jeff quadratic root 2

Average Error: 19.6 → 7.4

Time: 31.2s

Precision: binary64

Cost: 38052

Math

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

↓

\[\begin{array}{l} t_0 := \frac{2 \cdot c}{\left(-b\right) - b}\\ t_1 := \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a}\\ \end{array}\\ t_2 := \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\\ t_3 := \frac{\left(-b\right) + t_2}{2 \cdot a}\\ t_4 := \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - t_2}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_4 \leq -4 \cdot 10^{-137}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array}\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (>= b 0.0)
   (/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
   (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))))

↓

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ (* 2.0 c) (- (- b) b)))
        (t_1 (if (>= b 0.0) t_0 (* -1.0 (/ b a))))
        (t_2 (sqrt (- (* b b) (* (* 4.0 a) c))))
        (t_3 (/ (+ (- b) t_2) (* 2.0 a)))
        (t_4 (if (>= b 0.0) (/ (* 2.0 c) (- (- b) t_2)) t_3)))
   (if (<= t_4 (- INFINITY))
     t_1
     (if (<= t_4 -4e-137)
       t_4
       (if (<= t_4 0.0)
         (if (>= b 0.0) t_0 t_3)
         (if (<= t_4 5e+274) t_4 t_1))))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = (2.0 * c) / (-b - sqrt(((b * b) - ((4.0 * a) * c))));
	} else {
		tmp = (-b + sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a);
	}
	return tmp;
}

↓

double code(double a, double b, double c) {
	double t_0 = (2.0 * c) / (-b - b);
	double tmp;
	if (b >= 0.0) {
		tmp = t_0;
	} else {
		tmp = -1.0 * (b / a);
	}
	double t_1 = tmp;
	double t_2 = sqrt(((b * b) - ((4.0 * a) * c)));
	double t_3 = (-b + t_2) / (2.0 * a);
	double tmp_1;
	if (b >= 0.0) {
		tmp_1 = (2.0 * c) / (-b - t_2);
	} else {
		tmp_1 = t_3;
	}
	double t_4 = tmp_1;
	double tmp_2;
	if (t_4 <= -((double) INFINITY)) {
		tmp_2 = t_1;
	} else if (t_4 <= -4e-137) {
		tmp_2 = t_4;
	} else if (t_4 <= 0.0) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = t_0;
		} else {
			tmp_3 = t_3;
		}
		tmp_2 = tmp_3;
	} else if (t_4 <= 5e+274) {
		tmp_2 = t_4;
	} else {
		tmp_2 = t_1;
	}
	return tmp_2;
}

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = (2.0 * c) / (-b - Math.sqrt(((b * b) - ((4.0 * a) * c))));
	} else {
		tmp = (-b + Math.sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a);
	}
	return tmp;
}

↓

public static double code(double a, double b, double c) {
	double t_0 = (2.0 * c) / (-b - b);
	double tmp;
	if (b >= 0.0) {
		tmp = t_0;
	} else {
		tmp = -1.0 * (b / a);
	}
	double t_1 = tmp;
	double t_2 = Math.sqrt(((b * b) - ((4.0 * a) * c)));
	double t_3 = (-b + t_2) / (2.0 * a);
	double tmp_1;
	if (b >= 0.0) {
		tmp_1 = (2.0 * c) / (-b - t_2);
	} else {
		tmp_1 = t_3;
	}
	double t_4 = tmp_1;
	double tmp_2;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp_2 = t_1;
	} else if (t_4 <= -4e-137) {
		tmp_2 = t_4;
	} else if (t_4 <= 0.0) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = t_0;
		} else {
			tmp_3 = t_3;
		}
		tmp_2 = tmp_3;
	} else if (t_4 <= 5e+274) {
		tmp_2 = t_4;
	} else {
		tmp_2 = t_1;
	}
	return tmp_2;
}

Python

def code(a, b, c):
	tmp = 0
	if b >= 0.0:
		tmp = (2.0 * c) / (-b - math.sqrt(((b * b) - ((4.0 * a) * c))))
	else:
		tmp = (-b + math.sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a)
	return tmp

