NMSE Section 6.1 mentioned, B

Percentage Accurate: 78.5% → 99.7%

Time: 10.7s

Alternatives: 11

Speedup: 1.1×

Specification

Math

\[\begin{array}{l} \\ \left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right) \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b))))

C

double code(double a, double b) {
	return ((((double) M_PI) / 2.0) * (1.0 / ((b * b) - (a * a)))) * ((1.0 / a) - (1.0 / b));
}

Java

public static double code(double a, double b) {
	return ((Math.PI / 2.0) * (1.0 / ((b * b) - (a * a)))) * ((1.0 / a) - (1.0 / b));
}

Python

def code(a, b):
	return ((math.pi / 2.0) * (1.0 / ((b * b) - (a * a)))) * ((1.0 / a) - (1.0 / b))

Julia

function code(a, b)
	return Float64(Float64(Float64(pi / 2.0) * Float64(1.0 / Float64(Float64(b * b) - Float64(a * a)))) * Float64(Float64(1.0 / a) - Float64(1.0 / b)))
end

MATLAB

function tmp = code(a, b)
	tmp = ((pi / 2.0) * (1.0 / ((b * b) - (a * a)))) * ((1.0 / a) - (1.0 / b));
end

Wolfram

code[a_, b_] := N[(N[(N[(Pi / 2.0), $MachinePrecision] * N[(1.0 / N[(N[(b * b), $MachinePrecision] - N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 / a), $MachinePrecision] - N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right) \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b))))

C

double code(double a, double b) {
	return ((((double) M_PI) / 2.0) * (1.0 / ((b * b) - (a * a)))) * ((1.0 / a) - (1.0 / b));
}

Java

public static double code(double a, double b) {
	return ((Math.PI / 2.0) * (1.0 / ((b * b) - (a * a)))) * ((1.0 / a) - (1.0 / b));
}

Python

def code(a, b):
	return ((math.pi / 2.0) * (1.0 / ((b * b) - (a * a)))) * ((1.0 / a) - (1.0 / b))

Julia

function code(a, b)
	return Float64(Float64(Float64(pi / 2.0) * Float64(1.0 / Float64(Float64(b * b) - Float64(a * a)))) * Float64(Float64(1.0 / a) - Float64(1.0 / b)))
end

MATLAB

function tmp = code(a, b)
	tmp = ((pi / 2.0) * (1.0 / ((b * b) - (a * a)))) * ((1.0 / a) - (1.0 / b));
end

Wolfram

code[a_, b_] := N[(N[(N[(Pi / 2.0), $MachinePrecision] * N[(1.0 / N[(N[(b * b), $MachinePrecision] - N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 / a), $MachinePrecision] - N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq 7.5 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{\pi}{a}}{\left(a + b\right) \cdot \frac{b}{0.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{a \cdot b} \cdot \frac{0.5}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b)
 :precision binary64
 (if (<= b 7.5e+113)
   (/ (/ PI a) (* (+ a b) (/ b 0.5)))
   (* (/ PI (* a b)) (/ 0.5 b))))

C

assert(a < b);
double code(double a, double b) {
	double tmp;
	if (b <= 7.5e+113) {
		tmp = (((double) M_PI) / a) / ((a + b) * (b / 0.5));
	} else {
		tmp = (((double) M_PI) / (a * b)) * (0.5 / b);
	}
	return tmp;
}

Java

assert a < b;
public static double code(double a, double b) {
	double tmp;
	if (b <= 7.5e+113) {
		tmp = (Math.PI / a) / ((a + b) * (b / 0.5));
	} else {
		tmp = (Math.PI / (a * b)) * (0.5 / b);
	}
	return tmp;
}

Python

[a, b] = sort([a, b])
def code(a, b):
	tmp = 0
	if b <= 7.5e+113:
		tmp = (math.pi / a) / ((a + b) * (b / 0.5))
	else:
		tmp = (math.pi / (a * b)) * (0.5 / b)
	return tmp

