NMSE Section 6.1 mentioned, B

Percentage Accurate: 77.9% → 99.6%

Time: 11.9s

Alternatives: 16

Speedup: 1.0×

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: 77.9% 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: 99.6% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (a b)
 :precision binary64
 (/ (/ (* PI (* 0.5 (+ (/ 1.0 a) (/ -1.0 b)))) (+ a b)) (- b a)))

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(a, b)
	tmp = ((pi * (0.5 * ((1.0 / a) + (-1.0 / b)))) / (a + b)) / (b - a);
end

Wolfram

code[a_, b_] := N[(N[(N[(Pi * N[(0.5 * N[(N[(1.0 / a), $MachinePrecision] + N[(-1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + b), $MachinePrecision]), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{\frac{-0.5}{\frac{b}{\pi}}}{a}}{b - a}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-200}:\\ \;\;\;\;\left(\frac{1}{a} + \frac{-1}{b}\right) \cdot \frac{\frac{\frac{\pi}{2}}{b - a}}{a + b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{a \cdot b} \cdot \frac{0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= a -3.1e+47)
   (/ (/ (/ -0.5 (/ b PI)) a) (- b a))
   (if (<= a -3.5e-200)
     (* (+ (/ 1.0 a) (/ -1.0 b)) (/ (/ (/ PI 2.0) (- b a)) (+ a b)))
     (* (/ PI (* a b)) (/ 0.5 b)))))

C

double code(double a, double b) {
	double tmp;
	if (a <= -3.1e+47) {
		tmp = ((-0.5 / (b / ((double) M_PI))) / a) / (b - a);
	} else if (a <= -3.5e-200) {
		tmp = ((1.0 / a) + (-1.0 / b)) * (((((double) M_PI) / 2.0) / (b - a)) / (a + b));
	} else {
		tmp = (((double) M_PI) / (a * b)) * (0.5 / b);
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (a <= -3.1e+47) {
		tmp = ((-0.5 / (b / Math.PI)) / a) / (b - a);
	} else if (a <= -3.5e-200) {
		tmp = ((1.0 / a) + (-1.0 / b)) * (((Math.PI / 2.0) / (b - a)) / (a + b));
	} else {
		tmp = (Math.PI / (a * b)) * (0.5 / b);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if a <= -3.1e+47:
		tmp = ((-0.5 / (b / math.pi)) / a) / (b - a)
	elif a <= -3.5e-200:
		tmp = ((1.0 / a) + (-1.0 / b)) * (((math.pi / 2.0) / (b - a)) / (a + b))
	else:
		tmp = (math.pi / (a * b)) * (0.5 / b)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (a <= -3.1e+47)
		tmp = Float64(Float64(Float64(-0.5 / Float64(b / pi)) / a) / Float64(b - a));
	elseif (a <= -3.5e-200)
		tmp = Float64(Float64(Float64(1.0 / a) + Float64(-1.0 / b)) * Float64(Float64(Float64(pi / 2.0) / Float64(b - a)) / Float64(a + b)));
	else
		tmp = Float64(Float64(pi / Float64(a * b)) * Float64(0.5 / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -3.1e+47)
		tmp = ((-0.5 / (b / pi)) / a) / (b - a);
	elseif (a <= -3.5e-200)
		tmp = ((1.0 / a) + (-1.0 / b)) * (((pi / 2.0) / (b - a)) / (a + b));
	else
		tmp = (pi / (a * b)) * (0.5 / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[a, -3.1e+47], N[(N[(N[(-0.5 / N[(b / Pi), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.5e-200], N[(N[(N[(1.0 / a), $MachinePrecision] + N[(-1.0 / b), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(Pi / 2.0), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision] / N[(a + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / N[(a * b), $MachinePrecision]), $MachinePrecision] * N[(0.5 / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 3: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{\pi}{2}}{b - a} \cdot \frac{\frac{1}{a} + \frac{-1}{b}}{a + b} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 4: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 5: 74.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{-0.5 \cdot \frac{\pi}{b}}{a + b}}{b - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{b} \cdot \frac{\frac{0.5}{a}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= a -3.3e-119)
   (/ (/ (* -0.5 (/ PI b)) (+ a b)) (- b a))
   (* (/ PI b) (/ (/ 0.5 a) b))))

