jeff quadratic root 1

Percentage Accurate: 71.5% → 90.6%

Time: 16.5s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\\ \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - t_0}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) + t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* (* 4.0 a) c)))))
   (if (>= b 0.0) (/ (- (- b) t_0) (* 2.0 a)) (/ (* 2.0 c) (+ (- b) t_0)))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - ((4.0 * a) * c)));
	double tmp;
	if (b >= 0.0) {
		tmp = (-b - t_0) / (2.0 * a);
	} else {
		tmp = (2.0 * c) / (-b + t_0);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(((b * b) - ((4.0d0 * a) * c)))
    if (b >= 0.0d0) then
        tmp = (-b - t_0) / (2.0d0 * a)
    else
        tmp = (2.0d0 * c) / (-b + t_0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = Math.sqrt(((b * b) - ((4.0 * a) * c)));
	double tmp;
	if (b >= 0.0) {
		tmp = (-b - t_0) / (2.0 * a);
	} else {
		tmp = (2.0 * c) / (-b + t_0);
	}
	return tmp;
}

Python

def code(a, b, c):
	t_0 = math.sqrt(((b * b) - ((4.0 * a) * c)))
	tmp = 0
	if b >= 0.0:
		tmp = (-b - t_0) / (2.0 * a)
	else:
		tmp = (2.0 * c) / (-b + t_0)
	return tmp

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(Float64(4.0 * a) * c)))
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(Float64(Float64(-b) - t_0) / Float64(2.0 * a));
	else
		tmp = Float64(Float64(2.0 * c) / Float64(Float64(-b) + t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	t_0 = sqrt(((b * b) - ((4.0 * a) * c)));
	tmp = 0.0;
	if (b >= 0.0)
		tmp = (-b - t_0) / (2.0 * a);
	else
		tmp = (2.0 * c) / (-b + t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[GreaterEqual[b, 0.0], N[(N[((-b) - t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * c), $MachinePrecision] / N[((-b) + t$95$0), $MachinePrecision]), $MachinePrecision]]]

Initial Program: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\\ \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - t_0}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) + t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* (* 4.0 a) c)))))
   (if (>= b 0.0) (/ (- (- b) t_0) (* 2.0 a)) (/ (* 2.0 c) (+ (- b) t_0)))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - ((4.0 * a) * c)));
	double tmp;
	if (b >= 0.0) {
		tmp = (-b - t_0) / (2.0 * a);
	} else {
		tmp = (2.0 * c) / (-b + t_0);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(((b * b) - ((4.0d0 * a) * c)))
    if (b >= 0.0d0) then
        tmp = (-b - t_0) / (2.0d0 * a)
    else
        tmp = (2.0d0 * c) / (-b + t_0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = Math.sqrt(((b * b) - ((4.0 * a) * c)));
	double tmp;
	if (b >= 0.0) {
		tmp = (-b - t_0) / (2.0 * a);
	} else {
		tmp = (2.0 * c) / (-b + t_0);
	}
	return tmp;
}

Python

def code(a, b, c):
	t_0 = math.sqrt(((b * b) - ((4.0 * a) * c)))
	tmp = 0
	if b >= 0.0:
		tmp = (-b - t_0) / (2.0 * a)
	else:
		tmp = (2.0 * c) / (-b + t_0)
	return tmp

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(Float64(4.0 * a) * c)))
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(Float64(Float64(-b) - t_0) / Float64(2.0 * a));
	else
		tmp = Float64(Float64(2.0 * c) / Float64(Float64(-b) + t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	t_0 = sqrt(((b * b) - ((4.0 * a) * c)));
	tmp = 0.0;
	if (b >= 0.0)
		tmp = (-b - t_0) / (2.0 * a);
	else
		tmp = (2.0 * c) / (-b + t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[GreaterEqual[b, 0.0], N[(N[((-b) - t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * c), $MachinePrecision] / N[((-b) + t$95$0), $MachinePrecision]), $MachinePrecision]]]

