jeff quadratic root 2

Percentage Accurate: 72.6% → 91.2%

Time: 25.3s

Alternatives: 9

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: 72.6% 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: 91.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+146}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+127}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0 - b}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot -2}{\mathsf{fma}\left(-2, c \cdot \frac{a}{b}, b \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, b, 2 \cdot \frac{a}{\frac{b}{c}}\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (<= b -4.8e+146)
     (if (>= b 0.0) (/ (- c) b) (/ (- b) a))
     (if (<= b 5e+127)
       (if (>= b 0.0) (/ (* c 2.0) (- (- b) t_0)) (/ (- t_0 b) (* a 2.0)))
       (if (>= b 0.0)
         (/ (* c -2.0) (fma -2.0 (* c (/ a b)) (* b 2.0)))
         (/ (fma -2.0 b (* 2.0 (/ a (/ b c)))) (* a 2.0)))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -4.8e+146) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = -c / b;
		} else {
			tmp_2 = -b / a;
		}
		tmp_1 = tmp_2;
	} else if (b <= 5e+127) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (c * 2.0) / (-b - t_0);
		} else {
			tmp_3 = (t_0 - b) / (a * 2.0);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = (c * -2.0) / fma(-2.0, (c * (a / b)), (b * 2.0));
	} else {
		tmp_1 = fma(-2.0, b, (2.0 * (a / (b / c)))) / (a * 2.0);
	}
	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 <= -4.8e+146)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(Float64(-c) / b);
		else
			tmp_2 = Float64(Float64(-b) / a);
		end
		tmp_1 = tmp_2;
	elseif (b <= 5e+127)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(c * 2.0) / Float64(Float64(-b) - t_0));
		else
			tmp_3 = Float64(Float64(t_0 - b) / Float64(a * 2.0));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = Float64(Float64(c * -2.0) / fma(-2.0, Float64(c * Float64(a / b)), Float64(b * 2.0)));
	else
		tmp_1 = Float64(fma(-2.0, b, Float64(2.0 * Float64(a / Float64(b / c)))) / Float64(a * 2.0));
	end
	return tmp_1
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[LessEqual[b, -4.8e+146], If[GreaterEqual[b, 0.0], N[((-c) / b), $MachinePrecision], N[((-b) / a), $MachinePrecision]], If[LessEqual[b, 5e+127], If[GreaterEqual[b, 0.0], N[(N[(c * 2.0), $MachinePrecision] / N[((-b) - t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(N[(c * -2.0), $MachinePrecision] / N[(-2.0 * N[(c * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(b * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 * b + N[(2.0 * N[(a / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 2: 91.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+146}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+129}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{\left(-b\right) - t_0}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0 - b}{a \cdot 2}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot -2}{\mathsf{fma}\left(-2, c \cdot \frac{a}{b}, b \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, b, 2 \cdot \frac{a}{\frac{b}{c}}\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (<= b -4.6e+146)
     (if (>= b 0.0) (/ (- c) b) (/ (- b) a))
     (if (<= b 1.9e+129)
       (if (>= b 0.0) (/ 2.0 (/ (- (- b) t_0) c)) (/ (- t_0 b) (* a 2.0)))
       (if (>= b 0.0)
         (/ (* c -2.0) (fma -2.0 (* c (/ a b)) (* b 2.0)))
         (/ (fma -2.0 b (* 2.0 (/ a (/ b c)))) (* a 2.0)))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -4.6e+146) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = -c / b;
		} else {
			tmp_2 = -b / a;
		}
		tmp_1 = tmp_2;
	} else if (b <= 1.9e+129) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = 2.0 / ((-b - t_0) / c);
		} else {
			tmp_3 = (t_0 - b) / (a * 2.0);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = (c * -2.0) / fma(-2.0, (c * (a / b)), (b * 2.0));
	} else {
		tmp_1 = fma(-2.0, b, (2.0 * (a / (b / c)))) / (a * 2.0);
	}
	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 <= -4.6e+146)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(Float64(-c) / b);
		else
			tmp_2 = Float64(Float64(-b) / a);
		end
		tmp_1 = tmp_2;
	elseif (b <= 1.9e+129)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(2.0 / Float64(Float64(Float64(-b) - t_0) / c));
		else
			tmp_3 = Float64(Float64(t_0 - b) / Float64(a * 2.0));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = Float64(Float64(c * -2.0) / fma(-2.0, Float64(c * Float64(a / b)), Float64(b * 2.0)));
	else
		tmp_1 = Float64(fma(-2.0, b, Float64(2.0 * Float64(a / Float64(b / c)))) / Float64(a * 2.0));
	end
	return tmp_1
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[LessEqual[b, -4.6e+146], If[GreaterEqual[b, 0.0], N[((-c) / b), $MachinePrecision], N[((-b) / a), $MachinePrecision]], If[LessEqual[b, 1.9e+129], If[GreaterEqual[b, 0.0], N[(2.0 / N[(N[((-b) - t$95$0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(N[(c * -2.0), $MachinePrecision] / N[(-2.0 * N[(c * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(b * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 * b + N[(2.0 * N[(a / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 3: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.7 \cdot 10^{+145}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{2}{-2 \cdot \frac{b}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -8.7e+145)
   (if (>= b 0.0) (/ (- c) b) (/ (- b) a))
   (if (>= b 0.0)
     (/ 2.0 (* -2.0 (/ b c)))
     (/ (- (sqrt (- (* b b) (* c (* a 4.0)))) b) (* a 2.0)))))

