jeff quadratic root 2

Percentage Accurate: 72.4% → 89.9%

Time: 18.6s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

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 = (2.0 * c) / (-b - t_0);
	} else {
		tmp = (-b + t_0) / (2.0 * a);
	}
	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 = (2.0d0 * c) / (-b - t_0)
    else
        tmp = (-b + t_0) / (2.0d0 * a)
    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 = (2.0 * c) / (-b - t_0);
	} else {
		tmp = (-b + t_0) / (2.0 * a);
	}
	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 = (2.0 * c) / (-b - t_0)
	else:
		tmp = (-b + t_0) / (2.0 * a)
	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(2.0 * c) / Float64(Float64(-b) - t_0));
	else
		tmp = Float64(Float64(Float64(-b) + t_0) / Float64(2.0 * a));
	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 = (2.0 * c) / (-b - t_0);
	else
		tmp = (-b + t_0) / (2.0 * a);
	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[(2.0 * c), $MachinePrecision] / N[((-b) - t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[((-b) + t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]]

Initial Program: 72.4% accurate, 1.0× speedup

Math

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

FPCore

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

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 = (2.0 * c) / (-b - t_0);
	} else {
		tmp = (-b + t_0) / (2.0 * a);
	}
	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 = (2.0d0 * c) / (-b - t_0)
    else
        tmp = (-b + t_0) / (2.0d0 * a)
    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 = (2.0 * c) / (-b - t_0);
	} else {
		tmp = (-b + t_0) / (2.0 * a);
	}
	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 = (2.0 * c) / (-b - t_0)
	else:
		tmp = (-b + t_0) / (2.0 * a)
	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(2.0 * c) / Float64(Float64(-b) - t_0));
	else
		tmp = Float64(Float64(Float64(-b) + t_0) / Float64(2.0 * a));
	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 = (2.0 * c) / (-b - t_0);
	else
		tmp = (-b + t_0) / (2.0 * a);
	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[(2.0 * c), $MachinePrecision] / N[((-b) - t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[((-b) + t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]]

Alternative 1: 89.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{-a}\\ \end{array}\\ t_1 := a \cdot \left(c \cdot -4\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+163}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-136}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{2}{b \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\mathsf{fma}\left(b, b, t_1\right)} - b}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{+72}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{hypot}\left(b, \sqrt{t_1}\right) - b}{a \cdot 2}\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (if (>= b 0.0) (/ (- c) b) (/ b (- a)))) (t_1 (* a (* c -4.0))))
   (if (<= b -1.4e+163)
     t_0
     (if (<= b -5e-136)
       (if (>= b 0.0)
         (* c (/ 2.0 (* b -2.0)))
         (/ (- (sqrt (fma b b t_1)) b) (* a 2.0)))
       (if (<= b 1.72e+72)
         (if (>= b 0.0)
           (/ (* c 2.0) (- (- b) (sqrt (- (* b b) (* c (* a 4.0))))))
           (/ (- (hypot b (sqrt t_1)) b) (* a 2.0)))
         t_0)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = -c / b;
	} else {
		tmp = b / -a;
	}
	double t_0 = tmp;
	double t_1 = a * (c * -4.0);
	double tmp_1;
	if (b <= -1.4e+163) {
		tmp_1 = t_0;
	} else if (b <= -5e-136) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = c * (2.0 / (b * -2.0));
		} else {
			tmp_2 = (sqrt(fma(b, b, t_1)) - b) / (a * 2.0);
		}
		tmp_1 = tmp_2;
	} else if (b <= 1.72e+72) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (c * 2.0) / (-b - sqrt(((b * b) - (c * (a * 4.0)))));
		} else {
			tmp_3 = (hypot(b, sqrt(t_1)) - b) / (a * 2.0);
		}
		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);
	else
		tmp = Float64(b / Float64(-a));
	end
	t_0 = tmp
	t_1 = Float64(a * Float64(c * -4.0))
	tmp_1 = 0.0
	if (b <= -1.4e+163)
		tmp_1 = t_0;
	elseif (b <= -5e-136)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(c * Float64(2.0 / Float64(b * -2.0)));
		else
			tmp_2 = Float64(Float64(sqrt(fma(b, b, t_1)) - b) / Float64(a * 2.0));
		end
		tmp_1 = tmp_2;
	elseif (b <= 1.72e+72)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(c * 2.0) / Float64(Float64(-b) - sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))));
		else
			tmp_3 = Float64(Float64(hypot(b, sqrt(t_1)) - b) / Float64(a * 2.0));
		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[((-c) / b), $MachinePrecision], N[(b / (-a)), $MachinePrecision]]}, Block[{t$95$1 = N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+163], t$95$0, If[LessEqual[b, -5e-136], If[GreaterEqual[b, 0.0], N[(c * N[(2.0 / N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[N[(b * b + t$95$1), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 1.72e+72], If[GreaterEqual[b, 0.0], N[(N[(c * 2.0), $MachinePrecision] / N[((-b) - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[b ^ 2 + N[Sqrt[t$95$1], $MachinePrecision] ^ 2], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]], t$95$0]]]]]