Alternative 1: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{\mathsf{fma}\left(c, a \cdot -4, b \cdot b\right)}\\ t_1 := a \cdot \left(c \cdot -4\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+152}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{b \cdot -2}\\ \end{array}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+127}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - t_0}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{c}{t_0 - b}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{b}{a}, \frac{c}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{{b}^{2} - \mathsf{fma}\left(b, b, t_1\right)}{c \cdot \left(b - \mathsf{hypot}\left(b, \sqrt{t_1}\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (fma c (* a -4.0) (* b b)))) (t_1 (* a (* c -4.0))))
   (if (<= b -4e+152)
     (if (>= b 0.0) (- (/ c b) (/ b a)) (/ (* c 2.0) (* b -2.0)))
     (if (<= b 4.8e+127)
       (if (>= b 0.0) (/ (- (- b) t_0) (* a 2.0)) (* 2.0 (/ c (- t_0 b))))
       (if (>= b 0.0)
         (fma -1.0 (/ b a) (/ c b))
         (/
          2.0
          (/
           (- (pow b 2.0) (fma b b t_1))
           (* c (- b (hypot b (sqrt t_1)))))))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(fma(c, (a * -4.0), (b * b)));
	double t_1 = a * (c * -4.0);
	double tmp_1;
	if (b <= -4e+152) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = (c / b) - (b / a);
		} else {
			tmp_2 = (c * 2.0) / (b * -2.0);
		}
		tmp_1 = tmp_2;
	} else if (b <= 4.8e+127) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (-b - t_0) / (a * 2.0);
		} else {
			tmp_3 = 2.0 * (c / (t_0 - b));
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = fma(-1.0, (b / a), (c / b));
	} else {
		tmp_1 = 2.0 / ((pow(b, 2.0) - fma(b, b, t_1)) / (c * (b - hypot(b, sqrt(t_1)))));
	}
	return tmp_1;
}

Julia

function code(a, b, c)
	t_0 = sqrt(fma(c, Float64(a * -4.0), Float64(b * b)))
	t_1 = Float64(a * Float64(c * -4.0))
	tmp_1 = 0.0
	if (b <= -4e+152)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(Float64(c / b) - Float64(b / a));
		else
			tmp_2 = Float64(Float64(c * 2.0) / Float64(b * -2.0));
		end
		tmp_1 = tmp_2;
	elseif (b <= 4.8e+127)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(Float64(-b) - t_0) / Float64(a * 2.0));
		else
			tmp_3 = Float64(2.0 * Float64(c / Float64(t_0 - b)));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = fma(-1.0, Float64(b / a), Float64(c / b));
	else
		tmp_1 = Float64(2.0 / Float64(Float64((b ^ 2.0) - fma(b, b, t_1)) / Float64(c * Float64(b - hypot(b, sqrt(t_1))))));
	end
	return tmp_1
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision] + N[(b * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+152], If[GreaterEqual[b, 0.0], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * 2.0), $MachinePrecision] / N[(b * -2.0), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 4.8e+127], If[GreaterEqual[b, 0.0], N[(N[((-b) - t$95$0), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c / N[(t$95$0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(-1.0 * N[(b / a), $MachinePrecision] + N[(c / b), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(N[(N[Power[b, 2.0], $MachinePrecision] - N[(b * b + t$95$1), $MachinePrecision]), $MachinePrecision] / N[(c * N[(b - N[Sqrt[b ^ 2 + N[Sqrt[t$95$1], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 90.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{\mathsf{fma}\left(c, a \cdot -4, b \cdot b\right)}\\ \mathbf{if}\;b \leq -1 \cdot 10^{+152} \lor \neg \left(b \leq 1.9 \cdot 10^{+128}\right):\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{b \cdot -2}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - t_0}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{c}{t_0 - b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (fma c (* a -4.0) (* b b)))))
   (if (or (<= b -1e+152) (not (<= b 1.9e+128)))
     (if (>= b 0.0) (- (/ c b) (/ b a)) (/ (* c 2.0) (* b -2.0)))
     (if (>= b 0.0) (/ (- (- b) t_0) (* a 2.0)) (* 2.0 (/ c (- t_0 b)))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(fma(c, (a * -4.0), (b * b)));
	double tmp_1;
	if ((b <= -1e+152) || !(b <= 1.9e+128)) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = (c / b) - (b / a);
		} else {
			tmp_2 = (c * 2.0) / (b * -2.0);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = (-b - t_0) / (a * 2.0);
	} else {
		tmp_1 = 2.0 * (c / (t_0 - b));
	}
	return tmp_1;
}

