quad2m (problem 3.2.1, negative)

Percentage Accurate: 51.9% → 85.6%

Time: 10.4s

Alternatives: 8

Speedup: 15.9×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))

C

double code(double a, double b_2, double c) {
	return (-b_2 - sqrt(((b_2 * b_2) - (a * c)))) / a;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    code = (-b_2 - sqrt(((b_2 * b_2) - (a * c)))) / a
end function

Java

public static double code(double a, double b_2, double c) {
	return (-b_2 - Math.sqrt(((b_2 * b_2) - (a * c)))) / a;
}

Python

def code(a, b_2, c):
	return (-b_2 - math.sqrt(((b_2 * b_2) - (a * c)))) / a

Julia

function code(a, b_2, c)
	return Float64(Float64(Float64(-b_2) - sqrt(Float64(Float64(b_2 * b_2) - Float64(a * c)))) / a)
end

MATLAB

function tmp = code(a, b_2, c)
	tmp = (-b_2 - sqrt(((b_2 * b_2) - (a * c)))) / a;
end

Wolfram

code[a_, b$95$2_, c_] := N[(N[((-b$95$2) - N[Sqrt[N[(N[(b$95$2 * b$95$2), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Initial Program: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))

C

double code(double a, double b_2, double c) {
	return (-b_2 - sqrt(((b_2 * b_2) - (a * c)))) / a;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    code = (-b_2 - sqrt(((b_2 * b_2) - (a * c)))) / a
end function

Java

public static double code(double a, double b_2, double c) {
	return (-b_2 - Math.sqrt(((b_2 * b_2) - (a * c)))) / a;
}

Python

def code(a, b_2, c):
	return (-b_2 - math.sqrt(((b_2 * b_2) - (a * c)))) / a

Julia

function code(a, b_2, c)
	return Float64(Float64(Float64(-b_2) - sqrt(Float64(Float64(b_2 * b_2) - Float64(a * c)))) / a)
end

MATLAB

function tmp = code(a, b_2, c)
	tmp = (-b_2 - sqrt(((b_2 * b_2) - (a * c)))) / a;
end

Wolfram

code[a_, b$95$2_, c_] := N[(N[((-b$95$2) - N[Sqrt[N[(N[(b$95$2 * b$95$2), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Alternative 1: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b_2 \leq -4.8 \cdot 10^{-116}:\\ \;\;\;\;\frac{c \cdot -0.5}{b_2}\\ \mathbf{elif}\;b_2 \leq 4.1 \cdot 10^{+132}:\\ \;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - c \cdot a}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{b_2 \cdot -2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -4.8e-116)
   (/ (* c -0.5) b_2)
   (if (<= b_2 4.1e+132)
     (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a)
     (/ (* b_2 -2.0) a))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -4.8e-116) {
		tmp = (c * -0.5) / b_2;
	} else if (b_2 <= 4.1e+132) {
		tmp = (-b_2 - sqrt(((b_2 * b_2) - (c * a)))) / a;
	} else {
		tmp = (b_2 * -2.0) / a;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b_2 <= (-4.8d-116)) then
        tmp = (c * (-0.5d0)) / b_2
    else if (b_2 <= 4.1d+132) then
        tmp = (-b_2 - sqrt(((b_2 * b_2) - (c * a)))) / a
    else
        tmp = (b_2 * (-2.0d0)) / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -4.8e-116) {
		tmp = (c * -0.5) / b_2;
	} else if (b_2 <= 4.1e+132) {
		tmp = (-b_2 - Math.sqrt(((b_2 * b_2) - (c * a)))) / a;
	} else {
		tmp = (b_2 * -2.0) / a;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -4.8e-116:
		tmp = (c * -0.5) / b_2
	elif b_2 <= 4.1e+132:
		tmp = (-b_2 - math.sqrt(((b_2 * b_2) - (c * a)))) / a
	else:
		tmp = (b_2 * -2.0) / a
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -4.8e-116)
		tmp = Float64(Float64(c * -0.5) / b_2);
	elseif (b_2 <= 4.1e+132)
		tmp = Float64(Float64(Float64(-b_2) - sqrt(Float64(Float64(b_2 * b_2) - Float64(c * a)))) / a);
	else
		tmp = Float64(Float64(b_2 * -2.0) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -4.8e-116)
		tmp = (c * -0.5) / b_2;
	elseif (b_2 <= 4.1e+132)
		tmp = (-b_2 - sqrt(((b_2 * b_2) - (c * a)))) / a;
	else
		tmp = (b_2 * -2.0) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -4.8e-116], N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision], If[LessEqual[b$95$2, 4.1e+132], N[(N[((-b$95$2) - N[Sqrt[N[(N[(b$95$2 * b$95$2), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

