Cubic critical

Percentage Accurate: 51.7% → 84.3%

Time: 18.4s

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: 51.7% 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: 84.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+109}:\\ \;\;\;\;\frac{\frac{b}{-1.5}}{a}\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-274}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 3\right) \cdot c} - b}{a \cdot 3}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-218}:\\ \;\;\;\;\frac{b + \left(\mathsf{hypot}\left(b, \sqrt{c \cdot -3} \cdot \sqrt{a}\right) + \left(b + b\right)\right)}{a \cdot 3}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-44}:\\ \;\;\;\;{\left(\frac{a}{\left(b + \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -3\right)}\right)\right) \cdot 0.3333333333333333}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.65e+109)
   (/ (/ b -1.5) a)
   (if (<= b 2.95e-274)
     (/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
     (if (<= b 3.6e-218)
       (/ (+ b (+ (hypot b (* (sqrt (* c -3.0)) (sqrt a))) (+ b b))) (* a 3.0))
       (if (<= b 1.4e-44)
         (pow
          (/ a (* (+ b (hypot b (sqrt (* c (* a -3.0))))) 0.3333333333333333))
          -1.0)
         (/ (* c -0.5) b))))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.65e+109) {
		tmp = (b / -1.5) / a;
	} else if (b <= 2.95e-274) {
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else if (b <= 3.6e-218) {
		tmp = (b + (hypot(b, (sqrt((c * -3.0)) * sqrt(a))) + (b + b))) / (a * 3.0);
	} else if (b <= 1.4e-44) {
		tmp = pow((a / ((b + hypot(b, sqrt((c * (a * -3.0))))) * 0.3333333333333333)), -1.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.65e+109) {
		tmp = (b / -1.5) / a;
	} else if (b <= 2.95e-274) {
		tmp = (Math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else if (b <= 3.6e-218) {
		tmp = (b + (Math.hypot(b, (Math.sqrt((c * -3.0)) * Math.sqrt(a))) + (b + b))) / (a * 3.0);
	} else if (b <= 1.4e-44) {
		tmp = Math.pow((a / ((b + Math.hypot(b, Math.sqrt((c * (a * -3.0))))) * 0.3333333333333333)), -1.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.65e+109:
		tmp = (b / -1.5) / a
	elif b <= 2.95e-274:
		tmp = (math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0)
	elif b <= 3.6e-218:
		tmp = (b + (math.hypot(b, (math.sqrt((c * -3.0)) * math.sqrt(a))) + (b + b))) / (a * 3.0)
	elif b <= 1.4e-44:
		tmp = math.pow((a / ((b + math.hypot(b, math.sqrt((c * (a * -3.0))))) * 0.3333333333333333)), -1.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.65e+109)
		tmp = Float64(Float64(b / -1.5) / a);
	elseif (b <= 2.95e-274)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(Float64(a * 3.0) * c))) - b) / Float64(a * 3.0));
	elseif (b <= 3.6e-218)
		tmp = Float64(Float64(b + Float64(hypot(b, Float64(sqrt(Float64(c * -3.0)) * sqrt(a))) + Float64(b + b))) / Float64(a * 3.0));
	elseif (b <= 1.4e-44)
		tmp = Float64(a / Float64(Float64(b + hypot(b, sqrt(Float64(c * Float64(a * -3.0))))) * 0.3333333333333333)) ^ -1.0;
	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 <= -1.65e+109)
		tmp = (b / -1.5) / a;
	elseif (b <= 2.95e-274)
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	elseif (b <= 3.6e-218)
		tmp = (b + (hypot(b, (sqrt((c * -3.0)) * sqrt(a))) + (b + b))) / (a * 3.0);
	elseif (b <= 1.4e-44)
		tmp = (a / ((b + hypot(b, sqrt((c * (a * -3.0))))) * 0.3333333333333333)) ^ -1.0;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.65e+109], N[(N[(b / -1.5), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 2.95e-274], 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, 3.6e-218], N[(N[(b + N[(N[Sqrt[b ^ 2 + N[(N[Sqrt[N[(c * -3.0), $MachinePrecision]], $MachinePrecision] * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision] + N[(b + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-44], N[Power[N[(a / N[(N[(b + N[Sqrt[b ^ 2 + N[Sqrt[N[(c * N[(a * -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