Derivation

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

Alternative 2: 89.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-c}{b}\\ t_1 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ t_2 := \frac{c \cdot 2}{\left(-b\right) - t_1}\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+49}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right)\\ \end{array}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-117}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 - b}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \leq 1.66 \cdot 10^{+72}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{hypot}\left(b, \sqrt{a \cdot \left(c \cdot -4\right)}\right) - b}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ (- c) b))
        (t_1 (sqrt (- (* b b) (* c (* a 4.0)))))
        (t_2 (/ (* c 2.0) (- (- b) t_1))))
   (if (<= b -1.25e+49)
     (if (>= b 0.0) t_0 (* -0.5 (+ (* -2.0 (/ c b)) (* 2.0 (/ b a)))))
     (if (<= b -2e-117)
       (if (>= b 0.0) t_2 (/ (- t_1 b) (* a 2.0)))
       (if (<= b 1.66e+72)
         (if (>= b 0.0)
           t_2
           (/ (- (hypot b (sqrt (* a (* c -4.0)))) b) (* a 2.0)))
         (if (>= b 0.0) t_0 (/ b (- a))))))))

C

double code(double a, double b, double c) {
	double t_0 = -c / b;
	double t_1 = sqrt(((b * b) - (c * (a * 4.0))));
	double t_2 = (c * 2.0) / (-b - t_1);
	double tmp_1;
	if (b <= -1.25e+49) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		}
		tmp_1 = tmp_2;
	} else if (b <= -2e-117) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = t_2;
		} else {
			tmp_3 = (t_1 - b) / (a * 2.0);
		}
		tmp_1 = tmp_3;
	} else if (b <= 1.66e+72) {
		double tmp_4;
		if (b >= 0.0) {
			tmp_4 = t_2;
		} else {
			tmp_4 = (hypot(b, sqrt((a * (c * -4.0)))) - b) / (a * 2.0);
		}
		tmp_1 = tmp_4;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = b / -a;
	}
	return tmp_1;
}

Java

public static double code(double a, double b, double c) {
	double t_0 = -c / b;
	double t_1 = Math.sqrt(((b * b) - (c * (a * 4.0))));
	double t_2 = (c * 2.0) / (-b - t_1);
	double tmp_1;
	if (b <= -1.25e+49) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		}
		tmp_1 = tmp_2;
	} else if (b <= -2e-117) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = t_2;
		} else {
			tmp_3 = (t_1 - b) / (a * 2.0);
		}
		tmp_1 = tmp_3;
	} else if (b <= 1.66e+72) {
		double tmp_4;
		if (b >= 0.0) {
			tmp_4 = t_2;
		} else {
			tmp_4 = (Math.hypot(b, Math.sqrt((a * (c * -4.0)))) - b) / (a * 2.0);
		}
		tmp_1 = tmp_4;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = b / -a;
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = -c / b
	t_1 = math.sqrt(((b * b) - (c * (a * 4.0))))
	t_2 = (c * 2.0) / (-b - t_1)
	tmp_1 = 0
	if b <= -1.25e+49:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = t_0
		else:
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)))
		tmp_1 = tmp_2
	elif b <= -2e-117:
		tmp_3 = 0
		if b >= 0.0:
			tmp_3 = t_2
		else:
			tmp_3 = (t_1 - b) / (a * 2.0)
		tmp_1 = tmp_3
	elif b <= 1.66e+72:
		tmp_4 = 0
		if b >= 0.0:
			tmp_4 = t_2
		else:
			tmp_4 = (math.hypot(b, math.sqrt((a * (c * -4.0)))) - b) / (a * 2.0)
		tmp_1 = tmp_4
	elif b >= 0.0:
		tmp_1 = t_0
	else:
		tmp_1 = b / -a
	return tmp_1