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

Alternative 2: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{c \cdot \left(-a\right)}\\ \mathbf{if}\;b_2 \leq -4.8 \cdot 10^{-116}:\\ \;\;\;\;\frac{c \cdot -0.5}{b_2}\\ \mathbf{elif}\;b_2 \leq 2.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{b_2 - t_0}{a}\\ \mathbf{elif}\;b_2 \leq 9.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{b_2 \cdot -2 + 0.5 \cdot \frac{c \cdot a}{b_2}}{a}\\ \mathbf{elif}\;b_2 \leq 2.4 \cdot 10^{-51}:\\ \;\;\;\;\frac{\left(-b_2\right) - t_0}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{b_2 \cdot -2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (let* ((t_0 (sqrt (* c (- a)))))
   (if (<= b_2 -4.8e-116)
     (/ (* c -0.5) b_2)
     (if (<= b_2 2.5e-146)
       (/ (- b_2 t_0) a)
       (if (<= b_2 9.2e-71)
         (/ (+ (* b_2 -2.0) (* 0.5 (/ (* c a) b_2))) a)
         (if (<= b_2 2.4e-51) (/ (- (- b_2) t_0) a) (/ (* b_2 -2.0) a)))))))

C

double code(double a, double b_2, double c) {
	double t_0 = sqrt((c * -a));
	double tmp;
	if (b_2 <= -4.8e-116) {
		tmp = (c * -0.5) / b_2;
	} else if (b_2 <= 2.5e-146) {
		tmp = (b_2 - t_0) / a;
	} else if (b_2 <= 9.2e-71) {
		tmp = ((b_2 * -2.0) + (0.5 * ((c * a) / b_2))) / a;
	} else if (b_2 <= 2.4e-51) {
		tmp = (-b_2 - t_0) / a;
	} else {
		tmp = (b_2 * -2.0) / a;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt((c * -a))
    if (b_2 <= (-4.8d-116)) then
        tmp = (c * (-0.5d0)) / b_2
    else if (b_2 <= 2.5d-146) then
        tmp = (b_2 - t_0) / a
    else if (b_2 <= 9.2d-71) then
        tmp = ((b_2 * (-2.0d0)) + (0.5d0 * ((c * a) / b_2))) / a
    else if (b_2 <= 2.4d-51) then
        tmp = (-b_2 - t_0) / a
    else
        tmp = (b_2 * (-2.0d0)) / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double t_0 = Math.sqrt((c * -a));
	double tmp;
	if (b_2 <= -4.8e-116) {
		tmp = (c * -0.5) / b_2;
	} else if (b_2 <= 2.5e-146) {
		tmp = (b_2 - t_0) / a;
	} else if (b_2 <= 9.2e-71) {
		tmp = ((b_2 * -2.0) + (0.5 * ((c * a) / b_2))) / a;
	} else if (b_2 <= 2.4e-51) {
		tmp = (-b_2 - t_0) / a;
	} else {
		tmp = (b_2 * -2.0) / a;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	t_0 = math.sqrt((c * -a))
	tmp = 0
	if b_2 <= -4.8e-116:
		tmp = (c * -0.5) / b_2
	elif b_2 <= 2.5e-146:
		tmp = (b_2 - t_0) / a
	elif b_2 <= 9.2e-71:
		tmp = ((b_2 * -2.0) + (0.5 * ((c * a) / b_2))) / a
	elif b_2 <= 2.4e-51:
		tmp = (-b_2 - t_0) / a
	else:
		tmp = (b_2 * -2.0) / a
	return tmp