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1. Add Preprocessing

Alternative 2: 84.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+107}:\\ \;\;\;\;\frac{\frac{b}{-1.5}}{a}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-273}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 3\right) \cdot c} - b}{a \cdot 3}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-218}:\\ \;\;\;\;\left(\mathsf{hypot}\left(b, \sqrt{c \cdot -3} \cdot \sqrt{a}\right) - b\right) \cdot \frac{0.3333333333333333}{a}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-46}:\\ \;\;\;\;{\left(\frac{a}{\left(b + \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -3\right)}\right)\right) \cdot 0.3333333333333333}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2.4e+107)
   (/ (/ b -1.5) a)
   (if (<= b 1.7e-273)
     (/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
     (if (<= b 3.4e-218)
       (*
        (- (hypot b (* (sqrt (* c -3.0)) (sqrt a))) b)
        (/ 0.3333333333333333 a))
       (if (<= b 5.3e-46)
         (pow
          (/ a (* (+ b (hypot b (sqrt (* c (* a -3.0))))) 0.3333333333333333))
          -1.0)
         (/ (* c -0.5) b))))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.4e+107) {
		tmp = (b / -1.5) / a;
	} else if (b <= 1.7e-273) {
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else if (b <= 3.4e-218) {
		tmp = (hypot(b, (sqrt((c * -3.0)) * sqrt(a))) - b) * (0.3333333333333333 / a);
	} else if (b <= 5.3e-46) {
		tmp = pow((a / ((b + hypot(b, sqrt((c * (a * -3.0))))) * 0.3333333333333333)), -1.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.4e+107) {
		tmp = (b / -1.5) / a;
	} else if (b <= 1.7e-273) {
		tmp = (Math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else if (b <= 3.4e-218) {
		tmp = (Math.hypot(b, (Math.sqrt((c * -3.0)) * Math.sqrt(a))) - b) * (0.3333333333333333 / a);
	} else if (b <= 5.3e-46) {
		tmp = Math.pow((a / ((b + Math.hypot(b, Math.sqrt((c * (a * -3.0))))) * 0.3333333333333333)), -1.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2.4e+107:
		tmp = (b / -1.5) / a
	elif b <= 1.7e-273:
		tmp = (math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0)
	elif b <= 3.4e-218:
		tmp = (math.hypot(b, (math.sqrt((c * -3.0)) * math.sqrt(a))) - b) * (0.3333333333333333 / a)
	elif b <= 5.3e-46:
		tmp = math.pow((a / ((b + math.hypot(b, math.sqrt((c * (a * -3.0))))) * 0.3333333333333333)), -1.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2.4e+107)
		tmp = Float64(Float64(b / -1.5) / a);
	elseif (b <= 1.7e-273)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(Float64(a * 3.0) * c))) - b) / Float64(a * 3.0));
	elseif (b <= 3.4e-218)
		tmp = Float64(Float64(hypot(b, Float64(sqrt(Float64(c * -3.0)) * sqrt(a))) - b) * Float64(0.3333333333333333 / a));
	elseif (b <= 5.3e-46)
		tmp = Float64(a / Float64(Float64(b + hypot(b, sqrt(Float64(c * Float64(a * -3.0))))) * 0.3333333333333333)) ^ -1.0;
	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 <= -2.4e+107)
		tmp = (b / -1.5) / a;
	elseif (b <= 1.7e-273)
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	elseif (b <= 3.4e-218)
		tmp = (hypot(b, (sqrt((c * -3.0)) * sqrt(a))) - b) * (0.3333333333333333 / a);
	elseif (b <= 5.3e-46)
		tmp = (a / ((b + hypot(b, sqrt((c * (a * -3.0))))) * 0.3333333333333333)) ^ -1.0;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2.4e+107], N[(N[(b / -1.5), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 1.7e-273], 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, 3.4e-218], N[(N[(N[Sqrt[b ^ 2 + N[(N[Sqrt[N[(c * -3.0), $MachinePrecision]], $MachinePrecision] * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision] - b), $MachinePrecision] * N[(0.3333333333333333 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.3e-46], N[Power[N[(a / N[(N[(b + N[Sqrt[b ^ 2 + N[Sqrt[N[(c * N[(a * -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