Julia

function code(a, b, c)
	t_0 = Float64(Float64(-c) / b)
	t_1 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	t_2 = Float64(Float64(c * 2.0) / Float64(Float64(-b) - t_1))
	tmp_1 = 0.0
	if (b <= -1.25e+49)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = t_0;
		else
			tmp_2 = Float64(-0.5 * Float64(Float64(-2.0 * Float64(c / b)) + Float64(2.0 * Float64(b / a))));
		end
		tmp_1 = tmp_2;
	elseif (b <= -2e-117)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = t_2;
		else
			tmp_3 = Float64(Float64(t_1 - b) / Float64(a * 2.0));
		end
		tmp_1 = tmp_3;
	elseif (b <= 1.66e+72)
		tmp_4 = 0.0
		if (b >= 0.0)
			tmp_4 = t_2;
		else
			tmp_4 = Float64(Float64(hypot(b, sqrt(Float64(a * Float64(c * -4.0)))) - b) / Float64(a * 2.0));
		end
		tmp_1 = tmp_4;
	elseif (b >= 0.0)
		tmp_1 = t_0;
	else
		tmp_1 = Float64(b / Float64(-a));
	end
	return tmp_1
end

MATLAB

function tmp_6 = code(a, b, c)
	t_0 = -c / b;
	t_1 = sqrt(((b * b) - (c * (a * 4.0))));
	t_2 = (c * 2.0) / (-b - t_1);
	tmp_2 = 0.0;
	if (b <= -1.25e+49)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = t_0;
		else
			tmp_3 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		end
		tmp_2 = tmp_3;
	elseif (b <= -2e-117)
		tmp_4 = 0.0;
		if (b >= 0.0)
			tmp_4 = t_2;
		else
			tmp_4 = (t_1 - b) / (a * 2.0);
		end
		tmp_2 = tmp_4;
	elseif (b <= 1.66e+72)
		tmp_5 = 0.0;
		if (b >= 0.0)
			tmp_5 = t_2;
		else
			tmp_5 = (hypot(b, sqrt((a * (c * -4.0)))) - b) / (a * 2.0);
		end
		tmp_2 = tmp_5;
	elseif (b >= 0.0)
		tmp_2 = t_0;
	else
		tmp_2 = b / -a;
	end
	tmp_6 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[((-c) / b), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * 2.0), $MachinePrecision] / N[((-b) - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+49], If[GreaterEqual[b, 0.0], t$95$0, N[(-0.5 * N[(N[(-2.0 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, -2e-117], If[GreaterEqual[b, 0.0], t$95$2, N[(N[(t$95$1 - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 1.66e+72], If[GreaterEqual[b, 0.0], t$95$2, N[(N[(N[Sqrt[b ^ 2 + N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], t$95$0, N[(b / (-a)), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 3: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-c}{b}\\ t_1 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+49}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right)\\ \end{array}\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{+72}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 - b}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ (- c) b)) (t_1 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (<= b -1.15e+49)
     (if (>= b 0.0) t_0 (* -0.5 (+ (* -2.0 (/ c b)) (* 2.0 (/ b a)))))
     (if (<= b 1.72e+72)
       (if (>= b 0.0) (/ (* c 2.0) (- (- b) t_1)) (/ (- t_1 b) (* a 2.0)))
       (if (>= b 0.0) t_0 (/ b (- a)))))))

C

double code(double a, double b, double c) {
	double t_0 = -c / b;
	double t_1 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -1.15e+49) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		}
		tmp_1 = tmp_2;
	} else if (b <= 1.72e+72) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (c * 2.0) / (-b - t_1);
		} else {
			tmp_3 = (t_1 - b) / (a * 2.0);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = b / -a;
	}
	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
    t_0 = -c / b
    t_1 = sqrt(((b * b) - (c * (a * 4.0d0))))
    if (b <= (-1.15d+49)) then
        if (b >= 0.0d0) then
            tmp_2 = t_0
        else
            tmp_2 = (-0.5d0) * (((-2.0d0) * (c / b)) + (2.0d0 * (b / a)))
        end if
        tmp_1 = tmp_2
    else if (b <= 1.72d+72) then
        if (b >= 0.0d0) then
            tmp_3 = (c * 2.0d0) / (-b - t_1)
        else
            tmp_3 = (t_1 - b) / (a * 2.0d0)
        end if
        tmp_1 = tmp_3
    else if (b >= 0.0d0) then
        tmp_1 = t_0
    else
        tmp_1 = b / -a
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = -c / b;
	double t_1 = Math.sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -1.15e+49) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		}
		tmp_1 = tmp_2;
	} else if (b <= 1.72e+72) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (c * 2.0) / (-b - t_1);
		} else {
			tmp_3 = (t_1 - b) / (a * 2.0);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = b / -a;
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = -c / b
	t_1 = math.sqrt(((b * b) - (c * (a * 4.0))))
	tmp_1 = 0
	if b <= -1.15e+49:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = t_0
		else:
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)))
		tmp_1 = tmp_2
	elif b <= 1.72e+72:
		tmp_3 = 0
		if b >= 0.0:
			tmp_3 = (c * 2.0) / (-b - t_1)
		else:
			tmp_3 = (t_1 - b) / (a * 2.0)
		tmp_1 = tmp_3
	elif b >= 0.0:
		tmp_1 = t_0
	else:
		tmp_1 = b / -a
	return tmp_1