Julia

function code(a, b_2, c)
	t_0 = sqrt(Float64(c * Float64(-a)))
	tmp = 0.0
	if (b_2 <= -4.8e-116)
		tmp = Float64(Float64(c * -0.5) / b_2);
	elseif (b_2 <= 2.5e-146)
		tmp = Float64(Float64(b_2 - t_0) / a);
	elseif (b_2 <= 9.2e-71)
		tmp = Float64(Float64(Float64(b_2 * -2.0) + Float64(0.5 * Float64(Float64(c * a) / b_2))) / a);
	elseif (b_2 <= 2.4e-51)
		tmp = Float64(Float64(Float64(-b_2) - t_0) / a);
	else
		tmp = Float64(Float64(b_2 * -2.0) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	t_0 = sqrt((c * -a));
	tmp = 0.0;
	if (b_2 <= -4.8e-116)
		tmp = (c * -0.5) / b_2;
	elseif (b_2 <= 2.5e-146)
		tmp = (b_2 - t_0) / a;
	elseif (b_2 <= 9.2e-71)
		tmp = ((b_2 * -2.0) + (0.5 * ((c * a) / b_2))) / a;
	elseif (b_2 <= 2.4e-51)
		tmp = (-b_2 - t_0) / a;
	else
		tmp = (b_2 * -2.0) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := Block[{t$95$0 = N[Sqrt[N[(c * (-a)), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b$95$2, -4.8e-116], N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision], If[LessEqual[b$95$2, 2.5e-146], N[(N[(b$95$2 - t$95$0), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b$95$2, 9.2e-71], N[(N[(N[(b$95$2 * -2.0), $MachinePrecision] + N[(0.5 * N[(N[(c * a), $MachinePrecision] / b$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b$95$2, 2.4e-51], N[(N[((-b$95$2) - t$95$0), $MachinePrecision] / a), $MachinePrecision], N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

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

Alternative 3: 79.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b_2 - \sqrt{c \cdot \left(-a\right)}}{a}\\ \mathbf{if}\;b_2 \leq -2.7 \cdot 10^{-117}:\\ \;\;\;\;\frac{c \cdot -0.5}{b_2}\\ \mathbf{elif}\;b_2 \leq 2.5 \cdot 10^{-146}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b_2 \leq 2.5 \cdot 10^{-72}:\\ \;\;\;\;\frac{b_2 \cdot -2 + 0.5 \cdot \frac{c \cdot a}{b_2}}{a}\\ \mathbf{elif}\;b_2 \leq 3.8 \cdot 10^{-51}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b_2 \cdot -2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (let* ((t_0 (/ (- b_2 (sqrt (* c (- a)))) a)))
   (if (<= b_2 -2.7e-117)
     (/ (* c -0.5) b_2)
     (if (<= b_2 2.5e-146)
       t_0
       (if (<= b_2 2.5e-72)
         (/ (+ (* b_2 -2.0) (* 0.5 (/ (* c a) b_2))) a)
         (if (<= b_2 3.8e-51) t_0 (/ (* b_2 -2.0) a)))))))

C

double code(double a, double b_2, double c) {
	double t_0 = (b_2 - sqrt((c * -a))) / a;
	double tmp;
	if (b_2 <= -2.7e-117) {
		tmp = (c * -0.5) / b_2;
	} else if (b_2 <= 2.5e-146) {
		tmp = t_0;
	} else if (b_2 <= 2.5e-72) {
		tmp = ((b_2 * -2.0) + (0.5 * ((c * a) / b_2))) / a;
	} else if (b_2 <= 3.8e-51) {
		tmp = t_0;
	} else {
		tmp = (b_2 * -2.0) / a;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (b_2 - sqrt((c * -a))) / a
    if (b_2 <= (-2.7d-117)) then
        tmp = (c * (-0.5d0)) / b_2
    else if (b_2 <= 2.5d-146) then
        tmp = t_0
    else if (b_2 <= 2.5d-72) then
        tmp = ((b_2 * (-2.0d0)) + (0.5d0 * ((c * a) / b_2))) / a
    else if (b_2 <= 3.8d-51) then
        tmp = t_0
    else
        tmp = (b_2 * (-2.0d0)) / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double t_0 = (b_2 - Math.sqrt((c * -a))) / a;
	double tmp;
	if (b_2 <= -2.7e-117) {
		tmp = (c * -0.5) / b_2;
	} else if (b_2 <= 2.5e-146) {
		tmp = t_0;
	} else if (b_2 <= 2.5e-72) {
		tmp = ((b_2 * -2.0) + (0.5 * ((c * a) / b_2))) / a;
	} else if (b_2 <= 3.8e-51) {
		tmp = t_0;
	} else {
		tmp = (b_2 * -2.0) / a;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	t_0 = (b_2 - math.sqrt((c * -a))) / a
	tmp = 0
	if b_2 <= -2.7e-117:
		tmp = (c * -0.5) / b_2
	elif b_2 <= 2.5e-146:
		tmp = t_0
	elif b_2 <= 2.5e-72:
		tmp = ((b_2 * -2.0) + (0.5 * ((c * a) / b_2))) / a
	elif b_2 <= 3.8e-51:
		tmp = t_0
	else:
		tmp = (b_2 * -2.0) / a
	return tmp