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1. Add Preprocessing

Alternative 3: 84.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+109}:\\ \;\;\;\;\frac{\frac{b}{-1.5}}{a}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-275}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 3\right) \cdot c} - b}{a \cdot 3}\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-218}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\mathsf{hypot}\left(b, \sqrt{c \cdot -3} \cdot \sqrt{a}\right) - b}{a}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-44}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{b \cdot 3 + \mathsf{hypot}\left(b, \sqrt{a \cdot \left(c \cdot -3\right)}\right)}{3}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.7e+109)
   (/ (/ b -1.5) a)
   (if (<= b 1.45e-275)
     (/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
     (if (<= b 3.9e-218)
       (*
        0.3333333333333333
        (/ (- (hypot b (* (sqrt (* c -3.0)) (sqrt a))) b) a))
       (if (<= b 6e-44)
         (/ 1.0 (/ a (/ (+ (* b 3.0) (hypot b (sqrt (* a (* c -3.0))))) 3.0)))
         (/ (* c -0.5) b))))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.7e+109) {
		tmp = (b / -1.5) / a;
	} else if (b <= 1.45e-275) {
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else if (b <= 3.9e-218) {
		tmp = 0.3333333333333333 * ((hypot(b, (sqrt((c * -3.0)) * sqrt(a))) - b) / a);
	} else if (b <= 6e-44) {
		tmp = 1.0 / (a / (((b * 3.0) + hypot(b, sqrt((a * (c * -3.0))))) / 3.0));
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.7e+109) {
		tmp = (b / -1.5) / a;
	} else if (b <= 1.45e-275) {
		tmp = (Math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else if (b <= 3.9e-218) {
		tmp = 0.3333333333333333 * ((Math.hypot(b, (Math.sqrt((c * -3.0)) * Math.sqrt(a))) - b) / a);
	} else if (b <= 6e-44) {
		tmp = 1.0 / (a / (((b * 3.0) + Math.hypot(b, Math.sqrt((a * (c * -3.0))))) / 3.0));
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.7e+109:
		tmp = (b / -1.5) / a
	elif b <= 1.45e-275:
		tmp = (math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0)
	elif b <= 3.9e-218:
		tmp = 0.3333333333333333 * ((math.hypot(b, (math.sqrt((c * -3.0)) * math.sqrt(a))) - b) / a)
	elif b <= 6e-44:
		tmp = 1.0 / (a / (((b * 3.0) + math.hypot(b, math.sqrt((a * (c * -3.0))))) / 3.0))
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.7e+109)
		tmp = Float64(Float64(b / -1.5) / a);
	elseif (b <= 1.45e-275)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(Float64(a * 3.0) * c))) - b) / Float64(a * 3.0));
	elseif (b <= 3.9e-218)
		tmp = Float64(0.3333333333333333 * Float64(Float64(hypot(b, Float64(sqrt(Float64(c * -3.0)) * sqrt(a))) - b) / a));
	elseif (b <= 6e-44)
		tmp = Float64(1.0 / Float64(a / Float64(Float64(Float64(b * 3.0) + hypot(b, sqrt(Float64(a * Float64(c * -3.0))))) / 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 <= -1.7e+109)
		tmp = (b / -1.5) / a;
	elseif (b <= 1.45e-275)
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	elseif (b <= 3.9e-218)
		tmp = 0.3333333333333333 * ((hypot(b, (sqrt((c * -3.0)) * sqrt(a))) - b) / a);
	elseif (b <= 6e-44)
		tmp = 1.0 / (a / (((b * 3.0) + hypot(b, sqrt((a * (c * -3.0))))) / 3.0));
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.7e+109], N[(N[(b / -1.5), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 1.45e-275], 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, 3.9e-218], N[(0.3333333333333333 * N[(N[(N[Sqrt[b ^ 2 + N[(N[Sqrt[N[(c * -3.0), $MachinePrecision]], $MachinePrecision] * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision] - b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-44], N[(1.0 / N[(a / N[(N[(N[(b * 3.0), $MachinePrecision] + N[Sqrt[b ^ 2 + N[Sqrt[N[(a * N[(c * -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

