Cubic critical

Percentage Accurate: 51.6% → 90.4%

Time: 20.1s

Alternatives: 13

Speedup: 16.4×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-b + sqrt(((b * b) - ((3.0d0 * a) * c)))) / (3.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(3.0 * a) * c)))) / Float64(3.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(3.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(3.0 * a), $MachinePrecision]), $MachinePrecision]

Initial Program: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-b + sqrt(((b * b) - ((3.0d0 * a) * c)))) / (3.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(3.0 * a) * c)))) / Float64(3.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(3.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(3.0 * a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{\frac{a}{b} \cdot -1.5}\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-301}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 3\right) \cdot c} - b}{a \cdot 3}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+92}:\\ \;\;\;\;\frac{c \cdot \left(--3\right)}{-3 \cdot \left(b + \sqrt{{b}^{2} + a \cdot \left(c \cdot -3\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.2e+143)
   (/ 1.0 (* (/ a b) -1.5))
   (if (<= b -6.6e-301)
     (/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
     (if (<= b 2.1e+92)
       (/
        (* c (- -3.0))
        (* -3.0 (+ b (sqrt (+ (pow b 2.0) (* a (* c -3.0)))))))
       (/ (* c -0.5) b)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.2e+143) {
		tmp = 1.0 / ((a / b) * -1.5);
	} else if (b <= -6.6e-301) {
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else if (b <= 2.1e+92) {
		tmp = (c * -(-3.0)) / (-3.0 * (b + sqrt((pow(b, 2.0) + (a * (c * -3.0))))));
	} else {
		tmp = (c * -0.5) / 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 <= (-3.2d+143)) then
        tmp = 1.0d0 / ((a / b) * (-1.5d0))
    else if (b <= (-6.6d-301)) then
        tmp = (sqrt(((b * b) - ((a * 3.0d0) * c))) - b) / (a * 3.0d0)
    else if (b <= 2.1d+92) then
        tmp = (c * -(-3.0d0)) / ((-3.0d0) * (b + sqrt(((b ** 2.0d0) + (a * (c * (-3.0d0)))))))
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.2e+143) {
		tmp = 1.0 / ((a / b) * -1.5);
	} else if (b <= -6.6e-301) {
		tmp = (Math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else if (b <= 2.1e+92) {
		tmp = (c * -(-3.0)) / (-3.0 * (b + Math.sqrt((Math.pow(b, 2.0) + (a * (c * -3.0))))));
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -3.2e+143:
		tmp = 1.0 / ((a / b) * -1.5)
	elif b <= -6.6e-301:
		tmp = (math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0)
	elif b <= 2.1e+92:
		tmp = (c * -(-3.0)) / (-3.0 * (b + math.sqrt((math.pow(b, 2.0) + (a * (c * -3.0))))))
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.2e+143)
		tmp = Float64(1.0 / Float64(Float64(a / b) * -1.5));
	elseif (b <= -6.6e-301)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(Float64(a * 3.0) * c))) - b) / Float64(a * 3.0));
	elseif (b <= 2.1e+92)
		tmp = Float64(Float64(c * Float64(-(-3.0))) / Float64(-3.0 * Float64(b + sqrt(Float64((b ^ 2.0) + Float64(a * Float64(c * -3.0)))))));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -3.2e+143)
		tmp = 1.0 / ((a / b) * -1.5);
	elseif (b <= -6.6e-301)
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	elseif (b <= 2.1e+92)
		tmp = (c * -(-3.0)) / (-3.0 * (b + sqrt(((b ^ 2.0) + (a * (c * -3.0))))));
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.2e+143], N[(1.0 / N[(N[(a / b), $MachinePrecision] * -1.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.6e-301], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(a * 3.0), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+92], N[(N[(c * (--3.0)), $MachinePrecision] / N[(-3.0 * N[(b + N[Sqrt[N[(N[Power[b, 2.0], $MachinePrecision] + N[(a * N[(c * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]