Julia

function code(a, b_2, c)
	t_0 = Float64(Float64(b_2 - sqrt(Float64(c * Float64(-a)))) / a)
	tmp = 0.0
	if (b_2 <= -2.7e-117)
		tmp = Float64(Float64(c * -0.5) / b_2);
	elseif (b_2 <= 2.5e-146)
		tmp = t_0;
	elseif (b_2 <= 2.5e-72)
		tmp = Float64(Float64(Float64(b_2 * -2.0) + Float64(0.5 * Float64(Float64(c * a) / b_2))) / a);
	elseif (b_2 <= 3.8e-51)
		tmp = t_0;
	else
		tmp = Float64(Float64(b_2 * -2.0) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	t_0 = (b_2 - sqrt((c * -a))) / a;
	tmp = 0.0;
	if (b_2 <= -2.7e-117)
		tmp = (c * -0.5) / b_2;
	elseif (b_2 <= 2.5e-146)
		tmp = t_0;
	elseif (b_2 <= 2.5e-72)
		tmp = ((b_2 * -2.0) + (0.5 * ((c * a) / b_2))) / a;
	elseif (b_2 <= 3.8e-51)
		tmp = t_0;
	else
		tmp = (b_2 * -2.0) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := Block[{t$95$0 = N[(N[(b$95$2 - N[Sqrt[N[(c * (-a)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[b$95$2, -2.7e-117], N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision], If[LessEqual[b$95$2, 2.5e-146], t$95$0, If[LessEqual[b$95$2, 2.5e-72], N[(N[(N[(b$95$2 * -2.0), $MachinePrecision] + N[(0.5 * N[(N[(c * a), $MachinePrecision] / b$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b$95$2, 3.8e-51], t$95$0, N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 68.2% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b_2 \leq -1 \cdot 10^{-310}:\\ \;\;\;\;\frac{c \cdot -0.5}{b_2}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b_2}{a} + 0.5 \cdot \frac{c}{b_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -1e-310)
   (/ (* c -0.5) b_2)
   (+ (* -2.0 (/ b_2 a)) (* 0.5 (/ c b_2)))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1e-310) {
		tmp = (c * -0.5) / b_2;
	} else {
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2));
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b_2 <= (-1d-310)) then
        tmp = (c * (-0.5d0)) / b_2
    else
        tmp = ((-2.0d0) * (b_2 / a)) + (0.5d0 * (c / b_2))
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1e-310) {
		tmp = (c * -0.5) / b_2;
	} else {
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2));
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -1e-310:
		tmp = (c * -0.5) / b_2
	else:
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2))
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -1e-310)
		tmp = Float64(Float64(c * -0.5) / b_2);
	else
		tmp = Float64(Float64(-2.0 * Float64(b_2 / a)) + Float64(0.5 * Float64(c / b_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -1e-310)
		tmp = (c * -0.5) / b_2;
	else
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -1e-310], N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision], N[(N[(-2.0 * N[(b$95$2 / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 48.2% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b_2 \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b_2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -1.9e-284) (* -0.5 (/ c b_2)) (/ (- b_2) a)))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1.9e-284) {
		tmp = -0.5 * (c / b_2);
	} else {
		tmp = -b_2 / a;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b_2 <= (-1.9d-284)) then
        tmp = (-0.5d0) * (c / b_2)
    else
        tmp = -b_2 / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1.9e-284) {
		tmp = -0.5 * (c / b_2);
	} else {
		tmp = -b_2 / a;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -1.9e-284:
		tmp = -0.5 * (c / b_2)
	else:
		tmp = -b_2 / a
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -1.9e-284)
		tmp = Float64(-0.5 * Float64(c / b_2));
	else
		tmp = Float64(Float64(-b_2) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -1.9e-284)
		tmp = -0.5 * (c / b_2);
	else
		tmp = -b_2 / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -1.9e-284], N[(-0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision], N[((-b$95$2) / a), $MachinePrecision]]