Julia

function code(a, b, c)
	t_0 = Float64(Float64(-c) / b)
	t_1 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	tmp_1 = 0.0
	if (b <= -1.15e+49)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = t_0;
		else
			tmp_2 = Float64(-0.5 * Float64(Float64(-2.0 * Float64(c / b)) + Float64(2.0 * Float64(b / a))));
		end
		tmp_1 = tmp_2;
	elseif (b <= 1.72e+72)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(c * 2.0) / Float64(Float64(-b) - t_1));
		else
			tmp_3 = Float64(Float64(t_1 - b) / Float64(a * 2.0));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = t_0;
	else
		tmp_1 = Float64(b / Float64(-a));
	end
	return tmp_1
end

MATLAB

function tmp_5 = code(a, b, c)
	t_0 = -c / b;
	t_1 = sqrt(((b * b) - (c * (a * 4.0))));
	tmp_2 = 0.0;
	if (b <= -1.15e+49)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = t_0;
		else
			tmp_3 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		end
		tmp_2 = tmp_3;
	elseif (b <= 1.72e+72)
		tmp_4 = 0.0;
		if (b >= 0.0)
			tmp_4 = (c * 2.0) / (-b - t_1);
		else
			tmp_4 = (t_1 - b) / (a * 2.0);
		end
		tmp_2 = tmp_4;
	elseif (b >= 0.0)
		tmp_2 = t_0;
	else
		tmp_2 = b / -a;
	end
	tmp_5 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[((-c) / b), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -1.15e+49], If[GreaterEqual[b, 0.0], t$95$0, N[(-0.5 * N[(N[(-2.0 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 1.72e+72], If[GreaterEqual[b, 0.0], N[(N[(c * 2.0), $MachinePrecision] / N[((-b) - t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], t$95$0, N[(b / (-a)), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 79.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-c}{b}\\ t_1 := \sqrt{-4 \cdot \left(c \cdot a\right)}\\ \mathbf{if}\;b \leq -5.6 \cdot 10^{-73}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right)\\ \end{array}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-279}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{b - t_1}{a}\\ \end{array}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-56}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + t_1}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{b + b}{a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ (- c) b)) (t_1 (sqrt (* -4.0 (* c a)))))
   (if (<= b -5.6e-73)
     (if (>= b 0.0) t_0 (* -0.5 (+ (* -2.0 (/ c b)) (* 2.0 (/ b a)))))
     (if (<= b 2.8e-279)
       (if (>= b 0.0) t_0 (* -0.5 (/ (- b t_1) a)))
       (if (<= b 2.1e-56)
         (if (>= b 0.0) (* c (/ -2.0 (+ b t_1))) (* -0.5 (/ (+ b b) a)))
         (if (>= b 0.0) t_0 (/ b (- a))))))))