Julia

function code(a, b, c)
	t_0 = sqrt(fma(c, Float64(a * -4.0), Float64(b * b)))
	tmp_1 = 0.0
	if ((b <= -1e+152) || !(b <= 1.9e+128))
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(Float64(c / b) - Float64(b / a));
		else
			tmp_2 = Float64(Float64(c * 2.0) / Float64(b * -2.0));
		end
		tmp_1 = tmp_2;
	elseif (b >= 0.0)
		tmp_1 = Float64(Float64(Float64(-b) - t_0) / Float64(a * 2.0));
	else
		tmp_1 = Float64(2.0 * Float64(c / Float64(t_0 - b)));
	end
	return tmp_1
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision] + N[(b * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[b, -1e+152], N[Not[LessEqual[b, 1.9e+128]], $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * 2.0), $MachinePrecision] / N[(b * -2.0), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(N[((-b) - t$95$0), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c / N[(t$95$0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}\\ \mathbf{if}\;b \leq -3 \cdot 10^{+138} \lor \neg \left(b \leq 2 \cdot 10^{+128}\right):\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{b \cdot -2}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - t_0}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{t_0 - b}{c}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* 4.0 (* c a))))))
   (if (or (<= b -3e+138) (not (<= b 2e+128)))
     (if (>= b 0.0) (- (/ c b) (/ b a)) (/ (* c 2.0) (* b -2.0)))
     (if (>= b 0.0) (/ (- (- b) t_0) (* a 2.0)) (/ 2.0 (/ (- t_0 b) c))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - (4.0 * (c * a))));
	double tmp_1;
	if ((b <= -3e+138) || !(b <= 2e+128)) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = (c / b) - (b / a);
		} else {
			tmp_2 = (c * 2.0) / (b * -2.0);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = (-b - t_0) / (a * 2.0);
	} else {
		tmp_1 = 2.0 / ((t_0 - b) / c);
	}
	return tmp_1;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    t_0 = sqrt(((b * b) - (4.0d0 * (c * a))))
    if ((b <= (-3d+138)) .or. (.not. (b <= 2d+128))) then
        if (b >= 0.0d0) then
            tmp_2 = (c / b) - (b / a)
        else
            tmp_2 = (c * 2.0d0) / (b * (-2.0d0))
        end if
        tmp_1 = tmp_2
    else if (b >= 0.0d0) then
        tmp_1 = (-b - t_0) / (a * 2.0d0)
    else
        tmp_1 = 2.0d0 / ((t_0 - b) / c)
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = Math.sqrt(((b * b) - (4.0 * (c * a))));
	double tmp_1;
	if ((b <= -3e+138) || !(b <= 2e+128)) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = (c / b) - (b / a);
		} else {
			tmp_2 = (c * 2.0) / (b * -2.0);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = (-b - t_0) / (a * 2.0);
	} else {
		tmp_1 = 2.0 / ((t_0 - b) / c);
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = math.sqrt(((b * b) - (4.0 * (c * a))))
	tmp_1 = 0
	if (b <= -3e+138) or not (b <= 2e+128):
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = (c / b) - (b / a)
		else:
			tmp_2 = (c * 2.0) / (b * -2.0)
		tmp_1 = tmp_2
	elif b >= 0.0:
		tmp_1 = (-b - t_0) / (a * 2.0)
	else:
		tmp_1 = 2.0 / ((t_0 - b) / c)
	return tmp_1

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(c * a))))
	tmp_1 = 0.0
	if ((b <= -3e+138) || !(b <= 2e+128))
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(Float64(c / b) - Float64(b / a));
		else
			tmp_2 = Float64(Float64(c * 2.0) / Float64(b * -2.0));
		end
		tmp_1 = tmp_2;
	elseif (b >= 0.0)
		tmp_1 = Float64(Float64(Float64(-b) - t_0) / Float64(a * 2.0));
	else
		tmp_1 = Float64(2.0 / Float64(Float64(t_0 - b) / c));
	end
	return tmp_1
end

