The quadratic formula (r2)

Percentage Accurate: 51.2% → 85.2%

Time: 13.2s

Alternatives: 11

Speedup: 19.1×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))

C

double code(double a, double b, double c) {
	return (-b - sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * 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) - (4.0d0 * (a * c))))) / (2.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b - Math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}

Python

def code(a, b, c):
	return (-b - math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) - sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c))))) / Float64(2.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b - sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Initial Program: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))

C

double code(double a, double b, double c) {
	return (-b - sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * 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) - (4.0d0 * (a * c))))) / (2.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b - Math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}

Python

def code(a, b, c):
	return (-b - math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) - sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c))))) / Float64(2.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b - sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-33}:\\ \;\;\;\;-0.5 \cdot \frac{1}{-0.5 \cdot \frac{a}{b} + 0.5 \cdot \frac{b}{c}}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+150}:\\ \;\;\;\;-\frac{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -6.2e-33)
   (* -0.5 (/ 1.0 (+ (* -0.5 (/ a b)) (* 0.5 (/ b c)))))
   (if (<= b 5.6e+150)
     (- (/ (+ b (sqrt (fma b b (* c (* a -4.0))))) (* a 2.0)))
     (/ (- b) a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -6.2e-33) {
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	} else if (b <= 5.6e+150) {
		tmp = -((b + sqrt(fma(b, b, (c * (a * -4.0))))) / (a * 2.0));
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -6.2e-33)
		tmp = Float64(-0.5 * Float64(1.0 / Float64(Float64(-0.5 * Float64(a / b)) + Float64(0.5 * Float64(b / c)))));
	elseif (b <= 5.6e+150)
		tmp = Float64(-Float64(Float64(b + sqrt(fma(b, b, Float64(c * Float64(a * -4.0))))) / Float64(a * 2.0)));
	else
		tmp = Float64(Float64(-b) / a);
	end
	return tmp
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -6.2e-33], N[(-0.5 * N[(1.0 / N[(N[(-0.5 * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+150], (-N[(N[(b + N[Sqrt[N[(b * b + N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), N[((-b) / a), $MachinePrecision]]]

Derivation

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

Alternative 2: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;-0.5 \cdot \frac{1}{-0.5 \cdot \frac{a}{b} + 0.5 \cdot \frac{b}{c}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+150}:\\ \;\;\;\;-0.5 \cdot \frac{b + \sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.6e-33)
   (* -0.5 (/ 1.0 (+ (* -0.5 (/ a b)) (* 0.5 (/ b c)))))
   (if (<= b 5e+150)
     (* -0.5 (/ (+ b (sqrt (fma a (* c -4.0) (* b b)))) a))
     (/ (- b) a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.6e-33) {
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	} else if (b <= 5e+150) {
		tmp = -0.5 * ((b + sqrt(fma(a, (c * -4.0), (b * b)))) / a);
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.6e-33)
		tmp = Float64(-0.5 * Float64(1.0 / Float64(Float64(-0.5 * Float64(a / b)) + Float64(0.5 * Float64(b / c)))));
	elseif (b <= 5e+150)
		tmp = Float64(-0.5 * Float64(Float64(b + sqrt(fma(a, Float64(c * -4.0), Float64(b * b)))) / a));
	else
		tmp = Float64(Float64(-b) / a);
	end
	return tmp
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.6e-33], N[(-0.5 * N[(1.0 / N[(N[(-0.5 * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+150], N[(-0.5 * N[(N[(b + N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision] + N[(b * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[((-b) / a), $MachinePrecision]]]