C

double code(double a, double b, double c) {
	double t_0 = -c / b;
	double t_1 = sqrt((-4.0 * (c * a)));
	double tmp_1;
	if (b <= -5.6e-73) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		}
		tmp_1 = tmp_2;
	} else if (b <= 2.8e-279) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = t_0;
		} else {
			tmp_3 = -0.5 * ((b - t_1) / a);
		}
		tmp_1 = tmp_3;
	} else if (b <= 2.1e-56) {
		double tmp_4;
		if (b >= 0.0) {
			tmp_4 = c * (-2.0 / (b + t_1));
		} else {
			tmp_4 = -0.5 * ((b + b) / a);
		}
		tmp_1 = tmp_4;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = b / -a;
	}
	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
    real(8) :: tmp_4
    t_0 = -c / b
    t_1 = sqrt(((-4.0d0) * (c * a)))
    if (b <= (-5.6d-73)) then
        if (b >= 0.0d0) then
            tmp_2 = t_0
        else
            tmp_2 = (-0.5d0) * (((-2.0d0) * (c / b)) + (2.0d0 * (b / a)))
        end if
        tmp_1 = tmp_2
    else if (b <= 2.8d-279) then
        if (b >= 0.0d0) then
            tmp_3 = t_0
        else
            tmp_3 = (-0.5d0) * ((b - t_1) / a)
        end if
        tmp_1 = tmp_3
    else if (b <= 2.1d-56) then
        if (b >= 0.0d0) then
            tmp_4 = c * ((-2.0d0) / (b + t_1))
        else
            tmp_4 = (-0.5d0) * ((b + b) / a)
        end if
        tmp_1 = tmp_4
    else if (b >= 0.0d0) then
        tmp_1 = t_0
    else
        tmp_1 = b / -a
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = -c / b;
	double t_1 = Math.sqrt((-4.0 * (c * a)));
	double tmp_1;
	if (b <= -5.6e-73) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		}
		tmp_1 = tmp_2;
	} else if (b <= 2.8e-279) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = t_0;
		} else {
			tmp_3 = -0.5 * ((b - t_1) / a);
		}
		tmp_1 = tmp_3;
	} else if (b <= 2.1e-56) {
		double tmp_4;
		if (b >= 0.0) {
			tmp_4 = c * (-2.0 / (b + t_1));
		} else {
			tmp_4 = -0.5 * ((b + b) / a);
		}
		tmp_1 = tmp_4;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = b / -a;
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = -c / b
	t_1 = math.sqrt((-4.0 * (c * a)))
	tmp_1 = 0
	if b <= -5.6e-73:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = t_0
		else:
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)))
		tmp_1 = tmp_2
	elif b <= 2.8e-279:
		tmp_3 = 0
		if b >= 0.0:
			tmp_3 = t_0
		else:
			tmp_3 = -0.5 * ((b - t_1) / a)
		tmp_1 = tmp_3
	elif b <= 2.1e-56:
		tmp_4 = 0
		if b >= 0.0:
			tmp_4 = c * (-2.0 / (b + t_1))
		else:
			tmp_4 = -0.5 * ((b + b) / a)
		tmp_1 = tmp_4
	elif b >= 0.0:
		tmp_1 = t_0
	else:
		tmp_1 = b / -a
	return tmp_1

Julia

function code(a, b, c)
	t_0 = Float64(Float64(-c) / b)
	t_1 = sqrt(Float64(-4.0 * Float64(c * a)))
	tmp_1 = 0.0
	if (b <= -5.6e-73)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = t_0;
		else
			tmp_2 = Float64(-0.5 * Float64(Float64(-2.0 * Float64(c / b)) + Float64(2.0 * Float64(b / a))));
		end
		tmp_1 = tmp_2;
	elseif (b <= 2.8e-279)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = t_0;
		else
			tmp_3 = Float64(-0.5 * Float64(Float64(b - t_1) / a));
		end
		tmp_1 = tmp_3;
	elseif (b <= 2.1e-56)
		tmp_4 = 0.0
		if (b >= 0.0)
			tmp_4 = Float64(c * Float64(-2.0 / Float64(b + t_1)));
		else
			tmp_4 = Float64(-0.5 * Float64(Float64(b + b) / a));
		end
		tmp_1 = tmp_4;
	elseif (b >= 0.0)
		tmp_1 = t_0;
	else
		tmp_1 = Float64(b / Float64(-a));
	end
	return tmp_1
end

MATLAB

function tmp_6 = code(a, b, c)
	t_0 = -c / b;
	t_1 = sqrt((-4.0 * (c * a)));
	tmp_2 = 0.0;
	if (b <= -5.6e-73)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = t_0;
		else
			tmp_3 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		end
		tmp_2 = tmp_3;
	elseif (b <= 2.8e-279)
		tmp_4 = 0.0;
		if (b >= 0.0)
			tmp_4 = t_0;
		else
			tmp_4 = -0.5 * ((b - t_1) / a);
		end
		tmp_2 = tmp_4;
	elseif (b <= 2.1e-56)
		tmp_5 = 0.0;
		if (b >= 0.0)
			tmp_5 = c * (-2.0 / (b + t_1));
		else
			tmp_5 = -0.5 * ((b + b) / a);
		end
		tmp_2 = tmp_5;
	elseif (b >= 0.0)
		tmp_2 = t_0;
	else
		tmp_2 = b / -a;
	end
	tmp_6 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[((-c) / b), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(-4.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -5.6e-73], If[GreaterEqual[b, 0.0], t$95$0, N[(-0.5 * N[(N[(-2.0 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 2.8e-279], If[GreaterEqual[b, 0.0], t$95$0, N[(-0.5 * N[(N[(b - t$95$1), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 2.1e-56], If[GreaterEqual[b, 0.0], N[(c * N[(-2.0 / N[(b + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(b + b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], t$95$0, N[(b / (-a)), $MachinePrecision]]]]]]]