↓

def code(a, b, c):
	t_0 = (2.0 * c) / (-b - b)
	tmp = 0
	if b >= 0.0:
		tmp = t_0
	else:
		tmp = -1.0 * (b / a)
	t_1 = tmp
	t_2 = math.sqrt(((b * b) - ((4.0 * a) * c)))
	t_3 = (-b + t_2) / (2.0 * a)
	tmp_1 = 0
	if b >= 0.0:
		tmp_1 = (2.0 * c) / (-b - t_2)
	else:
		tmp_1 = t_3
	t_4 = tmp_1
	tmp_2 = 0
	if t_4 <= -math.inf:
		tmp_2 = t_1
	elif t_4 <= -4e-137:
		tmp_2 = t_4
	elif t_4 <= 0.0:
		tmp_3 = 0
		if b >= 0.0:
			tmp_3 = t_0
		else:
			tmp_3 = t_3
		tmp_2 = tmp_3
	elif t_4 <= 5e+274:
		tmp_2 = t_4
	else:
		tmp_2 = t_1
	return tmp_2

Julia

function code(a, b, c)
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(Float64(2.0 * c) / Float64(Float64(-b) - sqrt(Float64(Float64(b * b) - Float64(Float64(4.0 * a) * c)))));
	else
		tmp = Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(4.0 * a) * c)))) / Float64(2.0 * a));
	end
	return tmp
end

↓

function code(a, b, c)
	t_0 = Float64(Float64(2.0 * c) / Float64(Float64(-b) - b))
	tmp = 0.0
	if (b >= 0.0)
		tmp = t_0;
	else
		tmp = Float64(-1.0 * Float64(b / a));
	end
	t_1 = tmp
	t_2 = sqrt(Float64(Float64(b * b) - Float64(Float64(4.0 * a) * c)))
	t_3 = Float64(Float64(Float64(-b) + t_2) / Float64(2.0 * a))
	tmp_1 = 0.0
	if (b >= 0.0)
		tmp_1 = Float64(Float64(2.0 * c) / Float64(Float64(-b) - t_2));
	else
		tmp_1 = t_3;
	end
	t_4 = tmp_1
	tmp_2 = 0.0
	if (t_4 <= Float64(-Inf))
		tmp_2 = t_1;
	elseif (t_4 <= -4e-137)
		tmp_2 = t_4;
	elseif (t_4 <= 0.0)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = t_0;
		else
			tmp_3 = t_3;
		end
		tmp_2 = tmp_3;
	elseif (t_4 <= 5e+274)
		tmp_2 = t_4;
	else
		tmp_2 = t_1;
	end
	return tmp_2
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b >= 0.0)
		tmp = (2.0 * c) / (-b - sqrt(((b * b) - ((4.0 * a) * c))));
	else
		tmp = (-b + sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a);
	end
	tmp_2 = tmp;
end

↓

function tmp_5 = code(a, b, c)
	t_0 = (2.0 * c) / (-b - b);
	tmp = 0.0;
	if (b >= 0.0)
		tmp = t_0;
	else
		tmp = -1.0 * (b / a);
	end
	t_1 = tmp;
	t_2 = sqrt(((b * b) - ((4.0 * a) * c)));
	t_3 = (-b + t_2) / (2.0 * a);
	tmp_2 = 0.0;
	if (b >= 0.0)
		tmp_2 = (2.0 * c) / (-b - t_2);
	else
		tmp_2 = t_3;
	end
	t_4 = tmp_2;
	tmp_3 = 0.0;
	if (t_4 <= -Inf)
		tmp_3 = t_1;
	elseif (t_4 <= -4e-137)
		tmp_3 = t_4;
	elseif (t_4 <= 0.0)
		tmp_4 = 0.0;
		if (b >= 0.0)
			tmp_4 = t_0;
		else
			tmp_4 = t_3;
		end
		tmp_3 = tmp_4;
	elseif (t_4 <= 5e+274)
		tmp_3 = t_4;
	else
		tmp_3 = t_1;
	end
	tmp_5 = tmp_3;
end