Derivation

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

Alternative 3: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;-0.5 \cdot \frac{1}{-0.5 \cdot \frac{a}{b} + 0.5 \cdot \frac{b}{c}}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+150}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.6e-33)
   (* -0.5 (/ 1.0 (+ (* -0.5 (/ a b)) (* 0.5 (/ b c)))))
   (if (<= b 4.8e+150)
     (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a 2.0))
     (/ (- b) a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.6e-33) {
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	} else if (b <= 4.8e+150) {
		tmp = (-b - sqrt(((b * b) - (4.0 * (a * c))))) / (a * 2.0);
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.6d-33)) then
        tmp = (-0.5d0) * (1.0d0 / (((-0.5d0) * (a / b)) + (0.5d0 * (b / c))))
    else if (b <= 4.8d+150) then
        tmp = (-b - sqrt(((b * b) - (4.0d0 * (a * c))))) / (a * 2.0d0)
    else
        tmp = -b / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.6e-33) {
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	} else if (b <= 4.8e+150) {
		tmp = (-b - Math.sqrt(((b * b) - (4.0 * (a * c))))) / (a * 2.0);
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.6e-33:
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))))
	elif b <= 4.8e+150:
		tmp = (-b - math.sqrt(((b * b) - (4.0 * (a * c))))) / (a * 2.0)
	else:
		tmp = -b / a
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.6e-33)
		tmp = Float64(-0.5 * Float64(1.0 / Float64(Float64(-0.5 * Float64(a / b)) + Float64(0.5 * Float64(b / c)))));
	elseif (b <= 4.8e+150)
		tmp = Float64(Float64(Float64(-b) - sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c))))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(-b) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1.6e-33)
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	elseif (b <= 4.8e+150)
		tmp = (-b - sqrt(((b * b) - (4.0 * (a * c))))) / (a * 2.0);
	else
		tmp = -b / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.6e-33], N[(-0.5 * N[(1.0 / N[(N[(-0.5 * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e+150], N[(N[((-b) - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[((-b) / a), $MachinePrecision]]]

Derivation

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

Alternative 4: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;-0.5 \cdot \frac{1}{-0.5 \cdot \frac{a}{b} + 0.5 \cdot \frac{b}{c}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+150}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.6e-33)
   (* -0.5 (/ 1.0 (+ (* -0.5 (/ a b)) (* 0.5 (/ b c)))))
   (if (<= b 5e+150)
     (/ (- (- b) (sqrt (- (* b b) (* c (* a 4.0))))) (* a 2.0))
     (/ (- b) a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.6e-33) {
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	} else if (b <= 5e+150) {
		tmp = (-b - sqrt(((b * b) - (c * (a * 4.0))))) / (a * 2.0);
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.6d-33)) then
        tmp = (-0.5d0) * (1.0d0 / (((-0.5d0) * (a / b)) + (0.5d0 * (b / c))))
    else if (b <= 5d+150) then
        tmp = (-b - sqrt(((b * b) - (c * (a * 4.0d0))))) / (a * 2.0d0)
    else
        tmp = -b / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.6e-33) {
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	} else if (b <= 5e+150) {
		tmp = (-b - Math.sqrt(((b * b) - (c * (a * 4.0))))) / (a * 2.0);
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.6e-33:
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))))
	elif b <= 5e+150:
		tmp = (-b - math.sqrt(((b * b) - (c * (a * 4.0))))) / (a * 2.0)
	else:
		tmp = -b / a
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.6e-33)
		tmp = Float64(-0.5 * Float64(1.0 / Float64(Float64(-0.5 * Float64(a / b)) + Float64(0.5 * Float64(b / c)))));
	elseif (b <= 5e+150)
		tmp = Float64(Float64(Float64(-b) - sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(-b) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1.6e-33)
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	elseif (b <= 5e+150)
		tmp = (-b - sqrt(((b * b) - (c * (a * 4.0))))) / (a * 2.0);
	else
		tmp = -b / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.6e-33], N[(-0.5 * N[(1.0 / N[(N[(-0.5 * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+150], N[(N[((-b) - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[((-b) / a), $MachinePrecision]]]