C

double code(double a, double b) {
	double tmp;
	if (a <= -3.3e-119) {
		tmp = ((-0.5 * (((double) M_PI) / b)) / (a + b)) / (b - a);
	} else {
		tmp = (((double) M_PI) / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (a <= -3.3e-119) {
		tmp = ((-0.5 * (Math.PI / b)) / (a + b)) / (b - a);
	} else {
		tmp = (Math.PI / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if a <= -3.3e-119:
		tmp = ((-0.5 * (math.pi / b)) / (a + b)) / (b - a)
	else:
		tmp = (math.pi / b) * ((0.5 / a) / b)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (a <= -3.3e-119)
		tmp = Float64(Float64(Float64(-0.5 * Float64(pi / b)) / Float64(a + b)) / Float64(b - a));
	else
		tmp = Float64(Float64(pi / b) * Float64(Float64(0.5 / a) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -3.3e-119)
		tmp = ((-0.5 * (pi / b)) / (a + b)) / (b - a);
	else
		tmp = (pi / b) * ((0.5 / a) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[a, -3.3e-119], N[(N[(N[(-0.5 * N[(Pi / b), $MachinePrecision]), $MachinePrecision] / N[(a + b), $MachinePrecision]), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / b), $MachinePrecision] * N[(N[(0.5 / a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 6: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.6 \cdot 10^{-48}:\\ \;\;\;\;\frac{-0.5 \cdot \frac{-\pi}{a}}{a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \frac{\frac{\frac{0.5}{a}}{b}}{b - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= b 4.6e-48)
   (/ (* -0.5 (/ (- PI) a)) (* a b))
   (* PI (/ (/ (/ 0.5 a) b) (- b a)))))

C

double code(double a, double b) {
	double tmp;
	if (b <= 4.6e-48) {
		tmp = (-0.5 * (-((double) M_PI) / a)) / (a * b);
	} else {
		tmp = ((double) M_PI) * (((0.5 / a) / b) / (b - a));
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (b <= 4.6e-48) {
		tmp = (-0.5 * (-Math.PI / a)) / (a * b);
	} else {
		tmp = Math.PI * (((0.5 / a) / b) / (b - a));
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if b <= 4.6e-48:
		tmp = (-0.5 * (-math.pi / a)) / (a * b)
	else:
		tmp = math.pi * (((0.5 / a) / b) / (b - a))
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (b <= 4.6e-48)
		tmp = Float64(Float64(-0.5 * Float64(Float64(-pi) / a)) / Float64(a * b));
	else
		tmp = Float64(pi * Float64(Float64(Float64(0.5 / a) / b) / Float64(b - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b <= 4.6e-48)
		tmp = (-0.5 * (-pi / a)) / (a * b);
	else
		tmp = pi * (((0.5 / a) / b) / (b - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[b, 4.6e-48], N[(N[(-0.5 * N[((-Pi) / a), $MachinePrecision]), $MachinePrecision] / N[(a * b), $MachinePrecision]), $MachinePrecision], N[(Pi * N[(N[(N[(0.5 / a), $MachinePrecision] / b), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{-0.5 \cdot \frac{-\pi}{a}}{a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{a \cdot b} \cdot \frac{0.5}{b - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= b 8.5e-48)
   (/ (* -0.5 (/ (- PI) a)) (* a b))
   (* (/ PI (* a b)) (/ 0.5 (- b a)))))

C

double code(double a, double b) {
	double tmp;
	if (b <= 8.5e-48) {
		tmp = (-0.5 * (-((double) M_PI) / a)) / (a * b);
	} else {
		tmp = (((double) M_PI) / (a * b)) * (0.5 / (b - a));
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (b <= 8.5e-48) {
		tmp = (-0.5 * (-Math.PI / a)) / (a * b);
	} else {
		tmp = (Math.PI / (a * b)) * (0.5 / (b - a));
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if b <= 8.5e-48:
		tmp = (-0.5 * (-math.pi / a)) / (a * b)
	else:
		tmp = (math.pi / (a * b)) * (0.5 / (b - a))
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (b <= 8.5e-48)
		tmp = Float64(Float64(-0.5 * Float64(Float64(-pi) / a)) / Float64(a * b));
	else
		tmp = Float64(Float64(pi / Float64(a * b)) * Float64(0.5 / Float64(b - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b <= 8.5e-48)
		tmp = (-0.5 * (-pi / a)) / (a * b);
	else
		tmp = (pi / (a * b)) * (0.5 / (b - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[b, 8.5e-48], N[(N[(-0.5 * N[((-Pi) / a), $MachinePrecision]), $MachinePrecision] / N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / N[(a * b), $MachinePrecision]), $MachinePrecision] * N[(0.5 / N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 74.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{-0.5 \cdot \frac{\pi}{b - a}}{a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{b} \cdot \frac{\frac{0.5}{a}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= a -7.8e-119)
   (/ (* -0.5 (/ PI (- b a))) (* a b))
   (* (/ PI b) (/ (/ 0.5 a) b))))