C

double code(double a, double b, double c) {
	double tmp_1;
	if (b <= -8.7e+145) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = -c / b;
		} else {
			tmp_2 = -b / a;
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = 2.0 / (-2.0 * (b / c));
	} else {
		tmp_1 = (sqrt(((b * b) - (c * (a * 4.0)))) - b) / (a * 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 <= (-8.7d+145)) then
        if (b >= 0.0d0) then
            tmp_2 = -c / b
        else
            tmp_2 = -b / a
        end if
        tmp_1 = tmp_2
    else if (b >= 0.0d0) then
        tmp_1 = 2.0d0 / ((-2.0d0) * (b / c))
    else
        tmp_1 = (sqrt(((b * b) - (c * (a * 4.0d0)))) - b) / (a * 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 <= -8.7e+145) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = -c / b;
		} else {
			tmp_2 = -b / a;
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = 2.0 / (-2.0 * (b / c));
	} else {
		tmp_1 = (Math.sqrt(((b * b) - (c * (a * 4.0)))) - b) / (a * 2.0);
	}
	return tmp_1;
}

Python

def code(a, b, c):
	tmp_1 = 0
	if b <= -8.7e+145:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = -c / b
		else:
			tmp_2 = -b / a
		tmp_1 = tmp_2
	elif b >= 0.0:
		tmp_1 = 2.0 / (-2.0 * (b / c))
	else:
		tmp_1 = (math.sqrt(((b * b) - (c * (a * 4.0)))) - b) / (a * 2.0)
	return tmp_1

Julia

function code(a, b, c)
	tmp_1 = 0.0
	if (b <= -8.7e+145)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(Float64(-c) / b);
		else
			tmp_2 = Float64(Float64(-b) / a);
		end
		tmp_1 = tmp_2;
	elseif (b >= 0.0)
		tmp_1 = Float64(2.0 / Float64(-2.0 * Float64(b / c)));
	else
		tmp_1 = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0)))) - b) / Float64(a * 2.0));
	end
	return tmp_1
end

MATLAB

function tmp_4 = code(a, b, c)
	tmp_2 = 0.0;
	if (b <= -8.7e+145)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = -c / b;
		else
			tmp_3 = -b / a;
		end
		tmp_2 = tmp_3;
	elseif (b >= 0.0)
		tmp_2 = 2.0 / (-2.0 * (b / c));
	else
		tmp_2 = (sqrt(((b * b) - (c * (a * 4.0)))) - b) / (a * 2.0);
	end
	tmp_4 = tmp_2;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -8.7e+145], If[GreaterEqual[b, 0.0], N[((-c) / b), $MachinePrecision], N[((-b) / a), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(2.0 / N[(-2.0 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 4: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{-2 \cdot \frac{b}{c}}\\ \mathbf{if}\;b \leq -2.25 \cdot 10^{-152}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\left(c \cdot a\right) \cdot -4} - b}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ 2.0 (* -2.0 (/ b c)))))
   (if (<= b -2.25e-152)
     (if (>= b 0.0) t_0 (- (/ c b) (/ b a)))
     (if (>= b 0.0) t_0 (/ (- (sqrt (* (* c a) -4.0)) b) (* a 2.0))))))