Derivation

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

Alternative 5: 80.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;-0.5 \cdot \frac{1}{-0.5 \cdot \frac{a}{b} + 0.5 \cdot \frac{b}{c}}\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-51}:\\ \;\;\;\;-0.5 \cdot \frac{b + \sqrt{a \cdot \left(c \cdot -4\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.6e-33)
   (* -0.5 (/ 1.0 (+ (* -0.5 (/ a b)) (* 0.5 (/ b c)))))
   (if (<= b 2.45e-51)
     (* -0.5 (/ (+ b (sqrt (* a (* c -4.0)))) a))
     (- (/ c b) (/ b a)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.6e-33) {
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	} else if (b <= 2.45e-51) {
		tmp = -0.5 * ((b + sqrt((a * (c * -4.0)))) / a);
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.6d-33)) then
        tmp = (-0.5d0) * (1.0d0 / (((-0.5d0) * (a / b)) + (0.5d0 * (b / c))))
    else if (b <= 2.45d-51) then
        tmp = (-0.5d0) * ((b + sqrt((a * (c * (-4.0d0))))) / a)
    else
        tmp = (c / b) - (b / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.6e-33) {
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	} else if (b <= 2.45e-51) {
		tmp = -0.5 * ((b + Math.sqrt((a * (c * -4.0)))) / a);
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.6e-33:
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))))
	elif b <= 2.45e-51:
		tmp = -0.5 * ((b + math.sqrt((a * (c * -4.0)))) / a)
	else:
		tmp = (c / b) - (b / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.6e-33)
		tmp = Float64(-0.5 * Float64(1.0 / Float64(Float64(-0.5 * Float64(a / b)) + Float64(0.5 * Float64(b / c)))));
	elseif (b <= 2.45e-51)
		tmp = Float64(-0.5 * Float64(Float64(b + sqrt(Float64(a * Float64(c * -4.0)))) / a));
	else
		tmp = Float64(Float64(c / b) - Float64(b / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1.6e-33)
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	elseif (b <= 2.45e-51)
		tmp = -0.5 * ((b + sqrt((a * (c * -4.0)))) / a);
	else
		tmp = (c / b) - (b / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.6e-33], N[(-0.5 * N[(1.0 / N[(N[(-0.5 * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.45e-51], N[(-0.5 * N[(N[(b + N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 6: 68.8% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-311}:\\ \;\;\;\;-0.5 \cdot \frac{1}{-0.5 \cdot \frac{a}{b} + 0.5 \cdot \frac{b}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2e-311)
   (* -0.5 (/ 1.0 (+ (* -0.5 (/ a b)) (* 0.5 (/ b c)))))
   (- (/ c b) (/ b a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-311) {
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2d-311)) then
        tmp = (-0.5d0) * (1.0d0 / (((-0.5d0) * (a / b)) + (0.5d0 * (b / c))))
    else
        tmp = (c / b) - (b / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-311) {
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2e-311:
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))))
	else:
		tmp = (c / b) - (b / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2e-311)
		tmp = Float64(-0.5 * Float64(1.0 / Float64(Float64(-0.5 * Float64(a / b)) + Float64(0.5 * Float64(b / c)))));
	else
		tmp = Float64(Float64(c / b) - Float64(b / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -2e-311)
		tmp = -0.5 * (1.0 / ((-0.5 * (a / b)) + (0.5 * (b / c))));
	else
		tmp = (c / b) - (b / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2e-311], N[(-0.5 * N[(1.0 / N[(N[(-0.5 * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 69.1% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-311}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2e-311) (/ (- c) b) (- (/ c b) (/ b a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-311) {
		tmp = -c / b;
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2d-311)) then
        tmp = -c / b
    else
        tmp = (c / b) - (b / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-311) {
		tmp = -c / b;
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2e-311:
		tmp = -c / b
	else:
		tmp = (c / b) - (b / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2e-311)
		tmp = Float64(Float64(-c) / b);
	else
		tmp = Float64(Float64(c / b) - Float64(b / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -2e-311)
		tmp = -c / b;
	else
		tmp = (c / b) - (b / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2e-311], N[((-c) / b), $MachinePrecision], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 43.6% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{c}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (if (<= b -9.2e+47) (/ c b) (/ (- b) a)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -9.2e+47) {
		tmp = c / b;
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-9.2d+47)) then
        tmp = c / b
    else
        tmp = -b / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -9.2e+47) {
		tmp = c / b;
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -9.2e+47:
		tmp = c / b
	else:
		tmp = -b / a
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -9.2e+47)
		tmp = Float64(c / b);
	else
		tmp = Float64(Float64(-b) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -9.2e+47)
		tmp = c / b;
	else
		tmp = -b / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -9.2e+47], N[(c / b), $MachinePrecision], N[((-b) / a), $MachinePrecision]]

