Average Error: 34.3 → 10.4
Time: 5.0s
Precision: binary64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \leq -3.178178917587814 \cdot 10^{+151}:\\ \;\;\;\;\frac{c}{b} \cdot 0.5 - 0.6666666666666666 \cdot \frac{b}{a}\\ \mathbf{elif}\;b \leq 5.20071916789479 \cdot 10^{-20}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 3\right)} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -0.5\\ \end{array}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}
↓
\begin{array}{l}
\mathbf{if}\;b \leq -3.178178917587814 \cdot 10^{+151}:\\
\;\;\;\;\frac{c}{b} \cdot 0.5 - 0.6666666666666666 \cdot \frac{b}{a}\\

\mathbf{elif}\;b \leq 5.20071916789479 \cdot 10^{-20}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 3\right)} - b}{a \cdot 3}\\

\mathbf{else}:\\
\;\;\;\;\frac{c}{b} \cdot -0.5\\

\end{array}
double code(double a, double b, double c) {
	return (((double) (((double) -(b)) + ((double) sqrt(((double) (((double) (b * b)) - ((double) (((double) (3.0 * a)) * c)))))))) / ((double) (3.0 * a)));
}
↓
double code(double a, double b, double c) {
	double VAR;
	if ((b <= -3.178178917587814e+151)) {
		VAR = ((double) (((double) ((c / b) * 0.5)) - ((double) (0.6666666666666666 * (b / a)))));
	} else {
		double VAR_1;
		if ((b <= 5.20071916789479e-20)) {
			VAR_1 = (((double) (((double) sqrt(((double) (((double) (b * b)) - ((double) (c * ((double) (a * 3.0)))))))) - b)) / ((double) (a * 3.0)));
		} else {
			VAR_1 = ((double) ((c / b) * -0.5));
		}
		VAR = VAR_1;
	}
	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 < -3.17817891758781373e151

    1. Initial program 62.7

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]

    2. Taylor expanded around -inf 2.7

      \[\leadsto \color{blue}{0.5 \cdot \frac{c}{b} - 0.6666666666666666 \cdot \frac{b}{a}}\]

    3. Simplified2.7

      \[\leadsto \color{blue}{\frac{c}{b} \cdot 0.5 - 0.6666666666666666 \cdot \frac{b}{a}}\]

    if -3.17817891758781373e151 < b < 5.2007191678947901e-20

    1. Initial program 14.7

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]

    if 5.2007191678947901e-20 < b

    1. Initial program 54.8

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]

    2. Taylor expanded around inf 6.4

      \[\leadsto \color{blue}{-0.5 \cdot \frac{c}{b}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.178178917587814 \cdot 10^{+151}:\\ \;\;\;\;\frac{c}{b} \cdot 0.5 - 0.6666666666666666 \cdot \frac{b}{a}\\ \mathbf{elif}\;b \leq 5.20071916789479 \cdot 10^{-20}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 3\right)} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -0.5\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(FPCore (a b c)
  :name "Cubic critical"
  :precision binary64
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))