Julia

a, b = sort([a, b])
function code(a, b)
	tmp = 0.0
	if (b <= 7.5e+113)
		tmp = Float64(Float64(pi / a) / Float64(Float64(a + b) * Float64(b / 0.5)));
	else
		tmp = Float64(Float64(pi / Float64(a * b)) * Float64(0.5 / b));
	end
	return tmp
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b <= 7.5e+113)
		tmp = (pi / a) / ((a + b) * (b / 0.5));
	else
		tmp = (pi / (a * b)) * (0.5 / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := If[LessEqual[b, 7.5e+113], N[(N[(Pi / a), $MachinePrecision] / N[(N[(a + b), $MachinePrecision] * N[(b / 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / N[(a * b), $MachinePrecision]), $MachinePrecision] * N[(0.5 / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \frac{\left(\pi \cdot 0.5\right) \cdot \frac{\frac{1}{a} + \frac{-1}{b}}{a + b}}{b - a} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b)
 :precision binary64
 (/ (* (* PI 0.5) (/ (+ (/ 1.0 a) (/ -1.0 b)) (+ a b))) (- b a)))

C

assert(a < b);
double code(double a, double b) {
	return ((((double) M_PI) * 0.5) * (((1.0 / a) + (-1.0 / b)) / (a + b))) / (b - a);
}

Java

assert a < b;
public static double code(double a, double b) {
	return ((Math.PI * 0.5) * (((1.0 / a) + (-1.0 / b)) / (a + b))) / (b - a);
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return ((math.pi * 0.5) * (((1.0 / a) + (-1.0 / b)) / (a + b))) / (b - a)

Julia

a, b = sort([a, b])
function code(a, b)
	return Float64(Float64(Float64(pi * 0.5) * Float64(Float64(Float64(1.0 / a) + Float64(-1.0 / b)) / Float64(a + b))) / Float64(b - a))
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = ((pi * 0.5) * (((1.0 / a) + (-1.0 / b)) / (a + b))) / (b - a);
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[(N[(N[(Pi * 0.5), $MachinePrecision] * N[(N[(N[(1.0 / a), $MachinePrecision] + N[(-1.0 / b), $MachinePrecision]), $MachinePrecision] / N[(a + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 3: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \frac{\frac{1}{a} + \frac{-1}{b}}{a + b} \cdot \frac{\frac{\pi}{2}}{b - a} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b)
 :precision binary64
 (* (/ (+ (/ 1.0 a) (/ -1.0 b)) (+ a b)) (/ (/ PI 2.0) (- b a))))

C

assert(a < b);
double code(double a, double b) {
	return (((1.0 / a) + (-1.0 / b)) / (a + b)) * ((((double) M_PI) / 2.0) / (b - a));
}

Java

assert a < b;
public static double code(double a, double b) {
	return (((1.0 / a) + (-1.0 / b)) / (a + b)) * ((Math.PI / 2.0) / (b - a));
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return (((1.0 / a) + (-1.0 / b)) / (a + b)) * ((math.pi / 2.0) / (b - a))

Julia

a, b = sort([a, b])
function code(a, b)
	return Float64(Float64(Float64(Float64(1.0 / a) + Float64(-1.0 / b)) / Float64(a + b)) * Float64(Float64(pi / 2.0) / Float64(b - a)))
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = (((1.0 / a) + (-1.0 / b)) / (a + b)) * ((pi / 2.0) / (b - a));
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[(N[(N[(N[(1.0 / a), $MachinePrecision] + N[(-1.0 / b), $MachinePrecision]), $MachinePrecision] / N[(a + b), $MachinePrecision]), $MachinePrecision] * N[(N[(Pi / 2.0), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 4: 92.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-86}:\\ \;\;\;\;\frac{\pi}{a} \cdot \frac{\frac{-0.5}{b}}{b - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{a \cdot b} \cdot \frac{0.5}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b)
 :precision binary64
 (if (<= a -1.85e-86)
   (* (/ PI a) (/ (/ -0.5 b) (- b a)))
   (* (/ PI (* a b)) (/ 0.5 b))))

C

assert(a < b);
double code(double a, double b) {
	double tmp;
	if (a <= -1.85e-86) {
		tmp = (((double) M_PI) / a) * ((-0.5 / b) / (b - a));
	} else {
		tmp = (((double) M_PI) / (a * b)) * (0.5 / b);
	}
	return tmp;
}

Java

assert a < b;
public static double code(double a, double b) {
	double tmp;
	if (a <= -1.85e-86) {
		tmp = (Math.PI / a) * ((-0.5 / b) / (b - a));
	} else {
		tmp = (Math.PI / (a * b)) * (0.5 / b);
	}
	return tmp;
}