C

double code(double a, double b) {
	double tmp;
	if (a <= -7.8e-119) {
		tmp = (-0.5 * (((double) M_PI) / (b - a))) / (a * b);
	} else {
		tmp = (((double) M_PI) / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (a <= -7.8e-119) {
		tmp = (-0.5 * (Math.PI / (b - a))) / (a * b);
	} else {
		tmp = (Math.PI / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if a <= -7.8e-119:
		tmp = (-0.5 * (math.pi / (b - a))) / (a * b)
	else:
		tmp = (math.pi / b) * ((0.5 / a) / b)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (a <= -7.8e-119)
		tmp = Float64(Float64(-0.5 * Float64(pi / Float64(b - a))) / Float64(a * b));
	else
		tmp = Float64(Float64(pi / b) * Float64(Float64(0.5 / a) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -7.8e-119)
		tmp = (-0.5 * (pi / (b - a))) / (a * b);
	else
		tmp = (pi / b) * ((0.5 / a) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[a, -7.8e-119], N[(N[(-0.5 * N[(Pi / N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / b), $MachinePrecision] * N[(N[(0.5 / a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.9 \cdot 10^{-47}:\\ \;\;\;\;\frac{-0.5 \cdot \frac{-\pi}{a}}{a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \frac{\pi}{a \cdot b}}{b - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= b 7.9e-47)
   (/ (* -0.5 (/ (- PI) a)) (* a b))
   (/ (* 0.5 (/ PI (* a b))) (- b a))))

C

double code(double a, double b) {
	double tmp;
	if (b <= 7.9e-47) {
		tmp = (-0.5 * (-((double) M_PI) / a)) / (a * b);
	} else {
		tmp = (0.5 * (((double) M_PI) / (a * b))) / (b - a);
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (b <= 7.9e-47) {
		tmp = (-0.5 * (-Math.PI / a)) / (a * b);
	} else {
		tmp = (0.5 * (Math.PI / (a * b))) / (b - a);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if b <= 7.9e-47:
		tmp = (-0.5 * (-math.pi / a)) / (a * b)
	else:
		tmp = (0.5 * (math.pi / (a * b))) / (b - a)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (b <= 7.9e-47)
		tmp = Float64(Float64(-0.5 * Float64(Float64(-pi) / a)) / Float64(a * b));
	else
		tmp = Float64(Float64(0.5 * Float64(pi / Float64(a * b))) / Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b <= 7.9e-47)
		tmp = (-0.5 * (-pi / a)) / (a * b);
	else
		tmp = (0.5 * (pi / (a * b))) / (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[b, 7.9e-47], N[(N[(-0.5 * N[((-Pi) / a), $MachinePrecision]), $MachinePrecision] / N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(Pi / N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 74.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{\pi \cdot -0.5}{a \cdot b}}{b - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{b} \cdot \frac{\frac{0.5}{a}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= a -7e-119)
   (/ (/ (* PI -0.5) (* a b)) (- b a))
   (* (/ PI b) (/ (/ 0.5 a) b))))