MATLAB

function tmp_4 = code(a, b, c)
	t_0 = sqrt(((b * b) - (4.0 * (c * a))));
	tmp_2 = 0.0;
	if ((b <= -3e+138) || ~((b <= 2e+128)))
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = (c / b) - (b / a);
		else
			tmp_3 = (c * 2.0) / (b * -2.0);
		end
		tmp_2 = tmp_3;
	elseif (b >= 0.0)
		tmp_2 = (-b - t_0) / (a * 2.0);
	else
		tmp_2 = 2.0 / ((t_0 - b) / c);
	end
	tmp_4 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[b, -3e+138], N[Not[LessEqual[b, 2e+128]], $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * 2.0), $MachinePrecision] / N[(b * -2.0), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(N[((-b) - t$95$0), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(N[(t$95$0 - b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 90.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+150} \lor \neg \left(b \leq 3.9 \cdot 10^{+127}\right):\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{b \cdot -2}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - t_0}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{t_0 - b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (or (<= b -1.5e+150) (not (<= b 3.9e+127)))
     (if (>= b 0.0) (- (/ c b) (/ b a)) (/ (* c 2.0) (* b -2.0)))
     (if (>= b 0.0) (/ (- (- b) t_0) (* a 2.0)) (/ (* c 2.0) (- t_0 b))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if ((b <= -1.5e+150) || !(b <= 3.9e+127)) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = (c / b) - (b / a);
		} else {
			tmp_2 = (c * 2.0) / (b * -2.0);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = (-b - t_0) / (a * 2.0);
	} else {
		tmp_1 = (c * 2.0) / (t_0 - b);
	}
	return tmp_1;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    t_0 = sqrt(((b * b) - (c * (a * 4.0d0))))
    if ((b <= (-1.5d+150)) .or. (.not. (b <= 3.9d+127))) then
        if (b >= 0.0d0) then
            tmp_2 = (c / b) - (b / a)
        else
            tmp_2 = (c * 2.0d0) / (b * (-2.0d0))
        end if
        tmp_1 = tmp_2
    else if (b >= 0.0d0) then
        tmp_1 = (-b - t_0) / (a * 2.0d0)
    else
        tmp_1 = (c * 2.0d0) / (t_0 - b)
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = Math.sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if ((b <= -1.5e+150) || !(b <= 3.9e+127)) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = (c / b) - (b / a);
		} else {
			tmp_2 = (c * 2.0) / (b * -2.0);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = (-b - t_0) / (a * 2.0);
	} else {
		tmp_1 = (c * 2.0) / (t_0 - b);
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = math.sqrt(((b * b) - (c * (a * 4.0))))
	tmp_1 = 0
	if (b <= -1.5e+150) or not (b <= 3.9e+127):
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = (c / b) - (b / a)
		else:
			tmp_2 = (c * 2.0) / (b * -2.0)
		tmp_1 = tmp_2
	elif b >= 0.0:
		tmp_1 = (-b - t_0) / (a * 2.0)
	else:
		tmp_1 = (c * 2.0) / (t_0 - b)
	return tmp_1

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	tmp_1 = 0.0
	if ((b <= -1.5e+150) || !(b <= 3.9e+127))
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(Float64(c / b) - Float64(b / a));
		else
			tmp_2 = Float64(Float64(c * 2.0) / Float64(b * -2.0));
		end
		tmp_1 = tmp_2;
	elseif (b >= 0.0)
		tmp_1 = Float64(Float64(Float64(-b) - t_0) / Float64(a * 2.0));
	else
		tmp_1 = Float64(Float64(c * 2.0) / Float64(t_0 - b));
	end
	return tmp_1
end