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1. Add Preprocessing

Alternative 4: 84.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+109}:\\ \;\;\;\;\frac{\frac{b}{-1.5}}{a}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-275}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 3\right) \cdot c} - b}{a \cdot 3}\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-218}:\\ \;\;\;\;\left(\mathsf{hypot}\left(b, \sqrt{c \cdot -3} \cdot \sqrt{a}\right) - b\right) \cdot \frac{0.3333333333333333}{a}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-46}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{b \cdot 3 + \mathsf{hypot}\left(b, \sqrt{a \cdot \left(c \cdot -3\right)}\right)}{3}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.7e+109)
   (/ (/ b -1.5) a)
   (if (<= b 1.45e-275)
     (/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
     (if (<= b 3.9e-218)
       (*
        (- (hypot b (* (sqrt (* c -3.0)) (sqrt a))) b)
        (/ 0.3333333333333333 a))
       (if (<= b 6e-46)
         (/ 1.0 (/ a (/ (+ (* b 3.0) (hypot b (sqrt (* a (* c -3.0))))) 3.0)))
         (/ (* c -0.5) b))))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.7e+109) {
		tmp = (b / -1.5) / a;
	} else if (b <= 1.45e-275) {
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else if (b <= 3.9e-218) {
		tmp = (hypot(b, (sqrt((c * -3.0)) * sqrt(a))) - b) * (0.3333333333333333 / a);
	} else if (b <= 6e-46) {
		tmp = 1.0 / (a / (((b * 3.0) + hypot(b, sqrt((a * (c * -3.0))))) / 3.0));
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.7e+109) {
		tmp = (b / -1.5) / a;
	} else if (b <= 1.45e-275) {
		tmp = (Math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else if (b <= 3.9e-218) {
		tmp = (Math.hypot(b, (Math.sqrt((c * -3.0)) * Math.sqrt(a))) - b) * (0.3333333333333333 / a);
	} else if (b <= 6e-46) {
		tmp = 1.0 / (a / (((b * 3.0) + Math.hypot(b, Math.sqrt((a * (c * -3.0))))) / 3.0));
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.7e+109:
		tmp = (b / -1.5) / a
	elif b <= 1.45e-275:
		tmp = (math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0)
	elif b <= 3.9e-218:
		tmp = (math.hypot(b, (math.sqrt((c * -3.0)) * math.sqrt(a))) - b) * (0.3333333333333333 / a)
	elif b <= 6e-46:
		tmp = 1.0 / (a / (((b * 3.0) + math.hypot(b, math.sqrt((a * (c * -3.0))))) / 3.0))
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.7e+109)
		tmp = Float64(Float64(b / -1.5) / a);
	elseif (b <= 1.45e-275)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(Float64(a * 3.0) * c))) - b) / Float64(a * 3.0));
	elseif (b <= 3.9e-218)
		tmp = Float64(Float64(hypot(b, Float64(sqrt(Float64(c * -3.0)) * sqrt(a))) - b) * Float64(0.3333333333333333 / a));
	elseif (b <= 6e-46)
		tmp = Float64(1.0 / Float64(a / Float64(Float64(Float64(b * 3.0) + hypot(b, sqrt(Float64(a * Float64(c * -3.0))))) / 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 <= -1.7e+109)
		tmp = (b / -1.5) / a;
	elseif (b <= 1.45e-275)
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	elseif (b <= 3.9e-218)
		tmp = (hypot(b, (sqrt((c * -3.0)) * sqrt(a))) - b) * (0.3333333333333333 / a);
	elseif (b <= 6e-46)
		tmp = 1.0 / (a / (((b * 3.0) + hypot(b, sqrt((a * (c * -3.0))))) / 3.0));
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.7e+109], N[(N[(b / -1.5), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 1.45e-275], 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, 3.9e-218], N[(N[(N[Sqrt[b ^ 2 + N[(N[Sqrt[N[(c * -3.0), $MachinePrecision]], $MachinePrecision] * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision] - b), $MachinePrecision] * N[(0.3333333333333333 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-46], N[(1.0 / N[(a / N[(N[(N[(b * 3.0), $MachinePrecision] + N[Sqrt[b ^ 2 + N[Sqrt[N[(a * N[(c * -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

