jeff quadratic root 1

Percentage Accurate: 72.3% → 90.0%

Time: 19.8s

Alternatives: 7

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: 72.3% 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: 90.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := c \cdot \frac{a}{b}\\ t_1 := \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}\\ \mathbf{if}\;b \leq -2 \cdot 10^{+155}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;-0.5 \cdot \frac{\mathsf{fma}\left(b, 2, -2 \cdot t_0\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\mathsf{fma}\left(2, t_0, -b\right) - b}\\ \end{array}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+61}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;-0.5 \cdot \frac{b + t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{t_1 - b}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;-\frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{-2 \cdot \frac{b}{c}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (* c (/ a b))) (t_1 (sqrt (fma b b (* a (* c -4.0))))))
   (if (<= b -2e+155)
     (if (>= b 0.0)
       (* -0.5 (/ (fma b 2.0 (* -2.0 t_0)) a))
       (/ (* 2.0 c) (- (fma 2.0 t_0 (- b)) b)))
     (if (<= b 7e+61)
       (if (>= b 0.0) (* -0.5 (/ (+ b t_1) a)) (/ (* 2.0 c) (- t_1 b)))
       (if (>= b 0.0) (- (/ b a)) (/ 2.0 (* -2.0 (/ b c))))))))

C

double code(double a, double b, double c) {
	double t_0 = c * (a / b);
	double t_1 = sqrt(fma(b, b, (a * (c * -4.0))));
	double tmp_1;
	if (b <= -2e+155) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = -0.5 * (fma(b, 2.0, (-2.0 * t_0)) / a);
		} else {
			tmp_2 = (2.0 * c) / (fma(2.0, t_0, -b) - b);
		}
		tmp_1 = tmp_2;
	} else if (b <= 7e+61) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = -0.5 * ((b + t_1) / a);
		} else {
			tmp_3 = (2.0 * c) / (t_1 - b);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = -(b / a);
	} else {
		tmp_1 = 2.0 / (-2.0 * (b / c));
	}
	return tmp_1;
}