MATLAB

function tmp_4 = code(a, b, c)
	t_0 = sqrt(((b * b) - (c * (a * 4.0))));
	tmp_2 = 0.0;
	if ((b <= -1.5e+150) || ~((b <= 3.9e+127)))
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = (c / b) - (b / a);
		else
			tmp_3 = (c * 2.0) / (b * -2.0);
		end
		tmp_2 = tmp_3;
	elseif (b >= 0.0)
		tmp_2 = (-b - t_0) / (a * 2.0);
	else
		tmp_2 = (c * 2.0) / (t_0 - b);
	end
	tmp_4 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[b, -1.5e+150], N[Not[LessEqual[b, 3.9e+127]], $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * 2.0), $MachinePrecision] / N[(b * -2.0), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(N[((-b) - t$95$0), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * 2.0), $MachinePrecision] / N[(t$95$0 - b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{b \cdot -2}\\ \end{array}\\ t_1 := -\left(b + b\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+140}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-310}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{t_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{c}}\\ \end{array}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-53}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{c \cdot \left(a \cdot -4\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{t_1}{c}}\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (if (>= b 0.0) (- (/ c b) (/ b a)) (/ (* c 2.0) (* b -2.0))))
        (t_1 (- (+ b b))))
   (if (<= b -1.2e+140)
     t_0
     (if (<= b -1e-310)
       (if (>= b 0.0)
         (/ t_1 (* a 2.0))
         (/ 2.0 (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) c)))
       (if (<= b 4e-53)
         (if (>= b 0.0)
           (/ (- (- b) (sqrt (* c (* a -4.0)))) (* a 2.0))
           (/ 2.0 (/ t_1 c)))
         t_0)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = (c * 2.0) / (b * -2.0);
	}
	double t_0 = tmp;
	double t_1 = -(b + b);
	double tmp_1;
	if (b <= -1.2e+140) {
		tmp_1 = t_0;
	} else if (b <= -1e-310) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_1 / (a * 2.0);
		} else {
			tmp_2 = 2.0 / ((sqrt(((b * b) - (4.0 * (c * a)))) - b) / c);
		}
		tmp_1 = tmp_2;
	} else if (b <= 4e-53) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (-b - sqrt((c * (a * -4.0)))) / (a * 2.0);
		} else {
			tmp_3 = 2.0 / (t_1 / c);
		}
		tmp_1 = tmp_3;
	} else {
		tmp_1 = t_0;
	}
	return tmp_1;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    real(8) :: tmp_3
    if (b >= 0.0d0) then
        tmp = (c / b) - (b / a)
    else
        tmp = (c * 2.0d0) / (b * (-2.0d0))
    end if
    t_0 = tmp
    t_1 = -(b + b)
    if (b <= (-1.2d+140)) then
        tmp_1 = t_0
    else if (b <= (-1d-310)) then
        if (b >= 0.0d0) then
            tmp_2 = t_1 / (a * 2.0d0)
        else
            tmp_2 = 2.0d0 / ((sqrt(((b * b) - (4.0d0 * (c * a)))) - b) / c)
        end if
        tmp_1 = tmp_2
    else if (b <= 4d-53) then
        if (b >= 0.0d0) then
            tmp_3 = (-b - sqrt((c * (a * (-4.0d0))))) / (a * 2.0d0)
        else
            tmp_3 = 2.0d0 / (t_1 / c)
        end if
        tmp_1 = tmp_3
    else
        tmp_1 = t_0
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = (c * 2.0) / (b * -2.0);
	}
	double t_0 = tmp;
	double t_1 = -(b + b);
	double tmp_1;
	if (b <= -1.2e+140) {
		tmp_1 = t_0;
	} else if (b <= -1e-310) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_1 / (a * 2.0);
		} else {
			tmp_2 = 2.0 / ((Math.sqrt(((b * b) - (4.0 * (c * a)))) - b) / c);
		}
		tmp_1 = tmp_2;
	} else if (b <= 4e-53) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (-b - Math.sqrt((c * (a * -4.0)))) / (a * 2.0);
		} else {
			tmp_3 = 2.0 / (t_1 / c);
		}
		tmp_1 = tmp_3;
	} else {
		tmp_1 = t_0;
	}
	return tmp_1;
}

Python

def code(a, b, c):
	tmp = 0
	if b >= 0.0:
		tmp = (c / b) - (b / a)
	else:
		tmp = (c * 2.0) / (b * -2.0)
	t_0 = tmp
	t_1 = -(b + b)
	tmp_1 = 0
	if b <= -1.2e+140:
		tmp_1 = t_0
	elif b <= -1e-310:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = t_1 / (a * 2.0)
		else:
			tmp_2 = 2.0 / ((math.sqrt(((b * b) - (4.0 * (c * a)))) - b) / c)
		tmp_1 = tmp_2
	elif b <= 4e-53:
		tmp_3 = 0
		if b >= 0.0:
			tmp_3 = (-b - math.sqrt((c * (a * -4.0)))) / (a * 2.0)
		else:
			tmp_3 = 2.0 / (t_1 / c)
		tmp_1 = tmp_3
	else:
		tmp_1 = t_0
	return tmp_1

Julia

function code(a, b, c)
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	else
		tmp = Float64(Float64(c * 2.0) / Float64(b * -2.0));
	end
	t_0 = tmp
	t_1 = Float64(-Float64(b + b))
	tmp_1 = 0.0
	if (b <= -1.2e+140)
		tmp_1 = t_0;
	elseif (b <= -1e-310)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(t_1 / Float64(a * 2.0));
		else
			tmp_2 = Float64(2.0 / Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(c * a)))) - b) / c));
		end
		tmp_1 = tmp_2;
	elseif (b <= 4e-53)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(Float64(-b) - sqrt(Float64(c * Float64(a * -4.0)))) / Float64(a * 2.0));
		else
			tmp_3 = Float64(2.0 / Float64(t_1 / c));
		end
		tmp_1 = tmp_3;
	else
		tmp_1 = t_0;
	end
	return tmp_1
end