C

double code(double a, double b) {
	double tmp;
	if (a <= -7e-119) {
		tmp = ((((double) M_PI) * -0.5) / (a * b)) / (b - a);
	} else {
		tmp = (((double) M_PI) / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (a <= -7e-119) {
		tmp = ((Math.PI * -0.5) / (a * b)) / (b - a);
	} else {
		tmp = (Math.PI / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if a <= -7e-119:
		tmp = ((math.pi * -0.5) / (a * b)) / (b - a)
	else:
		tmp = (math.pi / b) * ((0.5 / a) / b)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (a <= -7e-119)
		tmp = Float64(Float64(Float64(pi * -0.5) / Float64(a * b)) / Float64(b - a));
	else
		tmp = Float64(Float64(pi / b) * Float64(Float64(0.5 / a) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -7e-119)
		tmp = ((pi * -0.5) / (a * b)) / (b - a);
	else
		tmp = (pi / b) * ((0.5 / a) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[a, -7e-119], N[(N[(N[(Pi * -0.5), $MachinePrecision] / N[(a * b), $MachinePrecision]), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / b), $MachinePrecision] * N[(N[(0.5 / a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 74.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{\pi \cdot \frac{-0.5}{b}}{a}}{b - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{b} \cdot \frac{\frac{0.5}{a}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= a -7.8e-119)
   (/ (/ (* PI (/ -0.5 b)) a) (- b a))
   (* (/ PI b) (/ (/ 0.5 a) b))))

C

double code(double a, double b) {
	double tmp;
	if (a <= -7.8e-119) {
		tmp = ((((double) M_PI) * (-0.5 / b)) / a) / (b - a);
	} else {
		tmp = (((double) M_PI) / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (a <= -7.8e-119) {
		tmp = ((Math.PI * (-0.5 / b)) / a) / (b - a);
	} else {
		tmp = (Math.PI / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if a <= -7.8e-119:
		tmp = ((math.pi * (-0.5 / b)) / a) / (b - a)
	else:
		tmp = (math.pi / b) * ((0.5 / a) / b)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (a <= -7.8e-119)
		tmp = Float64(Float64(Float64(pi * Float64(-0.5 / b)) / a) / Float64(b - a));
	else
		tmp = Float64(Float64(pi / b) * Float64(Float64(0.5 / a) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -7.8e-119)
		tmp = ((pi * (-0.5 / b)) / a) / (b - a);
	else
		tmp = (pi / b) * ((0.5 / a) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[a, -7.8e-119], N[(N[(N[(Pi * N[(-0.5 / b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / b), $MachinePrecision] * N[(N[(0.5 / a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 74.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{\frac{-0.5}{\frac{b}{\pi}}}{a}}{b - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{b} \cdot \frac{\frac{0.5}{a}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= a -7.8e-119)
   (/ (/ (/ -0.5 (/ b PI)) a) (- b a))
   (* (/ PI b) (/ (/ 0.5 a) b))))

C

double code(double a, double b) {
	double tmp;
	if (a <= -7.8e-119) {
		tmp = ((-0.5 / (b / ((double) M_PI))) / a) / (b - a);
	} else {
		tmp = (((double) M_PI) / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (a <= -7.8e-119) {
		tmp = ((-0.5 / (b / Math.PI)) / a) / (b - a);
	} else {
		tmp = (Math.PI / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if a <= -7.8e-119:
		tmp = ((-0.5 / (b / math.pi)) / a) / (b - a)
	else:
		tmp = (math.pi / b) * ((0.5 / a) / b)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (a <= -7.8e-119)
		tmp = Float64(Float64(Float64(-0.5 / Float64(b / pi)) / a) / Float64(b - a));
	else
		tmp = Float64(Float64(pi / b) * Float64(Float64(0.5 / a) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -7.8e-119)
		tmp = ((-0.5 / (b / pi)) / a) / (b - a);
	else
		tmp = (pi / b) * ((0.5 / a) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[a, -7.8e-119], N[(N[(N[(-0.5 / N[(b / Pi), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / N[(b - a), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / b), $MachinePrecision] * N[(N[(0.5 / a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 13: 74.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 0.33:\\ \;\;\;\;\frac{-0.5 \cdot \frac{-\pi}{a}}{a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{b} \cdot \frac{\frac{0.5}{a}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= b 0.33)
   (/ (* -0.5 (/ (- PI) a)) (* a b))
   (* (/ PI b) (/ (/ 0.5 a) b))))