Derivation

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

Alternative 5: 79.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-c}{b}\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{-72}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right)\\ \end{array}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-279}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{b - \sqrt{-4 \cdot \left(c \cdot a\right)}}{a}\\ \end{array}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-56}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot -2}{b + \sqrt{a \cdot \left(c \cdot -4\right)}}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{b + b}{a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ (- c) b)))
   (if (<= b -1.1e-72)
     (if (>= b 0.0) t_0 (* -0.5 (+ (* -2.0 (/ c b)) (* 2.0 (/ b a)))))
     (if (<= b 2.8e-279)
       (if (>= b 0.0) t_0 (* -0.5 (/ (- b (sqrt (* -4.0 (* c a)))) a)))
       (if (<= b 3e-56)
         (if (>= b 0.0)
           (/ (* c -2.0) (+ b (sqrt (* a (* c -4.0)))))
           (* -0.5 (/ (+ b b) a)))
         (if (>= b 0.0) t_0 (/ b (- a))))))))

C

double code(double a, double b, double c) {
	double t_0 = -c / b;
	double tmp_1;
	if (b <= -1.1e-72) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		}
		tmp_1 = tmp_2;
	} else if (b <= 2.8e-279) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = t_0;
		} else {
			tmp_3 = -0.5 * ((b - sqrt((-4.0 * (c * a)))) / a);
		}
		tmp_1 = tmp_3;
	} else if (b <= 3e-56) {
		double tmp_4;
		if (b >= 0.0) {
			tmp_4 = (c * -2.0) / (b + sqrt((a * (c * -4.0))));
		} else {
			tmp_4 = -0.5 * ((b + b) / a);
		}
		tmp_1 = tmp_4;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = b / -a;
	}
	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
    real(8) :: tmp_3
    real(8) :: tmp_4
    t_0 = -c / b
    if (b <= (-1.1d-72)) then
        if (b >= 0.0d0) then
            tmp_2 = t_0
        else
            tmp_2 = (-0.5d0) * (((-2.0d0) * (c / b)) + (2.0d0 * (b / a)))
        end if
        tmp_1 = tmp_2
    else if (b <= 2.8d-279) then
        if (b >= 0.0d0) then
            tmp_3 = t_0
        else
            tmp_3 = (-0.5d0) * ((b - sqrt(((-4.0d0) * (c * a)))) / a)
        end if
        tmp_1 = tmp_3
    else if (b <= 3d-56) then
        if (b >= 0.0d0) then
            tmp_4 = (c * (-2.0d0)) / (b + sqrt((a * (c * (-4.0d0)))))
        else
            tmp_4 = (-0.5d0) * ((b + b) / a)
        end if
        tmp_1 = tmp_4
    else if (b >= 0.0d0) then
        tmp_1 = t_0
    else
        tmp_1 = b / -a
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = -c / b;
	double tmp_1;
	if (b <= -1.1e-72) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		}
		tmp_1 = tmp_2;
	} else if (b <= 2.8e-279) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = t_0;
		} else {
			tmp_3 = -0.5 * ((b - Math.sqrt((-4.0 * (c * a)))) / a);
		}
		tmp_1 = tmp_3;
	} else if (b <= 3e-56) {
		double tmp_4;
		if (b >= 0.0) {
			tmp_4 = (c * -2.0) / (b + Math.sqrt((a * (c * -4.0))));
		} else {
			tmp_4 = -0.5 * ((b + b) / a);
		}
		tmp_1 = tmp_4;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = b / -a;
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = -c / b
	tmp_1 = 0
	if b <= -1.1e-72:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = t_0
		else:
			tmp_2 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)))
		tmp_1 = tmp_2
	elif b <= 2.8e-279:
		tmp_3 = 0
		if b >= 0.0:
			tmp_3 = t_0
		else:
			tmp_3 = -0.5 * ((b - math.sqrt((-4.0 * (c * a)))) / a)
		tmp_1 = tmp_3
	elif b <= 3e-56:
		tmp_4 = 0
		if b >= 0.0:
			tmp_4 = (c * -2.0) / (b + math.sqrt((a * (c * -4.0))))
		else:
			tmp_4 = -0.5 * ((b + b) / a)
		tmp_1 = tmp_4
	elif b >= 0.0:
		tmp_1 = t_0
	else:
		tmp_1 = b / -a
	return tmp_1

Julia

function code(a, b, c)
	t_0 = Float64(Float64(-c) / b)
	tmp_1 = 0.0
	if (b <= -1.1e-72)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = t_0;
		else
			tmp_2 = Float64(-0.5 * Float64(Float64(-2.0 * Float64(c / b)) + Float64(2.0 * Float64(b / a))));
		end
		tmp_1 = tmp_2;
	elseif (b <= 2.8e-279)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = t_0;
		else
			tmp_3 = Float64(-0.5 * Float64(Float64(b - sqrt(Float64(-4.0 * Float64(c * a)))) / a));
		end
		tmp_1 = tmp_3;
	elseif (b <= 3e-56)
		tmp_4 = 0.0
		if (b >= 0.0)
			tmp_4 = Float64(Float64(c * -2.0) / Float64(b + sqrt(Float64(a * Float64(c * -4.0)))));
		else
			tmp_4 = Float64(-0.5 * Float64(Float64(b + b) / a));
		end
		tmp_1 = tmp_4;
	elseif (b >= 0.0)
		tmp_1 = t_0;
	else
		tmp_1 = Float64(b / Float64(-a));
	end
	return tmp_1
end