Julia

function code(a, b, c)
	t_0 = Float64(c * Float64(a / b))
	t_1 = sqrt(fma(b, b, Float64(a * Float64(c * -4.0))))
	tmp_1 = 0.0
	if (b <= -2e+155)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(-0.5 * Float64(fma(b, 2.0, Float64(-2.0 * t_0)) / a));
		else
			tmp_2 = Float64(Float64(2.0 * c) / Float64(fma(2.0, t_0, Float64(-b)) - b));
		end
		tmp_1 = tmp_2;
	elseif (b <= 7e+61)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(-0.5 * Float64(Float64(b + t_1) / a));
		else
			tmp_3 = Float64(Float64(2.0 * c) / Float64(t_1 - b));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = Float64(-Float64(b / a));
	else
		tmp_1 = Float64(2.0 / Float64(-2.0 * Float64(b / c)));
	end
	return tmp_1
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(c * N[(a / b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(b * b + N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -2e+155], If[GreaterEqual[b, 0.0], N[(-0.5 * N[(N[(b * 2.0 + N[(-2.0 * t$95$0), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * c), $MachinePrecision] / N[(N[(2.0 * t$95$0 + (-b)), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 7e+61], If[GreaterEqual[b, 0.0], N[(-0.5 * N[(N[(b + t$95$1), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * c), $MachinePrecision] / N[(t$95$1 - b), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], (-N[(b / a), $MachinePrecision]), N[(2.0 / N[(-2.0 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+91}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;-0.5 \cdot \frac{\mathsf{fma}\left(-2, \frac{a}{\frac{b}{c}}, b \cdot 2\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\mathsf{fma}\left(2, c \cdot \frac{a}{b}, b \cdot -2\right)}\\ \end{array}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+61}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - t_0}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{t_0 - b}{c}}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;-\frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{-2 \cdot \frac{b}{c}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* 4.0 (* c a))))))
   (if (<= b -4.4e+91)
     (if (>= b 0.0)
       (* -0.5 (/ (fma -2.0 (/ a (/ b c)) (* b 2.0)) a))
       (/ (* 2.0 c) (fma 2.0 (* c (/ a b)) (* b -2.0))))
     (if (<= b 7e+61)
       (if (>= b 0.0) (/ (- (- b) t_0) (* 2.0 a)) (/ 2.0 (/ (- t_0 b) c)))
       (if (>= b 0.0) (- (/ b a)) (/ 2.0 (* -2.0 (/ 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 <= -4.4e+91) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = -0.5 * (fma(-2.0, (a / (b / c)), (b * 2.0)) / a);
		} else {
			tmp_2 = (2.0 * c) / fma(2.0, (c * (a / b)), (b * -2.0));
		}
		tmp_1 = tmp_2;
	} else if (b <= 7e+61) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (-b - t_0) / (2.0 * a);
		} else {
			tmp_3 = 2.0 / ((t_0 - b) / c);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = -(b / a);
	} else {
		tmp_1 = 2.0 / (-2.0 * (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 <= -4.4e+91)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(-0.5 * Float64(fma(-2.0, Float64(a / Float64(b / c)), Float64(b * 2.0)) / a));
		else
			tmp_2 = Float64(Float64(2.0 * c) / fma(2.0, Float64(c * Float64(a / b)), Float64(b * -2.0)));
		end
		tmp_1 = tmp_2;
	elseif (b <= 7e+61)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(Float64(-b) - t_0) / Float64(2.0 * a));
		else
			tmp_3 = Float64(2.0 / Float64(Float64(t_0 - b) / c));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = Float64(-Float64(b / a));
	else
		tmp_1 = Float64(2.0 / Float64(-2.0 * Float64(b / c)));
	end
	return tmp_1
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[LessEqual[b, -4.4e+91], If[GreaterEqual[b, 0.0], N[(-0.5 * N[(N[(-2.0 * N[(a / N[(b / c), $MachinePrecision]), $MachinePrecision] + N[(b * 2.0), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * c), $MachinePrecision] / N[(2.0 * N[(c * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 7e+61], If[GreaterEqual[b, 0.0], N[(N[((-b) - t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(N[(t$95$0 - b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], (-N[(b / a), $MachinePrecision]), N[(2.0 / N[(-2.0 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 3: 90.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ t_1 := c \cdot \frac{a}{b}\\ \mathbf{if}\;b \leq -2 \cdot 10^{+155}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;-0.5 \cdot \frac{\mathsf{fma}\left(b, 2, -2 \cdot t_1\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{\mathsf{fma}\left(2, t_1, -b\right) - b}\\ \end{array}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+61}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - t_0}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot c}{t_0 - b}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;-\frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{-2 \cdot \frac{b}{c}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* c (* a 4.0))))) (t_1 (* c (/ a b))))
   (if (<= b -2e+155)
     (if (>= b 0.0)
       (* -0.5 (/ (fma b 2.0 (* -2.0 t_1)) a))
       (/ (* 2.0 c) (- (fma 2.0 t_1 (- b)) b)))
     (if (<= b 7e+61)
       (if (>= b 0.0) (/ (- (- b) t_0) (* 2.0 a)) (/ (* 2.0 c) (- t_0 b)))
       (if (>= b 0.0) (- (/ b a)) (/ 2.0 (* -2.0 (/ b c))))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - (c * (a * 4.0))));
	double t_1 = c * (a / b);
	double tmp_1;
	if (b <= -2e+155) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = -0.5 * (fma(b, 2.0, (-2.0 * t_1)) / a);
		} else {
			tmp_2 = (2.0 * c) / (fma(2.0, t_1, -b) - b);
		}
		tmp_1 = tmp_2;
	} else if (b <= 7e+61) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (-b - t_0) / (2.0 * a);
		} else {
			tmp_3 = (2.0 * c) / (t_0 - b);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = -(b / a);
	} else {
		tmp_1 = 2.0 / (-2.0 * (b / c));
	}
	return tmp_1;
}

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	t_1 = Float64(c * Float64(a / b))
	tmp_1 = 0.0
	if (b <= -2e+155)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(-0.5 * Float64(fma(b, 2.0, Float64(-2.0 * t_1)) / a));
		else
			tmp_2 = Float64(Float64(2.0 * c) / Float64(fma(2.0, t_1, Float64(-b)) - b));
		end
		tmp_1 = tmp_2;
	elseif (b <= 7e+61)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(Float64(-b) - t_0) / Float64(2.0 * a));
		else
			tmp_3 = Float64(Float64(2.0 * c) / Float64(t_0 - b));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = Float64(-Float64(b / a));
	else
		tmp_1 = Float64(2.0 / Float64(-2.0 * Float64(b / c)));
	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]}, Block[{t$95$1 = N[(c * N[(a / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+155], If[GreaterEqual[b, 0.0], N[(-0.5 * N[(N[(b * 2.0 + N[(-2.0 * t$95$1), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * c), $MachinePrecision] / N[(N[(2.0 * t$95$1 + (-b)), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 7e+61], 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[(t$95$0 - b), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], (-N[(b / a), $MachinePrecision]), N[(2.0 / N[(-2.0 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 78.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{-2 \cdot \frac{b}{c}}\\ \mathbf{if}\;b \leq 7 \cdot 10^{+61}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;-\frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ 2.0 (* -2.0 (/ b c)))))
   (if (<= b 7e+61)
     (if (>= b 0.0)
       (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))) (* 2.0 a))
       t_0)
     (if (>= b 0.0) (- (/ b a)) t_0))))