C

double code(double a, double b, double c) {
	double t_0 = 2.0 / (-2.0 * (b / c));
	double tmp_1;
	if (b <= -2.25e-152) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = (c / b) - (b / a);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = (sqrt(((c * a) * -4.0)) - b) / (a * 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) :: t_0
    real(8) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    t_0 = 2.0d0 / ((-2.0d0) * (b / c))
    if (b <= (-2.25d-152)) then
        if (b >= 0.0d0) then
            tmp_2 = t_0
        else
            tmp_2 = (c / b) - (b / a)
        end if
        tmp_1 = tmp_2
    else if (b >= 0.0d0) then
        tmp_1 = t_0
    else
        tmp_1 = (sqrt(((c * a) * (-4.0d0))) - b) / (a * 2.0d0)
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = 2.0 / (-2.0 * (b / c));
	double tmp_1;
	if (b <= -2.25e-152) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = (c / b) - (b / a);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = (Math.sqrt(((c * a) * -4.0)) - b) / (a * 2.0);
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = 2.0 / (-2.0 * (b / c))
	tmp_1 = 0
	if b <= -2.25e-152:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = t_0
		else:
			tmp_2 = (c / b) - (b / a)
		tmp_1 = tmp_2
	elif b >= 0.0:
		tmp_1 = t_0
	else:
		tmp_1 = (math.sqrt(((c * a) * -4.0)) - b) / (a * 2.0)
	return tmp_1

Julia

function code(a, b, c)
	t_0 = Float64(2.0 / Float64(-2.0 * Float64(b / c)))
	tmp_1 = 0.0
	if (b <= -2.25e-152)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = t_0;
		else
			tmp_2 = Float64(Float64(c / b) - Float64(b / a));
		end
		tmp_1 = tmp_2;
	elseif (b >= 0.0)
		tmp_1 = t_0;
	else
		tmp_1 = Float64(Float64(sqrt(Float64(Float64(c * a) * -4.0)) - b) / Float64(a * 2.0));
	end
	return tmp_1
end

MATLAB

function tmp_4 = code(a, b, c)
	t_0 = 2.0 / (-2.0 * (b / c));
	tmp_2 = 0.0;
	if (b <= -2.25e-152)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = t_0;
		else
			tmp_3 = (c / b) - (b / a);
		end
		tmp_2 = tmp_3;
	elseif (b >= 0.0)
		tmp_2 = t_0;
	else
		tmp_2 = (sqrt(((c * a) * -4.0)) - b) / (a * 2.0);
	end
	tmp_4 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(2.0 / N[(-2.0 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.25e-152], If[GreaterEqual[b, 0.0], t$95$0, N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], t$95$0, N[(N[(N[Sqrt[N[(N[(c * a), $MachinePrecision] * -4.0), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 5: 68.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (a b c)
 :precision binary64
 (if (>= b 0.0)
   (/ 2.0 (fma -2.0 (/ b c) (/ (* a 2.0) b)))
   (fma -1.0 (/ b a) (/ c b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = 2.0 / fma(-2.0, (b / c), ((a * 2.0) / b));
	} else {
		tmp = fma(-1.0, (b / a), (c / b));
	}
	return tmp;
}

Julia

function code(a, b, c)
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(2.0 / fma(-2.0, Float64(b / c), Float64(Float64(a * 2.0) / b)));
	else
		tmp = fma(-1.0, Float64(b / a), Float64(c / b));
	end
	return tmp
end

Wolfram

code[a_, b_, c_] := If[GreaterEqual[b, 0.0], N[(2.0 / N[(-2.0 * N[(b / c), $MachinePrecision] + N[(N[(a * 2.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(b / a), $MachinePrecision] + N[(c / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 68.3% accurate, 10.1× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 7: 68.7% accurate, 10.1× speedup

Math

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

FPCore

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

C

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

Python

def code(a, b, c):
	tmp = 0
	if b >= 0.0:
		tmp = -c / b
	else:
		tmp = (c / b) - (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(Float64(c / b) - 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 = (c / b) - (b / a);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

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

Alternative 8: 35.4% accurate, 13.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 9: 68.5% accurate, 13.4× 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(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 = -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 2024006 
(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))))