VAR_3;
		} else {
			double VAR_4;
			if ((b >= 0.0)) {
				VAR_4 = ((double) (((double) (((double) (2.0 * ((double) (c * ((double) (a / b)))))) + ((double) (b * -2.0)))) / ((double) (a * 2.0))));
			} else {
				VAR_4 = ((double) (((double) (c * 2.0)) / ((double) (((double) -(b)) + ((double) sqrt(((double) (((double) (b * b)) - ((double) (((double) (4.0 * a)) * c))))))))));
			}
			VAR_2 = VAR_4;
		}
		VAR = VAR_2;
	}
	return VAR;
}

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 < -4.60933729291689773e136

    1. Initial program 34.7

      \[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \end{array}\]

    2. Taylor expanded around -inf 5.8

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\color{blue}{\left(-b\right) + \left(2 \cdot \frac{a \cdot c}{b} - b\right)}}\\ \end{array}\]

    3. Simplified1.6

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\color{blue}{\left(-b\right) + \left(2 \cdot \left(c \cdot \frac{a}{b}\right) - b\right)}}\\ \end{array}\]

    if -4.60933729291689773e136 < b < 2.26281686210341001e69

    1. Initial program 9.1

      \[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \end{array}\]

    2. Simplified9.1

      \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{2}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}\\ \end{array}}\]

    if 2.26281686210341001e69 < b

    1. Initial program 40.9

      \[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \end{array}\]

    2. Taylor expanded around inf 10.5

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\color{blue}{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \end{array}\]

    3. Simplified4.8

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\color{blue}{2 \cdot \left(c \cdot \frac{a}{b}\right) + b \cdot -2}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \end{array}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification6.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.6093372929168977 \cdot 10^{+136}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) + \left(2 \cdot \left(c \cdot \frac{a}{b}\right) - b\right)}\\ \end{array}\\ \mathbf{elif}\;b \le 2.26281686210341 \cdot 10^{+69}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{2}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}\\ \end{array}\\ \mathbf{elif}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot \left(c \cdot \frac{a}{b}\right) + b \cdot -2}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (a b c)
  :name "jeff quadratic root 1"
  :precision binary64
  (if (>= b 0.0) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)) (/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))