Python

[a, b] = sort([a, b])
def code(a, b):
	tmp = 0
	if a <= -1.85e-86:
		tmp = (math.pi / a) * ((-0.5 / b) / (b - a))
	else:
		tmp = (math.pi / (a * b)) * (0.5 / b)
	return tmp

Julia

a, b = sort([a, b])
function code(a, b)
	tmp = 0.0
	if (a <= -1.85e-86)
		tmp = Float64(Float64(pi / a) * Float64(Float64(-0.5 / b) / Float64(b - a)));
	else
		tmp = Float64(Float64(pi / Float64(a * b)) * Float64(0.5 / b));
	end
	return tmp
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -1.85e-86)
		tmp = (pi / a) * ((-0.5 / b) / (b - a));
	else
		tmp = (pi / (a * b)) * (0.5 / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := If[LessEqual[a, -1.85e-86], N[(N[(Pi / a), $MachinePrecision] * N[(N[(-0.5 / b), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / N[(a * b), $MachinePrecision]), $MachinePrecision] * N[(0.5 / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 99.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+141}:\\ \;\;\;\;\frac{\pi}{a} \cdot \frac{\frac{-0.5}{b}}{b - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{b} \cdot \frac{\pi}{a \cdot \left(a + b\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b)
 :precision binary64
 (if (<= a -2e+141)
   (* (/ PI a) (/ (/ -0.5 b) (- b a)))
   (* (/ 0.5 b) (/ PI (* a (+ a b))))))

C

assert(a < b);
double code(double a, double b) {
	double tmp;
	if (a <= -2e+141) {
		tmp = (((double) M_PI) / a) * ((-0.5 / b) / (b - a));
	} else {
		tmp = (0.5 / b) * (((double) M_PI) / (a * (a + b)));
	}
	return tmp;
}

Java

assert a < b;
public static double code(double a, double b) {
	double tmp;
	if (a <= -2e+141) {
		tmp = (Math.PI / a) * ((-0.5 / b) / (b - a));
	} else {
		tmp = (0.5 / b) * (Math.PI / (a * (a + b)));
	}
	return tmp;
}

Python

[a, b] = sort([a, b])
def code(a, b):
	tmp = 0
	if a <= -2e+141:
		tmp = (math.pi / a) * ((-0.5 / b) / (b - a))
	else:
		tmp = (0.5 / b) * (math.pi / (a * (a + b)))
	return tmp

Julia

a, b = sort([a, b])
function code(a, b)
	tmp = 0.0
	if (a <= -2e+141)
		tmp = Float64(Float64(pi / a) * Float64(Float64(-0.5 / b) / Float64(b - a)));
	else
		tmp = Float64(Float64(0.5 / b) * Float64(pi / Float64(a * Float64(a + b))));
	end
	return tmp
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -2e+141)
		tmp = (pi / a) * ((-0.5 / b) / (b - a));
	else
		tmp = (0.5 / b) * (pi / (a * (a + b)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := If[LessEqual[a, -2e+141], N[(N[(Pi / a), $MachinePrecision] * N[(N[(-0.5 / b), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / b), $MachinePrecision] * N[(Pi / N[(a * N[(a + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 99.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+75}:\\ \;\;\;\;\frac{\pi \cdot -0.5}{a} \cdot \frac{-1}{a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{b} \cdot \frac{\pi}{a \cdot \left(a + b\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b)
 :precision binary64
 (if (<= a -4.4e+75)
   (* (/ (* PI -0.5) a) (/ -1.0 (* a b)))
   (* (/ 0.5 b) (/ PI (* a (+ a b))))))

C

assert(a < b);
double code(double a, double b) {
	double tmp;
	if (a <= -4.4e+75) {
		tmp = ((((double) M_PI) * -0.5) / a) * (-1.0 / (a * b));
	} else {
		tmp = (0.5 / b) * (((double) M_PI) / (a * (a + b)));
	}
	return tmp;
}

Java

assert a < b;
public static double code(double a, double b) {
	double tmp;
	if (a <= -4.4e+75) {
		tmp = ((Math.PI * -0.5) / a) * (-1.0 / (a * b));
	} else {
		tmp = (0.5 / b) * (Math.PI / (a * (a + b)));
	}
	return tmp;
}

Python

[a, b] = sort([a, b])
def code(a, b):
	tmp = 0
	if a <= -4.4e+75:
		tmp = ((math.pi * -0.5) / a) * (-1.0 / (a * b))
	else:
		tmp = (0.5 / b) * (math.pi / (a * (a + b)))
	return tmp