MATLAB

function tmp_6 = code(a, b, c)
	t_0 = -c / b;
	tmp_2 = 0.0;
	if (b <= -1.1e-72)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = t_0;
		else
			tmp_3 = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
		end
		tmp_2 = tmp_3;
	elseif (b <= 2.8e-279)
		tmp_4 = 0.0;
		if (b >= 0.0)
			tmp_4 = t_0;
		else
			tmp_4 = -0.5 * ((b - sqrt((-4.0 * (c * a)))) / a);
		end
		tmp_2 = tmp_4;
	elseif (b <= 3e-56)
		tmp_5 = 0.0;
		if (b >= 0.0)
			tmp_5 = (c * -2.0) / (b + sqrt((a * (c * -4.0))));
		else
			tmp_5 = -0.5 * ((b + b) / a);
		end
		tmp_2 = tmp_5;
	elseif (b >= 0.0)
		tmp_2 = t_0;
	else
		tmp_2 = b / -a;
	end
	tmp_6 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[((-c) / b), $MachinePrecision]}, If[LessEqual[b, -1.1e-72], If[GreaterEqual[b, 0.0], t$95$0, N[(-0.5 * N[(N[(-2.0 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 2.8e-279], If[GreaterEqual[b, 0.0], t$95$0, N[(-0.5 * N[(N[(b - N[Sqrt[N[(-4.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 3e-56], If[GreaterEqual[b, 0.0], N[(N[(c * -2.0), $MachinePrecision] / N[(b + N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(b + b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], t$95$0, N[(b / (-a)), $MachinePrecision]]]]]]

Derivation

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

Alternative 6: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{-4 \cdot \left(c \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{b + b}{a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 2.25e-57)
   (if (>= b 0.0)
     (* c (/ -2.0 (+ b (sqrt (* -4.0 (* c a))))))
     (* -0.5 (/ (+ b b) a)))
   (if (>= b 0.0) (/ (- c) b) (/ b (- a)))))

C

double code(double a, double b, double c) {
	double tmp_1;
	if (b <= 2.25e-57) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = c * (-2.0 / (b + sqrt((-4.0 * (c * a)))));
		} else {
			tmp_2 = -0.5 * ((b + b) / a);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = -c / b;
	} else {
		tmp_1 = b / -a;
	}
	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 <= 2.25d-57) then
        if (b >= 0.0d0) then
            tmp_2 = c * ((-2.0d0) / (b + sqrt(((-4.0d0) * (c * a)))))
        else
            tmp_2 = (-0.5d0) * ((b + b) / a)
        end if
        tmp_1 = tmp_2
    else if (b >= 0.0d0) then
        tmp_1 = -c / b
    else
        tmp_1 = b / -a
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double tmp_1;
	if (b <= 2.25e-57) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = c * (-2.0 / (b + Math.sqrt((-4.0 * (c * a)))));
		} else {
			tmp_2 = -0.5 * ((b + b) / a);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = -c / b;
	} else {
		tmp_1 = b / -a;
	}
	return tmp_1;
}

Python

def code(a, b, c):
	tmp_1 = 0
	if b <= 2.25e-57:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = c * (-2.0 / (b + math.sqrt((-4.0 * (c * a)))))
		else:
			tmp_2 = -0.5 * ((b + b) / a)
		tmp_1 = tmp_2
	elif b >= 0.0:
		tmp_1 = -c / b
	else:
		tmp_1 = b / -a
	return tmp_1

Julia

function code(a, b, c)
	tmp_1 = 0.0
	if (b <= 2.25e-57)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(c * Float64(-2.0 / Float64(b + sqrt(Float64(-4.0 * Float64(c * a))))));
		else
			tmp_2 = Float64(-0.5 * Float64(Float64(b + b) / a));
		end
		tmp_1 = tmp_2;
	elseif (b >= 0.0)
		tmp_1 = Float64(Float64(-c) / b);
	else
		tmp_1 = Float64(b / Float64(-a));
	end
	return tmp_1
end