MATLAB

function tmp_5 = code(a, b, c)
	tmp = 0.0;
	if (b >= 0.0)
		tmp = (c / b) - (b / a);
	else
		tmp = (c * 2.0) / (b * -2.0);
	end
	t_0 = tmp;
	t_1 = -(b + b);
	tmp_2 = 0.0;
	if (b <= -1.2e+140)
		tmp_2 = t_0;
	elseif (b <= -1e-310)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = t_1 / (a * 2.0);
		else
			tmp_3 = 2.0 / ((sqrt(((b * b) - (4.0 * (c * a)))) - b) / c);
		end
		tmp_2 = tmp_3;
	elseif (b <= 4e-53)
		tmp_4 = 0.0;
		if (b >= 0.0)
			tmp_4 = (-b - sqrt((c * (a * -4.0)))) / (a * 2.0);
		else
			tmp_4 = 2.0 / (t_1 / c);
		end
		tmp_2 = tmp_4;
	else
		tmp_2 = t_0;
	end
	tmp_5 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = If[GreaterEqual[b, 0.0], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * 2.0), $MachinePrecision] / N[(b * -2.0), $MachinePrecision]), $MachinePrecision]]}, Block[{t$95$1 = (-N[(b + b), $MachinePrecision])}, If[LessEqual[b, -1.2e+140], t$95$0, If[LessEqual[b, -1e-310], If[GreaterEqual[b, 0.0], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 4e-53], If[GreaterEqual[b, 0.0], N[(N[((-b) - N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(t$95$1 / c), $MachinePrecision]), $MachinePrecision]], t$95$0]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{b \cdot -2}\\ \end{array}\\ t_1 := \sqrt{c \cdot \left(a \cdot -4\right)}\\ \mathbf{if}\;b \leq -4100000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-310}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{b}{a}, \frac{c}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{t_1 - b}{c}}\\ \end{array}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-67}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - t_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{-\left(b + b\right)}{c}}\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (if (>= b 0.0) (- (/ c b) (/ b a)) (/ (* c 2.0) (* b -2.0))))
        (t_1 (sqrt (* c (* a -4.0)))))
   (if (<= b -4100000000000.0)
     t_0
     (if (<= b -1e-310)
       (if (>= b 0.0) (fma -1.0 (/ b a) (/ c b)) (/ 2.0 (/ (- t_1 b) c)))
       (if (<= b 4.5e-67)
         (if (>= b 0.0) (/ (- (- b) t_1) (* a 2.0)) (/ 2.0 (/ (- (+ b b)) c)))
         t_0)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = (c * 2.0) / (b * -2.0);
	}
	double t_0 = tmp;
	double t_1 = sqrt((c * (a * -4.0)));
	double tmp_1;
	if (b <= -4100000000000.0) {
		tmp_1 = t_0;
	} else if (b <= -1e-310) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = fma(-1.0, (b / a), (c / b));
		} else {
			tmp_2 = 2.0 / ((t_1 - b) / c);
		}
		tmp_1 = tmp_2;
	} else if (b <= 4.5e-67) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (-b - t_1) / (a * 2.0);
		} else {
			tmp_3 = 2.0 / (-(b + b) / c);
		}
		tmp_1 = tmp_3;
	} else {
		tmp_1 = t_0;
	}
	return tmp_1;
}