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

Alternative 5: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+108}:\\ \;\;\;\;\frac{\frac{b}{-1.5}}{a}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-45}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 3\right) \cdot c} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -9e+108)
   (/ (/ b -1.5) a)
   (if (<= b 4.8e-45)
     (/ (- (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 <= -9e+108) {
		tmp = (b / -1.5) / a;
	} else if (b <= 4.8e-45) {
		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 <= (-9d+108)) then
        tmp = (b / (-1.5d0)) / a
    else if (b <= 4.8d-45) 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 <= -9e+108) {
		tmp = (b / -1.5) / a;
	} else if (b <= 4.8e-45) {
		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 <= -9e+108:
		tmp = (b / -1.5) / a
	elif b <= 4.8e-45:
		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 <= -9e+108)
		tmp = Float64(Float64(b / -1.5) / a);
	elseif (b <= 4.8e-45)
		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 <= -9e+108)
		tmp = (b / -1.5) / a;
	elseif (b <= 4.8e-45)
		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, -9e+108], N[(N[(b / -1.5), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 4.8e-45], 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 6: 80.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{-81}:\\ \;\;\;\;-0.6666666666666666 \cdot \frac{b}{a} + 0.5 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-43}:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(c \cdot -3\right)} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -7.6e-81)
   (+ (* -0.6666666666666666 (/ b a)) (* 0.5 (/ c b)))
   (if (<= b 1.45e-43)
     (/ (- (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 <= -7.6e-81) {
		tmp = (-0.6666666666666666 * (b / a)) + (0.5 * (c / b));
	} else if (b <= 1.45e-43) {
		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 <= (-7.6d-81)) then
        tmp = ((-0.6666666666666666d0) * (b / a)) + (0.5d0 * (c / b))
    else if (b <= 1.45d-43) 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 <= -7.6e-81) {
		tmp = (-0.6666666666666666 * (b / a)) + (0.5 * (c / b));
	} else if (b <= 1.45e-43) {
		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 <= -7.6e-81:
		tmp = (-0.6666666666666666 * (b / a)) + (0.5 * (c / b))
	elif b <= 1.45e-43:
		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 <= -7.6e-81)
		tmp = Float64(Float64(-0.6666666666666666 * Float64(b / a)) + Float64(0.5 * Float64(c / b)));
	elseif (b <= 1.45e-43)
		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 <= -7.6e-81)
		tmp = (-0.6666666666666666 * (b / a)) + (0.5 * (c / b));
	elseif (b <= 1.45e-43)
		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, -7.6e-81], N[(N[(-0.6666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-43], 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 7: 80.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-91}:\\ \;\;\;\;-0.6666666666666666 \cdot \frac{b}{a} + 0.5 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{\sqrt{c \cdot \left(a \cdot -3\right)} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2.3e-91)
   (+ (* -0.6666666666666666 (/ b a)) (* 0.5 (/ c b)))
   (if (<= b 3.6e-44)
     (/ (- (sqrt (* c (* a -3.0))) b) (* a 3.0))
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.3e-91) {
		tmp = (-0.6666666666666666 * (b / a)) + (0.5 * (c / b));
	} else if (b <= 3.6e-44) {
		tmp = (sqrt((c * (a * -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 <= (-2.3d-91)) then
        tmp = ((-0.6666666666666666d0) * (b / a)) + (0.5d0 * (c / b))
    else if (b <= 3.6d-44) then
        tmp = (sqrt((c * (a * (-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 <= -2.3e-91) {
		tmp = (-0.6666666666666666 * (b / a)) + (0.5 * (c / b));
	} else if (b <= 3.6e-44) {
		tmp = (Math.sqrt((c * (a * -3.0))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2.3e-91:
		tmp = (-0.6666666666666666 * (b / a)) + (0.5 * (c / b))
	elif b <= 3.6e-44:
		tmp = (math.sqrt((c * (a * -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 <= -2.3e-91)
		tmp = Float64(Float64(-0.6666666666666666 * Float64(b / a)) + Float64(0.5 * Float64(c / b)));
	elseif (b <= 3.6e-44)
		tmp = Float64(Float64(sqrt(Float64(c * Float64(a * -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 <= -2.3e-91)
		tmp = (-0.6666666666666666 * (b / a)) + (0.5 * (c / b));
	elseif (b <= 3.6e-44)
		tmp = (sqrt((c * (a * -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, -2.3e-91], N[(N[(-0.6666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e-44], N[(N[(N[Sqrt[N[(c * N[(a * -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 8: 68.1% accurate, 8.9× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5e-310)
		tmp = Float64(Float64(-0.6666666666666666 * Float64(b / a)) + Float64(0.5 * Float64(c / b)));
	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 = (-0.6666666666666666 * (b / a)) + (0.5 * (c / b));
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