C

double code(double a, double b, double c) {
	double t_0 = 2.0 / (-2.0 * (b / c));
	double tmp_1;
	if (b <= 7e+61) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = (-b - sqrt(((b * b) - (4.0 * (c * a))))) / (2.0 * a);
		} else {
			tmp_2 = t_0;
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = -(b / a);
	} 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) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    t_0 = 2.0d0 / ((-2.0d0) * (b / c))
    if (b <= 7d+61) then
        if (b >= 0.0d0) then
            tmp_2 = (-b - sqrt(((b * b) - (4.0d0 * (c * a))))) / (2.0d0 * a)
        else
            tmp_2 = t_0
        end if
        tmp_1 = tmp_2
    else if (b >= 0.0d0) then
        tmp_1 = -(b / a)
    else
        tmp_1 = t_0
    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 <= 7e+61) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = (-b - Math.sqrt(((b * b) - (4.0 * (c * a))))) / (2.0 * a);
		} else {
			tmp_2 = t_0;
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = -(b / a);
	} else {
		tmp_1 = t_0;
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = 2.0 / (-2.0 * (b / c))
	tmp_1 = 0
	if b <= 7e+61:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = (-b - math.sqrt(((b * b) - (4.0 * (c * a))))) / (2.0 * a)
		else:
			tmp_2 = t_0
		tmp_1 = tmp_2
	elif b >= 0.0:
		tmp_1 = -(b / a)
	else:
		tmp_1 = t_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 <= 7e+61)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(Float64(Float64(-b) - sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(c * a))))) / Float64(2.0 * a));
		else
			tmp_2 = t_0;
		end
		tmp_1 = tmp_2;
	elseif (b >= 0.0)
		tmp_1 = Float64(-Float64(b / a));
	else
		tmp_1 = t_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 <= 7e+61)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = (-b - sqrt(((b * b) - (4.0 * (c * a))))) / (2.0 * a);
		else
			tmp_3 = t_0;
		end
		tmp_2 = tmp_3;
	elseif (b >= 0.0)
		tmp_2 = -(b / a);
	else
		tmp_2 = t_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, 7e+61], If[GreaterEqual[b, 0.0], N[(N[((-b) - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], t$95$0], If[GreaterEqual[b, 0.0], (-N[(b / a), $MachinePrecision]), t$95$0]]]

Derivation

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

Alternative 5: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.1 \cdot 10^{-81}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;-0.5 \cdot \frac{b + \sqrt{a \cdot \left(c \cdot -4\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\mathsf{fma}\left(2, \frac{a}{b}, -2 \cdot \frac{b}{c}\right)}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{2}{b \cdot -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 7.1e-81)
   (if (>= b 0.0)
     (* -0.5 (/ (+ b (sqrt (* a (* c -4.0)))) a))
     (/ 2.0 (fma 2.0 (/ a b) (* -2.0 (/ 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 <= 7.1e-81) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = -0.5 * ((b + sqrt((a * (c * -4.0)))) / a);
		} else {
			tmp_2 = 2.0 / fma(2.0, (a / b), (-2.0 * (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;
}

Julia

function code(a, b, c)
	tmp_1 = 0.0
	if (b <= 7.1e-81)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(-0.5 * Float64(Float64(b + sqrt(Float64(a * Float64(c * -4.0)))) / a));
		else
			tmp_2 = Float64(2.0 / fma(2.0, Float64(a / b), Float64(-2.0 * Float64(b / c))));
		end
		tmp_1 = tmp_2;
	elseif (b >= 0.0)
		tmp_1 = Float64(Float64(c / b) - Float64(b / a));
	else
		tmp_1 = Float64(c * Float64(2.0 / Float64(b * -2.0)));
	end
	return tmp_1
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 7.1e-81], If[GreaterEqual[b, 0.0], N[(-0.5 * N[(N[(b + N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(2.0 * N[(a / b), $MachinePrecision] + N[(-2.0 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[(c * N[(2.0 / N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 6: 67.6% accurate, 13.0× speedup

Math

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

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(c * Float64(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[(c * N[(2.0 / N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 67.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Python

def code(a, b, c):
	tmp = 0
	if b >= 0.0:
		tmp = (c / b) - (b / a)
	else:
		tmp = -c / b
	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) / b);
	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 / b;
	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[((-c) / b), $MachinePrecision]]

Derivation

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

Reproduce

herbie shell --seed 2023348 
(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)))))))