Julia

function code(a, b, c)
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	else
		tmp = Float64(Float64(c * 2.0) / Float64(b * -2.0));
	end
	t_0 = tmp
	t_1 = sqrt(Float64(c * Float64(a * -4.0)))
	tmp_1 = 0.0
	if (b <= -4100000000000.0)
		tmp_1 = t_0;
	elseif (b <= -1e-310)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = fma(-1.0, Float64(b / a), Float64(c / b));
		else
			tmp_2 = Float64(2.0 / Float64(Float64(t_1 - b) / c));
		end
		tmp_1 = tmp_2;
	elseif (b <= 4.5e-67)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(Float64(-b) - t_1) / Float64(a * 2.0));
		else
			tmp_3 = Float64(2.0 / Float64(Float64(-Float64(b + b)) / c));
		end
		tmp_1 = tmp_3;
	else
		tmp_1 = t_0;
	end
	return tmp_1
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = If[GreaterEqual[b, 0.0], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * 2.0), $MachinePrecision] / N[(b * -2.0), $MachinePrecision]), $MachinePrecision]]}, Block[{t$95$1 = N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -4100000000000.0], t$95$0, If[LessEqual[b, -1e-310], If[GreaterEqual[b, 0.0], N[(-1.0 * N[(b / a), $MachinePrecision] + N[(c / b), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(N[(t$95$1 - b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 4.5e-67], If[GreaterEqual[b, 0.0], N[(N[((-b) - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[((-N[(b + b), $MachinePrecision]) / c), $MachinePrecision]), $MachinePrecision]], t$95$0]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.9 \cdot 10^{-53}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{c \cdot \left(a \cdot -4\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{-\left(b + b\right)}{c}}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{b \cdot -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 2.9e-53)
   (if (>= b 0.0)
     (/ (- (- b) (sqrt (* c (* a -4.0)))) (* a 2.0))
     (/ 2.0 (/ (- (+ b b)) c)))
   (if (>= b 0.0) (- (/ c b) (/ b a)) (/ (* c 2.0) (* b -2.0)))))

C

double code(double a, double b, double c) {
	double tmp_1;
	if (b <= 2.9e-53) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = (-b - sqrt((c * (a * -4.0)))) / (a * 2.0);
		} else {
			tmp_2 = 2.0 / (-(b + b) / c);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = (c / b) - (b / a);
	} else {
		tmp_1 = (c * 2.0) / (b * -2.0);
	}
	return tmp_1;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    if (b <= 2.9d-53) then
        if (b >= 0.0d0) then
            tmp_2 = (-b - sqrt((c * (a * (-4.0d0))))) / (a * 2.0d0)
        else
            tmp_2 = 2.0d0 / (-(b + b) / c)
        end if
        tmp_1 = tmp_2
    else if (b >= 0.0d0) then
        tmp_1 = (c / b) - (b / a)
    else
        tmp_1 = (c * 2.0d0) / (b * (-2.0d0))
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double tmp_1;
	if (b <= 2.9e-53) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = (-b - Math.sqrt((c * (a * -4.0)))) / (a * 2.0);
		} else {
			tmp_2 = 2.0 / (-(b + b) / c);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = (c / b) - (b / a);
	} else {
		tmp_1 = (c * 2.0) / (b * -2.0);
	}
	return tmp_1;
}

Python

def code(a, b, c):
	tmp_1 = 0
	if b <= 2.9e-53:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = (-b - math.sqrt((c * (a * -4.0)))) / (a * 2.0)
		else:
			tmp_2 = 2.0 / (-(b + b) / c)
		tmp_1 = tmp_2
	elif b >= 0.0:
		tmp_1 = (c / b) - (b / a)
	else:
		tmp_1 = (c * 2.0) / (b * -2.0)
	return tmp_1

Julia

function code(a, b, c)
	tmp_1 = 0.0
	if (b <= 2.9e-53)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(Float64(Float64(-b) - sqrt(Float64(c * Float64(a * -4.0)))) / Float64(a * 2.0));
		else
			tmp_2 = Float64(2.0 / Float64(Float64(-Float64(b + b)) / c));
		end
		tmp_1 = tmp_2;
	elseif (b >= 0.0)
		tmp_1 = Float64(Float64(c / b) - Float64(b / a));
	else
		tmp_1 = Float64(Float64(c * 2.0) / Float64(b * -2.0));
	end
	return tmp_1
end

MATLAB

function tmp_4 = code(a, b, c)
	tmp_2 = 0.0;
	if (b <= 2.9e-53)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = (-b - sqrt((c * (a * -4.0)))) / (a * 2.0);
		else
			tmp_3 = 2.0 / (-(b + b) / c);
		end
		tmp_2 = tmp_3;
	elseif (b >= 0.0)
		tmp_2 = (c / b) - (b / a);
	else
		tmp_2 = (c * 2.0) / (b * -2.0);
	end
	tmp_4 = tmp_2;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2.9e-53], If[GreaterEqual[b, 0.0], N[(N[((-b) - N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[((-N[(b + b), $MachinePrecision]) / c), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * 2.0), $MachinePrecision] / N[(b * -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 67.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b >= 0.0d0) then
        tmp = (c / b) - (b / a)
    else
        tmp = (c * 2.0d0) / (b * (-2.0d0))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2024003 
(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)))))))