Derivation

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

Alternative 6: 68.0% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b_2 \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{b_2 \cdot -2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -1.9e-284) (* -0.5 (/ c b_2)) (/ (* b_2 -2.0) a)))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1.9e-284) {
		tmp = -0.5 * (c / b_2);
	} else {
		tmp = (b_2 * -2.0) / a;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b_2 <= (-1.9d-284)) then
        tmp = (-0.5d0) * (c / b_2)
    else
        tmp = (b_2 * (-2.0d0)) / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1.9e-284) {
		tmp = -0.5 * (c / b_2);
	} else {
		tmp = (b_2 * -2.0) / a;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -1.9e-284:
		tmp = -0.5 * (c / b_2)
	else:
		tmp = (b_2 * -2.0) / a
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -1.9e-284)
		tmp = Float64(-0.5 * Float64(c / b_2));
	else
		tmp = Float64(Float64(b_2 * -2.0) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -1.9e-284)
		tmp = -0.5 * (c / b_2);
	else
		tmp = (b_2 * -2.0) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -1.9e-284], N[(-0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision]]

Derivation

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

Alternative 7: 68.0% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b_2 \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;\frac{c \cdot -0.5}{b_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{b_2 \cdot -2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -1.9e-284) (/ (* c -0.5) b_2) (/ (* b_2 -2.0) a)))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1.9e-284) {
		tmp = (c * -0.5) / b_2;
	} else {
		tmp = (b_2 * -2.0) / a;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b_2 <= (-1.9d-284)) then
        tmp = (c * (-0.5d0)) / b_2
    else
        tmp = (b_2 * (-2.0d0)) / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1.9e-284) {
		tmp = (c * -0.5) / b_2;
	} else {
		tmp = (b_2 * -2.0) / a;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -1.9e-284:
		tmp = (c * -0.5) / b_2
	else:
		tmp = (b_2 * -2.0) / a
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -1.9e-284)
		tmp = Float64(Float64(c * -0.5) / b_2);
	else
		tmp = Float64(Float64(b_2 * -2.0) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -1.9e-284)
		tmp = (c * -0.5) / b_2;
	else
		tmp = (b_2 * -2.0) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -1.9e-284], N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision], N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision]]

Derivation

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

Alternative 8: 15.6% accurate, 28.0× speedup

Math

\[\begin{array}{l} \\ \frac{-b_2}{a} \end{array} \]

FPCore

(FPCore (a b_2 c) :precision binary64 (/ (- b_2) a))

C

double code(double a, double b_2, double c) {
	return -b_2 / a;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    code = -b_2 / a
end function

Java

public static double code(double a, double b_2, double c) {
	return -b_2 / a;
}

Python

def code(a, b_2, c):
	return -b_2 / a

Julia

function code(a, b_2, c)
	return Float64(Float64(-b_2) / a)
end

MATLAB

function tmp = code(a, b_2, c)
	tmp = -b_2 / a;
end

Wolfram

code[a_, b$95$2_, c_] := N[((-b$95$2) / a), $MachinePrecision]

Derivation

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

Developer target: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{\left|a\right|} \cdot \sqrt{\left|c\right|}\\ t_1 := \begin{array}{l} \mathbf{if}\;\mathsf{copysign}\left(a, c\right) = a:\\ \;\;\;\;\sqrt{\left|b_2\right| - t_0} \cdot \sqrt{\left|b_2\right| + t_0}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{hypot}\left(b_2, t_0\right)\\ \end{array}\\ \mathbf{if}\;b_2 < 0:\\ \;\;\;\;\frac{c}{t_1 - b_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{b_2 + t_1}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (let* ((t_0 (* (sqrt (fabs a)) (sqrt (fabs c))))
        (t_1
         (if (== (copysign a c) a)
           (* (sqrt (- (fabs b_2) t_0)) (sqrt (+ (fabs b_2) t_0)))
           (hypot b_2 t_0))))
   (if (< b_2 0.0) (/ c (- t_1 b_2)) (/ (+ b_2 t_1) (- a)))))

C

double code(double a, double b_2, double c) {
	double t_0 = sqrt(fabs(a)) * sqrt(fabs(c));
	double tmp;
	if (copysign(a, c) == a) {
		tmp = sqrt((fabs(b_2) - t_0)) * sqrt((fabs(b_2) + t_0));
	} else {
		tmp = hypot(b_2, t_0);
	}
	double t_1 = tmp;
	double tmp_1;
	if (b_2 < 0.0) {
		tmp_1 = c / (t_1 - b_2);
	} else {
		tmp_1 = (b_2 + t_1) / -a;
	}
	return tmp_1;
}