Derivation

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

Alternative 2: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{\frac{a}{b} \cdot -1.5}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 3 \cdot \left(a \cdot c\right)} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.5e+143)
   (/ 1.0 (* (/ a b) -1.5))
   (if (<= b 1.6e-59)
     (/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* a 3.0))
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.5e+143) {
		tmp = 1.0 / ((a / b) * -1.5);
	} else if (b <= 1.6e-59) {
		tmp = (sqrt(((b * b) - (3.0 * (a * c)))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / 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 <= (-3.5d+143)) then
        tmp = 1.0d0 / ((a / b) * (-1.5d0))
    else if (b <= 1.6d-59) then
        tmp = (sqrt(((b * b) - (3.0d0 * (a * c)))) - b) / (a * 3.0d0)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.5e+143) {
		tmp = 1.0 / ((a / b) * -1.5);
	} else if (b <= 1.6e-59) {
		tmp = (Math.sqrt(((b * b) - (3.0 * (a * c)))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -3.5e+143:
		tmp = 1.0 / ((a / b) * -1.5)
	elif b <= 1.6e-59:
		tmp = (math.sqrt(((b * b) - (3.0 * (a * c)))) - b) / (a * 3.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.5e+143)
		tmp = Float64(1.0 / Float64(Float64(a / b) * -1.5));
	elseif (b <= 1.6e-59)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(3.0 * Float64(a * c)))) - b) / Float64(a * 3.0));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -3.5e+143)
		tmp = 1.0 / ((a / b) * -1.5);
	elseif (b <= 1.6e-59)
		tmp = (sqrt(((b * b) - (3.0 * (a * c)))) - b) / (a * 3.0);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.5e+143], N[(1.0 / N[(N[(a / b), $MachinePrecision] * -1.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-59], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(3.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

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

Alternative 3: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{\frac{a}{b} \cdot -1.5}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 3\right) \cdot c} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.8e+143)
   (/ 1.0 (* (/ a b) -1.5))
   (if (<= b 5e-61)
     (/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.8e+143) {
		tmp = 1.0 / ((a / b) * -1.5);
	} else if (b <= 5e-61) {
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / 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 <= (-1.8d+143)) then
        tmp = 1.0d0 / ((a / b) * (-1.5d0))
    else if (b <= 5d-61) then
        tmp = (sqrt(((b * b) - ((a * 3.0d0) * c))) - b) / (a * 3.0d0)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.8e+143) {
		tmp = 1.0 / ((a / b) * -1.5);
	} else if (b <= 5e-61) {
		tmp = (Math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.8e+143:
		tmp = 1.0 / ((a / b) * -1.5)
	elif b <= 5e-61:
		tmp = (math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.8e+143)
		tmp = Float64(1.0 / Float64(Float64(a / b) * -1.5));
	elseif (b <= 5e-61)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(Float64(a * 3.0) * c))) - b) / Float64(a * 3.0));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1.8e+143)
		tmp = 1.0 / ((a / b) * -1.5);
	elseif (b <= 5e-61)
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.8e+143], N[(1.0 / N[(N[(a / b), $MachinePrecision] * -1.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e-61], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(a * 3.0), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

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

Alternative 4: 80.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{b \cdot -2}{a \cdot 3}\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-62}:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(c \cdot -3\right)} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2.8e-58)
   (/ (* b -2.0) (* a 3.0))
   (if (<= b 7.4e-62)
     (/ (- (sqrt (* a (* c -3.0))) b) (* a 3.0))
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.8e-58) {
		tmp = (b * -2.0) / (a * 3.0);
	} else if (b <= 7.4e-62) {
		tmp = (sqrt((a * (c * -3.0))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / 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 <= (-2.8d-58)) then
        tmp = (b * (-2.0d0)) / (a * 3.0d0)
    else if (b <= 7.4d-62) then
        tmp = (sqrt((a * (c * (-3.0d0)))) - b) / (a * 3.0d0)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.8e-58) {
		tmp = (b * -2.0) / (a * 3.0);
	} else if (b <= 7.4e-62) {
		tmp = (Math.sqrt((a * (c * -3.0))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2.8e-58:
		tmp = (b * -2.0) / (a * 3.0)
	elif b <= 7.4e-62:
		tmp = (math.sqrt((a * (c * -3.0))) - b) / (a * 3.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2.8e-58)
		tmp = Float64(Float64(b * -2.0) / Float64(a * 3.0));
	elseif (b <= 7.4e-62)
		tmp = Float64(Float64(sqrt(Float64(a * Float64(c * -3.0))) - b) / Float64(a * 3.0));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -2.8e-58)
		tmp = (b * -2.0) / (a * 3.0);
	elseif (b <= 7.4e-62)
		tmp = (sqrt((a * (c * -3.0))) - b) / (a * 3.0);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2.8e-58], N[(N[(b * -2.0), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.4e-62], N[(N[(N[Sqrt[N[(a * N[(c * -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