Derivation

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

Alternative 9: 68.9% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-311}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2e-311) (/ (- c) b) (/ (- b) a)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-311) {
		tmp = -c / b;
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2d-311)) then
        tmp = -c / b
    else
        tmp = -b / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-311) {
		tmp = -c / b;
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2e-311:
		tmp = -c / b
	else:
		tmp = -b / a
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2e-311)
		tmp = Float64(Float64(-c) / b);
	else
		tmp = Float64(Float64(-b) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -2e-311)
		tmp = -c / b;
	else
		tmp = -b / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2e-311], N[((-c) / b), $MachinePrecision], N[((-b) / a), $MachinePrecision]]

Derivation

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

Alternative 10: 2.5% accurate, 38.7× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c) {
	return 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 = b / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 11: 11.0% accurate, 38.7× speedup

Math

\[\begin{array}{l} \\ \frac{c}{b} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Developer target: 70.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\\ \mathbf{if}\;b < 0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + t_0}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - t_0}{2 \cdot a}\\ \end{array} \end{array} \]

FPCore

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

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - (4.0 * (a * c))));
	double tmp;
	if (b < 0.0) {
		tmp = c / (a * ((-b + t_0) / (2.0 * a)));
	} else {
		tmp = (-b - t_0) / (2.0 * a);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(((b * b) - (4.0d0 * (a * c))))
    if (b < 0.0d0) then
        tmp = c / (a * ((-b + t_0) / (2.0d0 * a)))
    else
        tmp = (-b - t_0) / (2.0d0 * a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = Math.sqrt(((b * b) - (4.0 * (a * c))));
	double tmp;
	if (b < 0.0) {
		tmp = c / (a * ((-b + t_0) / (2.0 * a)));
	} else {
		tmp = (-b - t_0) / (2.0 * a);
	}
	return tmp;
}

Python

def code(a, b, c):
	t_0 = math.sqrt(((b * b) - (4.0 * (a * c))))
	tmp = 0
	if b < 0.0:
		tmp = c / (a * ((-b + t_0) / (2.0 * a)))
	else:
		tmp = (-b - t_0) / (2.0 * a)
	return tmp

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c))))
	tmp = 0.0
	if (b < 0.0)
		tmp = Float64(c / Float64(a * Float64(Float64(Float64(-b) + t_0) / Float64(2.0 * a))));
	else
		tmp = Float64(Float64(Float64(-b) - t_0) / Float64(2.0 * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	t_0 = sqrt(((b * b) - (4.0 * (a * c))));
	tmp = 0.0;
	if (b < 0.0)
		tmp = c / (a * ((-b + t_0) / (2.0 * a)));
	else
		tmp = (-b - t_0) / (2.0 * a);
	end
	tmp_2 = tmp;
end

Wolfram

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

Reproduce

herbie shell --seed 2023364 
(FPCore (a b c)
  :name "The quadratic formula (r2)"
  :precision binary64

  :herbie-target
  (if (< b 0.0) (/ c (* a (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))) (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))

  (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))