C

double code(double a, double b) {
	double tmp;
	if (b <= 0.33) {
		tmp = (-0.5 * (-((double) M_PI) / a)) / (a * b);
	} else {
		tmp = (((double) M_PI) / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (b <= 0.33) {
		tmp = (-0.5 * (-Math.PI / a)) / (a * b);
	} else {
		tmp = (Math.PI / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if b <= 0.33:
		tmp = (-0.5 * (-math.pi / a)) / (a * b)
	else:
		tmp = (math.pi / b) * ((0.5 / a) / b)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (b <= 0.33)
		tmp = Float64(Float64(-0.5 * Float64(Float64(-pi) / a)) / Float64(a * b));
	else
		tmp = Float64(Float64(pi / b) * Float64(Float64(0.5 / a) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b <= 0.33)
		tmp = (-0.5 * (-pi / a)) / (a * b);
	else
		tmp = (pi / b) * ((0.5 / a) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[b, 0.33], N[(N[(-0.5 * N[((-Pi) / a), $MachinePrecision]), $MachinePrecision] / N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / b), $MachinePrecision] * N[(N[(0.5 / a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 66.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\pi}{a \cdot b}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+124}:\\ \;\;\;\;t_0 \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (let* ((t_0 (/ PI (* a b))))
   (if (<= a -2.3e+124) (* t_0 (/ -0.5 a)) (* t_0 (/ 0.5 b)))))

C

double code(double a, double b) {
	double t_0 = ((double) M_PI) / (a * b);
	double tmp;
	if (a <= -2.3e+124) {
		tmp = t_0 * (-0.5 / a);
	} else {
		tmp = t_0 * (0.5 / b);
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double t_0 = Math.PI / (a * b);
	double tmp;
	if (a <= -2.3e+124) {
		tmp = t_0 * (-0.5 / a);
	} else {
		tmp = t_0 * (0.5 / b);
	}
	return tmp;
}

Python

def code(a, b):
	t_0 = math.pi / (a * b)
	tmp = 0
	if a <= -2.3e+124:
		tmp = t_0 * (-0.5 / a)
	else:
		tmp = t_0 * (0.5 / b)
	return tmp

Julia

function code(a, b)
	t_0 = Float64(pi / Float64(a * b))
	tmp = 0.0
	if (a <= -2.3e+124)
		tmp = Float64(t_0 * Float64(-0.5 / a));
	else
		tmp = Float64(t_0 * Float64(0.5 / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	t_0 = pi / (a * b);
	tmp = 0.0;
	if (a <= -2.3e+124)
		tmp = t_0 * (-0.5 / a);
	else
		tmp = t_0 * (0.5 / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := Block[{t$95$0 = N[(Pi / N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+124], N[(t$95$0 * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(0.5 / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 15: 66.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+124}:\\ \;\;\;\;\frac{\pi}{a \cdot b} \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{b} \cdot \frac{\frac{0.5}{a}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= a -2.3e+124)
   (* (/ PI (* a b)) (/ -0.5 a))
   (* (/ PI b) (/ (/ 0.5 a) b))))

C

double code(double a, double b) {
	double tmp;
	if (a <= -2.3e+124) {
		tmp = (((double) M_PI) / (a * b)) * (-0.5 / a);
	} else {
		tmp = (((double) M_PI) / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Java

public static double code(double a, double b) {
	double tmp;
	if (a <= -2.3e+124) {
		tmp = (Math.PI / (a * b)) * (-0.5 / a);
	} else {
		tmp = (Math.PI / b) * ((0.5 / a) / b);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if a <= -2.3e+124:
		tmp = (math.pi / (a * b)) * (-0.5 / a)
	else:
		tmp = (math.pi / b) * ((0.5 / a) / b)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (a <= -2.3e+124)
		tmp = Float64(Float64(pi / Float64(a * b)) * Float64(-0.5 / a));
	else
		tmp = Float64(Float64(pi / b) * Float64(Float64(0.5 / a) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= -2.3e+124)
		tmp = (pi / (a * b)) * (-0.5 / a);
	else
		tmp = (pi / b) * ((0.5 / a) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[a, -2.3e+124], N[(N[(Pi / N[(a * b), $MachinePrecision]), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(Pi / b), $MachinePrecision] * N[(N[(0.5 / a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 16: 29.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{\pi}{a \cdot b} \cdot \frac{-0.5}{a} \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (* (/ PI (* a b)) (/ -0.5 a)))

C

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

Java

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

Python

def code(a, b):
	return (math.pi / (a * b)) * (-0.5 / a)

Julia

function code(a, b)
	return Float64(Float64(pi / Float64(a * b)) * Float64(-0.5 / a))
end

MATLAB

function tmp = code(a, b)
	tmp = (pi / (a * b)) * (-0.5 / a);
end

Wolfram

code[a_, b_] := N[(N[(Pi / N[(a * b), $MachinePrecision]), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023340 
(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))))