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

Alternative 5: 80.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{-58}:\\ \;\;\;\;\frac{b \cdot -2}{a \cdot 3}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-61}:\\ \;\;\;\;\frac{-\sqrt{a \cdot \left(c \cdot -3\right)}}{a \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2.2e-58)
   (/ (* b -2.0) (* a 3.0))
   (if (<= b 3.8e-61)
     (/ (- (sqrt (* a (* c -3.0)))) (* a -3.0))
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.2e-58) {
		tmp = (b * -2.0) / (a * 3.0);
	} else if (b <= 3.8e-61) {
		tmp = -sqrt((a * (c * -3.0))) / (a * -3.0);
	} else {
		tmp = (c * -0.5) / 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 <= (-2.2d-58)) then
        tmp = (b * (-2.0d0)) / (a * 3.0d0)
    else if (b <= 3.8d-61) then
        tmp = -sqrt((a * (c * (-3.0d0)))) / (a * (-3.0d0))
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.2e-58) {
		tmp = (b * -2.0) / (a * 3.0);
	} else if (b <= 3.8e-61) {
		tmp = -Math.sqrt((a * (c * -3.0))) / (a * -3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2.2e-58:
		tmp = (b * -2.0) / (a * 3.0)
	elif b <= 3.8e-61:
		tmp = -math.sqrt((a * (c * -3.0))) / (a * -3.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2.2e-58)
		tmp = Float64(Float64(b * -2.0) / Float64(a * 3.0));
	elseif (b <= 3.8e-61)
		tmp = Float64(Float64(-sqrt(Float64(a * Float64(c * -3.0)))) / Float64(a * -3.0));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -2.2e-58)
		tmp = (b * -2.0) / (a * 3.0);
	elseif (b <= 3.8e-61)
		tmp = -sqrt((a * (c * -3.0))) / (a * -3.0);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2.2e-58], N[(N[(b * -2.0), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e-61], N[((-N[Sqrt[N[(a * N[(c * -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / N[(a * -3.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

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

Alternative 6: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{b \cdot -2}{a \cdot 3}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-60}:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(c \cdot -0.3333333333333333\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2.8e-58)
   (/ (* b -2.0) (* a 3.0))
   (if (<= b 2.7e-60)
     (/ (sqrt (* a (* c -0.3333333333333333))) a)
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.8e-58) {
		tmp = (b * -2.0) / (a * 3.0);
	} else if (b <= 2.7e-60) {
		tmp = sqrt((a * (c * -0.3333333333333333))) / a;
	} else {
		tmp = (c * -0.5) / 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 <= (-2.8d-58)) then
        tmp = (b * (-2.0d0)) / (a * 3.0d0)
    else if (b <= 2.7d-60) then
        tmp = sqrt((a * (c * (-0.3333333333333333d0)))) / a
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.8e-58) {
		tmp = (b * -2.0) / (a * 3.0);
	} else if (b <= 2.7e-60) {
		tmp = Math.sqrt((a * (c * -0.3333333333333333))) / a;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2.8e-58:
		tmp = (b * -2.0) / (a * 3.0)
	elif b <= 2.7e-60:
		tmp = math.sqrt((a * (c * -0.3333333333333333))) / a
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2.8e-58)
		tmp = Float64(Float64(b * -2.0) / Float64(a * 3.0));
	elseif (b <= 2.7e-60)
		tmp = Float64(sqrt(Float64(a * Float64(c * -0.3333333333333333))) / a);
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -2.8e-58)
		tmp = (b * -2.0) / (a * 3.0);
	elseif (b <= 2.7e-60)
		tmp = sqrt((a * (c * -0.3333333333333333))) / a;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2.8e-58], N[(N[(b * -2.0), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e-60], N[(N[Sqrt[N[(a * N[(c * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / a), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

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

Alternative 7: 68.2% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{b \cdot -2}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -5e-310) (/ (* b -2.0) (* a 3.0)) (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-310) {
		tmp = (b * -2.0) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / 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 <= (-5d-310)) then
        tmp = (b * (-2.0d0)) / (a * 3.0d0)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-310) {
		tmp = (b * -2.0) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -5e-310:
		tmp = (b * -2.0) / (a * 3.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5e-310)
		tmp = Float64(Float64(b * -2.0) / Float64(a * 3.0));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -5e-310)
		tmp = (b * -2.0) / (a * 3.0);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -5e-310], N[(N[(b * -2.0), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

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

Alternative 8: 44.1% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{-301}:\\ \;\;\;\;-0.6666666666666666 \cdot \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -6.6e-301) (* -0.6666666666666666 (/ b a)) 0.0))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -6.6e-301) {
		tmp = -0.6666666666666666 * (b / a);
	} else {
		tmp = 0.0;
	}
	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 <= (-6.6d-301)) then
        tmp = (-0.6666666666666666d0) * (b / a)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -6.6e-301) {
		tmp = -0.6666666666666666 * (b / a);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -6.6e-301:
		tmp = -0.6666666666666666 * (b / a)
	else:
		tmp = 0.0
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -6.6e-301)
		tmp = Float64(-0.6666666666666666 * Float64(b / a));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -6.6e-301)
		tmp = -0.6666666666666666 * (b / a);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -6.6e-301], N[(-0.6666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