Julia

a, b = sort([a, b])
function code(a, b)
	tmp = 0.0
	if (a <= -4.4e+75)
		tmp = Float64(Float64(Float64(pi * -0.5) / a) * Float64(-1.0 / Float64(a * b)));
	else
		tmp = Float64(Float64(0.5 / b) * Float64(pi / Float64(a * Float64(a + b))));
	end
	return tmp
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -4.4e+75)
		tmp = ((pi * -0.5) / a) * (-1.0 / (a * b));
	else
		tmp = (0.5 / b) * (pi / (a * (a + b)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := If[LessEqual[a, -4.4e+75], N[(N[(N[(Pi * -0.5), $MachinePrecision] / a), $MachinePrecision] * N[(-1.0 / N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / b), $MachinePrecision] * N[(Pi / N[(a * N[(a + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 99.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq 3.3 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{\pi}{b}}{a + b} \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{a \cdot b} \cdot \frac{0.5}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b)
 :precision binary64
 (if (<= b 3.3e+84)
   (* (/ (/ PI b) (+ a b)) (/ 0.5 a))
   (* (/ PI (* a b)) (/ 0.5 b))))

C

assert(a < b);
double code(double a, double b) {
	double tmp;
	if (b <= 3.3e+84) {
		tmp = ((((double) M_PI) / b) / (a + b)) * (0.5 / a);
	} else {
		tmp = (((double) M_PI) / (a * b)) * (0.5 / b);
	}
	return tmp;
}

Java

assert a < b;
public static double code(double a, double b) {
	double tmp;
	if (b <= 3.3e+84) {
		tmp = ((Math.PI / b) / (a + b)) * (0.5 / a);
	} else {
		tmp = (Math.PI / (a * b)) * (0.5 / b);
	}
	return tmp;
}

Python

[a, b] = sort([a, b])
def code(a, b):
	tmp = 0
	if b <= 3.3e+84:
		tmp = ((math.pi / b) / (a + b)) * (0.5 / a)
	else:
		tmp = (math.pi / (a * b)) * (0.5 / b)
	return tmp

Julia

a, b = sort([a, b])
function code(a, b)
	tmp = 0.0
	if (b <= 3.3e+84)
		tmp = Float64(Float64(Float64(pi / b) / Float64(a + b)) * Float64(0.5 / a));
	else
		tmp = Float64(Float64(pi / Float64(a * b)) * Float64(0.5 / b));
	end
	return tmp
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b <= 3.3e+84)
		tmp = ((pi / b) / (a + b)) * (0.5 / a);
	else
		tmp = (pi / (a * b)) * (0.5 / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := If[LessEqual[b, 3.3e+84], N[(N[(N[(Pi / b), $MachinePrecision] / N[(a + b), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / N[(a * b), $MachinePrecision]), $MachinePrecision] * N[(0.5 / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 98.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+167}:\\ \;\;\;\;\frac{\pi \cdot -0.5}{a} \cdot \frac{-1}{a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \frac{\pi}{b}}{a \cdot \left(a + b\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b)
 :precision binary64
 (if (<= a -9.2e+167)
   (* (/ (* PI -0.5) a) (/ -1.0 (* a b)))
   (/ (* 0.5 (/ PI b)) (* a (+ a b)))))

C

assert(a < b);
double code(double a, double b) {
	double tmp;
	if (a <= -9.2e+167) {
		tmp = ((((double) M_PI) * -0.5) / a) * (-1.0 / (a * b));
	} else {
		tmp = (0.5 * (((double) M_PI) / b)) / (a * (a + b));
	}
	return tmp;
}

Java

assert a < b;
public static double code(double a, double b) {
	double tmp;
	if (a <= -9.2e+167) {
		tmp = ((Math.PI * -0.5) / a) * (-1.0 / (a * b));
	} else {
		tmp = (0.5 * (Math.PI / b)) / (a * (a + b));
	}
	return tmp;
}

Python

[a, b] = sort([a, b])
def code(a, b):
	tmp = 0
	if a <= -9.2e+167:
		tmp = ((math.pi * -0.5) / a) * (-1.0 / (a * b))
	else:
		tmp = (0.5 * (math.pi / b)) / (a * (a + b))
	return tmp