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

Alternative 9: 67.9% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.2 \cdot 10^{-304}:\\ \;\;\;\;-0.6666666666666666 \cdot \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 2.2e-304) (* -0.6666666666666666 (/ b a)) (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.2e-304) {
		tmp = -0.6666666666666666 * (b / 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 <= 2.2d-304) then
        tmp = (-0.6666666666666666d0) * (b / 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 <= 2.2e-304) {
		tmp = -0.6666666666666666 * (b / a);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 2.2e-304:
		tmp = -0.6666666666666666 * (b / a)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 2.2e-304)
		tmp = Float64(-0.6666666666666666 * Float64(b / 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 <= 2.2e-304)
		tmp = -0.6666666666666666 * (b / a);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2.2e-304], N[(-0.6666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

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

Alternative 10: 67.9% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.95 \cdot 10^{-304}:\\ \;\;\;\;\frac{\frac{b}{-1.5}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 1.95e-304) (/ (/ b -1.5) a) (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.95e-304) {
		tmp = (b / -1.5) / 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 <= 1.95d-304) then
        tmp = (b / (-1.5d0)) / 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 <= 1.95e-304) {
		tmp = (b / -1.5) / a;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 1.95e-304:
		tmp = (b / -1.5) / a
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 1.95e-304)
		tmp = Float64(Float64(b / -1.5) / 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 <= 1.95e-304)
		tmp = (b / -1.5) / a;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 1.95e-304], N[(N[(b / -1.5), $MachinePrecision] / a), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

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

Alternative 11: 15.1% accurate, 23.2× speedup

Math

\[\begin{array}{l} \\ \frac{b}{a} \cdot -1.3333333333333333 \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (* (/ b a) -1.3333333333333333))

C

double code(double a, double b, double c) {
	return (b / a) * -1.3333333333333333;
}

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 / a) * (-1.3333333333333333d0)
end function

Java

public static double code(double a, double b, double c) {
	return (b / a) * -1.3333333333333333;
}

Python

def code(a, b, c):
	return (b / a) * -1.3333333333333333

Julia

function code(a, b, c)
	return Float64(Float64(b / a) * -1.3333333333333333)
end

MATLAB

function tmp = code(a, b, c)
	tmp = (b / a) * -1.3333333333333333;
end

Wolfram

code[a_, b_, c_] := N[(N[(b / a), $MachinePrecision] * -1.3333333333333333), $MachinePrecision]

Derivation

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

Alternative 12: 35.0% accurate, 23.2× speedup

Math

\[\begin{array}{l} \\ b \cdot \frac{-0.6666666666666666}{a} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (* b (/ -0.6666666666666666 a)))

C

double code(double a, double b, double c) {
	return b * (-0.6666666666666666 / 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 * ((-0.6666666666666666d0) / a)
end function

Java

public static double code(double a, double b, double c) {
	return b * (-0.6666666666666666 / a);
}

Python

def code(a, b, c):
	return b * (-0.6666666666666666 / a)

Julia

function code(a, b, c)
	return Float64(b * Float64(-0.6666666666666666 / a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = b * (-0.6666666666666666 / a);
end

Wolfram

code[a_, b_, c_] := N[(b * N[(-0.6666666666666666 / a), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 13: 35.0% accurate, 23.2× speedup

Math

\[\begin{array}{l} \\ -0.6666666666666666 \cdot \frac{b}{a} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (* -0.6666666666666666 (/ b a)))

C

double code(double a, double b, double c) {
	return -0.6666666666666666 * (b / 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 = (-0.6666666666666666d0) * (b / a)
end function

Java

public static double code(double a, double b, double c) {
	return -0.6666666666666666 * (b / a);
}

Python

def code(a, b, c):
	return -0.6666666666666666 * (b / a)

Julia

function code(a, b, c)
	return Float64(-0.6666666666666666 * Float64(b / a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = -0.6666666666666666 * (b / a);
end

Wolfram

code[a_, b_, c_] := N[(-0.6666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2024003 
(FPCore (a b c)
  :name "Cubic critical"
  :precision binary64
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))