MATLAB

function tmp_4 = code(a, b, c)
	tmp_2 = 0.0;
	if (b <= 2.25e-57)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = c * (-2.0 / (b + sqrt((-4.0 * (c * a)))));
		else
			tmp_3 = -0.5 * ((b + b) / a);
		end
		tmp_2 = tmp_3;
	elseif (b >= 0.0)
		tmp_2 = -c / b;
	else
		tmp_2 = b / -a;
	end
	tmp_4 = tmp_2;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2.25e-57], If[GreaterEqual[b, 0.0], N[(c * N[(-2.0 / N[(b + N[Sqrt[N[(-4.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(b + b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[((-c) / b), $MachinePrecision], N[(b / (-a)), $MachinePrecision]]]

Derivation

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

Alternative 7: 67.5% accurate, 6.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \left(b + -2 \cdot \frac{a}{\frac{b}{c}}\right)}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{b + b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (>= b 0.0)
   (* c (/ -2.0 (+ b (+ b (* -2.0 (/ a (/ b c)))))))
   (* -0.5 (/ (+ b b) a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = c * (-2.0 / (b + (b + (-2.0 * (a / (b / c))))));
	} else {
		tmp = -0.5 * ((b + b) / a);
	}
	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 * ((-2.0d0) / (b + (b + ((-2.0d0) * (a / (b / c))))))
    else
        tmp = (-0.5d0) * ((b + b) / a)
    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 * (-2.0 / (b + (b + (-2.0 * (a / (b / c))))));
	} else {
		tmp = -0.5 * ((b + b) / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b >= 0.0:
		tmp = c * (-2.0 / (b + (b + (-2.0 * (a / (b / c))))))
	else:
		tmp = -0.5 * ((b + b) / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(c * Float64(-2.0 / Float64(b + Float64(b + Float64(-2.0 * Float64(a / Float64(b / c)))))));
	else
		tmp = Float64(-0.5 * Float64(Float64(b + b) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b >= 0.0)
		tmp = c * (-2.0 / (b + (b + (-2.0 * (a / (b / c))))));
	else
		tmp = -0.5 * ((b + b) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[GreaterEqual[b, 0.0], N[(c * N[(-2.0 / N[(b + N[(b + N[(-2.0 * N[(a / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(b + b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 67.6% accurate, 6.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{-2 \cdot \left(c \cdot \frac{a}{b}\right) + b \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{b + b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (>= b 0.0)
   (* c (/ -2.0 (+ (* -2.0 (* c (/ a b))) (* b 2.0))))
   (* -0.5 (/ (+ b b) a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = c * (-2.0 / ((-2.0 * (c * (a / b))) + (b * 2.0)));
	} else {
		tmp = -0.5 * ((b + b) / a);
	}
	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 * ((-2.0d0) / (((-2.0d0) * (c * (a / b))) + (b * 2.0d0)))
    else
        tmp = (-0.5d0) * ((b + b) / a)
    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 * (-2.0 / ((-2.0 * (c * (a / b))) + (b * 2.0)));
	} else {
		tmp = -0.5 * ((b + b) / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b >= 0.0:
		tmp = c * (-2.0 / ((-2.0 * (c * (a / b))) + (b * 2.0)))
	else:
		tmp = -0.5 * ((b + b) / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(c * Float64(-2.0 / Float64(Float64(-2.0 * Float64(c * Float64(a / b))) + Float64(b * 2.0))));
	else
		tmp = Float64(-0.5 * Float64(Float64(b + b) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b >= 0.0)
		tmp = c * (-2.0 / ((-2.0 * (c * (a / b))) + (b * 2.0)));
	else
		tmp = -0.5 * ((b + b) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[GreaterEqual[b, 0.0], N[(c * N[(-2.0 / N[(N[(-2.0 * N[(c * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(b + b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 67.7% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (>= b 0.0) (/ (- c) b) (* -0.5 (+ (* -2.0 (/ c b)) (* 2.0 (/ b a))))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = -c / b;
	} else {
		tmp = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
	}
	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
    else
        tmp = (-0.5d0) * (((-2.0d0) * (c / b)) + (2.0d0 * (b / a)))
    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;
	} else {
		tmp = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b >= 0.0:
		tmp = -c / b
	else:
		tmp = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)))
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(Float64(-c) / b);
	else
		tmp = Float64(-0.5 * Float64(Float64(-2.0 * Float64(c / b)) + Float64(2.0 * Float64(b / a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b >= 0.0)
		tmp = -c / b;
	else
		tmp = -0.5 * ((-2.0 * (c / b)) + (2.0 * (b / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[GreaterEqual[b, 0.0], N[((-c) / b), $MachinePrecision], N[(-0.5 * N[(N[(-2.0 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 67.6% accurate, 19.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2024008 
(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))))