Julia

a, b = sort([a, b])
function code(a, b)
	tmp = 0.0
	if (a <= -9.2e+167)
		tmp = Float64(Float64(Float64(pi * -0.5) / a) * Float64(-1.0 / Float64(a * b)));
	else
		tmp = Float64(Float64(0.5 * Float64(pi / b)) / Float64(a * Float64(a + b)));
	end
	return tmp
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -9.2e+167)
		tmp = ((pi * -0.5) / a) * (-1.0 / (a * b));
	else
		tmp = (0.5 * (pi / b)) / (a * (a + b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := If[LessEqual[a, -9.2e+167], N[(N[(N[(Pi * -0.5), $MachinePrecision] / a), $MachinePrecision] * N[(-1.0 / N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(Pi / b), $MachinePrecision]), $MachinePrecision] / N[(a * N[(a + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 90.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-38}:\\ \;\;\;\;\frac{\pi}{a \cdot \left(-b\right)} \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \frac{\pi}{b}}{a \cdot b}\\ \end{array} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b)
 :precision binary64
 (if (<= a -1.55e-38)
   (* (/ PI (* a (- b))) (/ -0.5 a))
   (/ (* 0.5 (/ PI b)) (* a b))))

C

assert(a < b);
double code(double a, double b) {
	double tmp;
	if (a <= -1.55e-38) {
		tmp = (((double) M_PI) / (a * -b)) * (-0.5 / a);
	} else {
		tmp = (0.5 * (((double) M_PI) / b)) / (a * b);
	}
	return tmp;
}

Java

assert a < b;
public static double code(double a, double b) {
	double tmp;
	if (a <= -1.55e-38) {
		tmp = (Math.PI / (a * -b)) * (-0.5 / a);
	} else {
		tmp = (0.5 * (Math.PI / b)) / (a * b);
	}
	return tmp;
}

Python

[a, b] = sort([a, b])
def code(a, b):
	tmp = 0
	if a <= -1.55e-38:
		tmp = (math.pi / (a * -b)) * (-0.5 / a)
	else:
		tmp = (0.5 * (math.pi / b)) / (a * b)
	return tmp

Julia

a, b = sort([a, b])
function code(a, b)
	tmp = 0.0
	if (a <= -1.55e-38)
		tmp = Float64(Float64(pi / Float64(a * Float64(-b))) * Float64(-0.5 / a));
	else
		tmp = Float64(Float64(0.5 * Float64(pi / b)) / Float64(a * b));
	end
	return tmp
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -1.55e-38)
		tmp = (pi / (a * -b)) * (-0.5 / a);
	else
		tmp = (0.5 * (pi / b)) / (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := If[LessEqual[a, -1.55e-38], N[(N[(Pi / N[(a * (-b)), $MachinePrecision]), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(Pi / b), $MachinePrecision]), $MachinePrecision] / N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 62.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \frac{\pi}{a \cdot b} \cdot \frac{0.5}{b} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (* (/ PI (* a b)) (/ 0.5 b)))

C

assert(a < b);
double code(double a, double b) {
	return (((double) M_PI) / (a * b)) * (0.5 / b);
}

Java

assert a < b;
public static double code(double a, double b) {
	return (Math.PI / (a * b)) * (0.5 / b);
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return (math.pi / (a * b)) * (0.5 / b)

Julia

a, b = sort([a, b])
function code(a, b)
	return Float64(Float64(pi / Float64(a * b)) * Float64(0.5 / b))
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = (pi / (a * b)) * (0.5 / b);
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[(N[(Pi / N[(a * b), $MachinePrecision]), $MachinePrecision] * N[(0.5 / b), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 11: 63.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \frac{0.5 \cdot \frac{\pi}{b}}{a \cdot b} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (/ (* 0.5 (/ PI b)) (* a b)))

C

assert(a < b);
double code(double a, double b) {
	return (0.5 * (((double) M_PI) / b)) / (a * b);
}

Java

assert a < b;
public static double code(double a, double b) {
	return (0.5 * (Math.PI / b)) / (a * b);
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return (0.5 * (math.pi / b)) / (a * b)

Julia

a, b = sort([a, b])
function code(a, b)
	return Float64(Float64(0.5 * Float64(pi / b)) / Float64(a * b))
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = (0.5 * (pi / b)) / (a * b);
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[(N[(0.5 * N[(Pi / b), $MachinePrecision]), $MachinePrecision] / N[(a * b), $MachinePrecision]), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023343 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  :precision binary64
  (* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b))))