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

Alternative 9: 67.9% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-310}:\\ \;\;\;\;-0.6666666666666666 \cdot \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{\frac{b}{c}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -5e-310) (* -0.6666666666666666 (/ b a)) (/ -0.5 (/ b c))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-310) {
		tmp = -0.6666666666666666 * (b / a);
	} else {
		tmp = -0.5 / (b / c);
	}
	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 <= (-5d-310)) then
        tmp = (-0.6666666666666666d0) * (b / a)
    else
        tmp = (-0.5d0) / (b / c)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-310) {
		tmp = -0.6666666666666666 * (b / a);
	} else {
		tmp = -0.5 / (b / c);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -5e-310:
		tmp = -0.6666666666666666 * (b / a)
	else:
		tmp = -0.5 / (b / c)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5e-310)
		tmp = Float64(-0.6666666666666666 * Float64(b / a));
	else
		tmp = Float64(-0.5 / Float64(b / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -5e-310)
		tmp = -0.6666666666666666 * (b / a);
	else
		tmp = -0.5 / (b / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -5e-310], N[(-0.6666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision], N[(-0.5 / N[(b / c), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 67.9% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 10^{-309}:\\ \;\;\;\;\frac{b}{\frac{a}{-0.6666666666666666}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{\frac{b}{c}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 1e-309) (/ b (/ a -0.6666666666666666)) (/ -0.5 (/ b c))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 1e-309) {
		tmp = b / (a / -0.6666666666666666);
	} else {
		tmp = -0.5 / (b / c);
	}
	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 <= 1d-309) then
        tmp = b / (a / (-0.6666666666666666d0))
    else
        tmp = (-0.5d0) / (b / c)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 1e-309) {
		tmp = b / (a / -0.6666666666666666);
	} else {
		tmp = -0.5 / (b / c);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 1e-309:
		tmp = b / (a / -0.6666666666666666)
	else:
		tmp = -0.5 / (b / c)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 1e-309)
		tmp = Float64(b / Float64(a / -0.6666666666666666));
	else
		tmp = Float64(-0.5 / Float64(b / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 1e-309)
		tmp = b / (a / -0.6666666666666666);
	else
		tmp = -0.5 / (b / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 1e-309], N[(b / N[(a / -0.6666666666666666), $MachinePrecision]), $MachinePrecision], N[(-0.5 / N[(b / c), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 68.3% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8 \cdot 10^{-309}:\\ \;\;\;\;\frac{b}{\frac{a}{-0.6666666666666666}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 8e-309) (/ b (/ a -0.6666666666666666)) (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 8e-309) {
		tmp = b / (a / -0.6666666666666666);
	} else {
		tmp = (c * -0.5) / 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 <= 8d-309) then
        tmp = b / (a / (-0.6666666666666666d0))
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 8e-309) {
		tmp = b / (a / -0.6666666666666666);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 8e-309:
		tmp = b / (a / -0.6666666666666666)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 8e-309)
		tmp = Float64(b / Float64(a / -0.6666666666666666));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 8e-309)
		tmp = b / (a / -0.6666666666666666);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 8e-309], N[(b / N[(a / -0.6666666666666666), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

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

Alternative 12: 68.3% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{b \cdot -0.6666666666666666}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -5e-310) (/ (* b -0.6666666666666666) a) (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-310) {
		tmp = (b * -0.6666666666666666) / a;
	} else {
		tmp = (c * -0.5) / 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 <= (-5d-310)) then
        tmp = (b * (-0.6666666666666666d0)) / a
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-310) {
		tmp = (b * -0.6666666666666666) / a;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -5e-310:
		tmp = (b * -0.6666666666666666) / a
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5e-310)
		tmp = Float64(Float64(b * -0.6666666666666666) / a);
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -5e-310)
		tmp = (b * -0.6666666666666666) / a;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -5e-310], N[(N[(b * -0.6666666666666666), $MachinePrecision] / a), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

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

Alternative 13: 11.3% accurate, 116.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 0.0)

C

double code(double a, double b, double c) {
	return 0.0;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = 0.0d0
end function

Java

public static double code(double a, double b, double c) {
	return 0.0;
}

Python

def code(a, b, c):
	return 0.0

Julia

function code(a, b, c)
	return 0.0
end

MATLAB

function tmp = code(a, b, c)
	tmp = 0.0;
end

Wolfram

code[a_, b_, c_] := 0.0

Derivation

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

Reproduce

herbie shell --seed 2024010 
(FPCore (a b c)
  :name "Cubic critical"
  :precision binary64
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))