Wolfram

code[a_, b_, c_] := If[GreaterEqual[b, 0.0], N[(N[(2.0 * c), $MachinePrecision] / N[((-b) - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]

↓

code[a_, b_, c_] := Block[{t$95$0 = N[(N[(2.0 * c), $MachinePrecision] / N[((-b) - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = If[GreaterEqual[b, 0.0], t$95$0, N[(-1.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]]}, Block[{t$95$2 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[((-b) + t$95$2), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = If[GreaterEqual[b, 0.0], N[(N[(2.0 * c), $MachinePrecision] / N[((-b) - t$95$2), $MachinePrecision]), $MachinePrecision], t$95$3]}, If[LessEqual[t$95$4, (-Infinity)], t$95$1, If[LessEqual[t$95$4, -4e-137], t$95$4, If[LessEqual[t$95$4, 0.0], If[GreaterEqual[b, 0.0], t$95$0, t$95$3], If[LessEqual[t$95$4, 5e+274], t$95$4, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))) < -inf.0 or 4.9999999999999998e274 < (if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))

   1. Initial program 61.3

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

   2. Taylor expanded in b around inf 59.7

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

   3. Taylor expanded in b around -inf 15.5

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - b}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a}\\ \end{array} \]

   if -inf.0 < (if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))) < -3.99999999999999991e-137 or -0.0 < (if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))) < 4.9999999999999998e274

   1. Initial program 2.9

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

   if -3.99999999999999991e-137 < (if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))) < -0.0

   1. Initial program 28.7

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

   2. Taylor expanded in b around inf 11.6

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

Alternatives

Alternative 1
Error	10.2
Cost	7888

\[\begin{array}{l} t_0 := \frac{2 \cdot c}{\left(-b\right) - b}\\ \mathbf{if}\;b \leq -2 \cdot 10^{-36}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} + \left(-\frac{b}{a}\right)\\ \end{array}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-308}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{-4 \cdot \left(c \cdot a\right)}}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+52}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-2}{b + \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}} \cdot c\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + -1 \cdot b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a}\\ \end{array} \]

Alternative 2
Error	7.1
Cost	7888

\[\begin{array}{l} t_0 := \frac{2 \cdot c}{\left(-b\right) - b}\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+86}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} + \left(-\frac{b}{a}\right)\\ \end{array}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-308}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+52}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-2}{b + \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}} \cdot c\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + -1 \cdot b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a}\\ \end{array} \]

Alternative 3
Error	13.4
Cost	7696

\[\begin{array}{l} t_0 := \frac{2 \cdot c}{\left(-b\right) - b}\\ t_1 := \sqrt{-4 \cdot \left(c \cdot a\right)}\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{-37}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} + \left(-\frac{b}{a}\right)\\ \end{array}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-308}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + t_1}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-48}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + -1 \cdot b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \]

Alternative 4
Error	13.3
Cost	7632

\[\begin{array}{l} t_0 := \frac{2 \cdot c}{\left(-b\right) - b}\\ t_1 := \sqrt{-4 \cdot \left(c \cdot a\right)}\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{-37}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} + \left(-\frac{b}{a}\right)\\ \end{array}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-308}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + t_1}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-50}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-2}{t_1 + b} \cdot c\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + -1 \cdot b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \]

Alternative 5
Error	18.2
Cost	7368

\[\begin{array}{l} \mathbf{if}\;b \leq 10^{-48}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-2}{\sqrt{-4 \cdot \left(c \cdot a\right)} + b} \cdot c\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + -1 \cdot b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \]

Alternative 6
Error	23.0
Cost	644

\[\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - b}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a}\\ \end{array} \]

Reproduce

herbie shell --seed 2023010 
(FPCore (a b c)
  :name "jeff quadratic root 2"
  :precision binary64
  (if (>= b 0.0) (/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))))