Java

public static double code(double a, double b_2, double c) {
	double t_0 = Math.sqrt(Math.abs(a)) * Math.sqrt(Math.abs(c));
	double tmp;
	if (Math.copySign(a, c) == a) {
		tmp = Math.sqrt((Math.abs(b_2) - t_0)) * Math.sqrt((Math.abs(b_2) + t_0));
	} else {
		tmp = Math.hypot(b_2, t_0);
	}
	double t_1 = tmp;
	double tmp_1;
	if (b_2 < 0.0) {
		tmp_1 = c / (t_1 - b_2);
	} else {
		tmp_1 = (b_2 + t_1) / -a;
	}
	return tmp_1;
}

Python

def code(a, b_2, c):
	t_0 = math.sqrt(math.fabs(a)) * math.sqrt(math.fabs(c))
	tmp = 0
	if math.copysign(a, c) == a:
		tmp = math.sqrt((math.fabs(b_2) - t_0)) * math.sqrt((math.fabs(b_2) + t_0))
	else:
		tmp = math.hypot(b_2, t_0)
	t_1 = tmp
	tmp_1 = 0
	if b_2 < 0.0:
		tmp_1 = c / (t_1 - b_2)
	else:
		tmp_1 = (b_2 + t_1) / -a
	return tmp_1

Julia

function code(a, b_2, c)
	t_0 = Float64(sqrt(abs(a)) * sqrt(abs(c)))
	tmp = 0.0
	if (copysign(a, c) == a)
		tmp = Float64(sqrt(Float64(abs(b_2) - t_0)) * sqrt(Float64(abs(b_2) + t_0)));
	else
		tmp = hypot(b_2, t_0);
	end
	t_1 = tmp
	tmp_1 = 0.0
	if (b_2 < 0.0)
		tmp_1 = Float64(c / Float64(t_1 - b_2));
	else
		tmp_1 = Float64(Float64(b_2 + t_1) / Float64(-a));
	end
	return tmp_1
end

MATLAB

function tmp_3 = code(a, b_2, c)
	t_0 = sqrt(abs(a)) * sqrt(abs(c));
	tmp = 0.0;
	if ((sign(c) * abs(a)) == a)
		tmp = sqrt((abs(b_2) - t_0)) * sqrt((abs(b_2) + t_0));
	else
		tmp = hypot(b_2, t_0);
	end
	t_1 = tmp;
	tmp_2 = 0.0;
	if (b_2 < 0.0)
		tmp_2 = c / (t_1 - b_2);
	else
		tmp_2 = (b_2 + t_1) / -a;
	end
	tmp_3 = tmp_2;
end

Wolfram

code[a_, b$95$2_, c_] := Block[{t$95$0 = N[(N[Sqrt[N[Abs[a], $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[Abs[c], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = If[Equal[N[With[{TMP1 = Abs[a], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], a], N[(N[Sqrt[N[(N[Abs[b$95$2], $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(N[Abs[b$95$2], $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Sqrt[b$95$2 ^ 2 + t$95$0 ^ 2], $MachinePrecision]]}, If[Less[b$95$2, 0.0], N[(c / N[(t$95$1 - b$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(b$95$2 + t$95$1), $MachinePrecision] / (-a)), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2023343 
(FPCore (a b_2 c)
  :name "quad2m (problem 3.2.1, negative)"
  :precision binary64
  :herbie-expected 10

  :herbie-target
  (if (< b_2 0.0) (/ c (- (if (== (copysign a c) a) (* (sqrt (- (fabs b_2) (* (sqrt (fabs a)) (sqrt (fabs c))))) (sqrt (+ (fabs b_2) (* (sqrt (fabs a)) (sqrt (fabs c)))))) (hypot b_2 (* (sqrt (fabs a)) (sqrt (fabs c))))) b_2)) (/ (+ b_2 (if (== (copysign a c) a) (* (sqrt (- (fabs b_2) (* (sqrt (fabs a)) (sqrt (fabs c))))) (sqrt (+ (fabs b_2) (* (sqrt (fabs a)) (sqrt (fabs c)))))) (hypot b_2 (* (sqrt (fabs a)) (sqrt (fabs c)))))) (- a)))

  (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))