Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 17.7s

Alternatives: 14

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))

C

double code(double x, double y, double z, double t, double a) {
	return ((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((log((x + y)) + log(z)) - t) + ((a - 0.5d0) * log(t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((Math.log((x + y)) + Math.log(z)) - t) + ((a - 0.5) * Math.log(t));
}

Python

def code(x, y, z, t, a):
	return ((math.log((x + y)) + math.log(z)) - t) + ((a - 0.5) * math.log(t))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(log(Float64(x + y)) + log(z)) - t) + Float64(Float64(a - 0.5) * log(t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))

C

double code(double x, double y, double z, double t, double a) {
	return ((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((log((x + y)) + log(z)) - t) + ((a - 0.5d0) * log(t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((Math.log((x + y)) + Math.log(z)) - t) + ((a - 0.5) * Math.log(t));
}

Python

def code(x, y, z, t, a):
	return ((math.log((x + y)) + math.log(z)) - t) + ((a - 0.5) * math.log(t))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(log(Float64(x + y)) + log(z)) - t) + Float64(Float64(a - 0.5) * log(t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (log (+ x y)) (- (log z) (fma (log t) (- 0.5 a) t))))

C

double code(double x, double y, double z, double t, double a) {
	return log((x + y)) + (log(z) - fma(log(t), (0.5 - a), t));
}

Julia

function code(x, y, z, t, a)
	return Float64(log(Float64(x + y)) + Float64(log(z) - fma(log(t), Float64(0.5 - a), t)))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * N[(0.5 - a), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log t \cdot \left(a - 0.5\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (- (+ (log (+ x y)) (log z)) t) (* (log t) (- a 0.5))))

C

double code(double x, double y, double z, double t, double a) {
	return ((log((x + y)) + log(z)) - t) + (log(t) * (a - 0.5));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((log((x + y)) + log(z)) - t) + (log(t) * (a - 0.5d0))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((Math.log((x + y)) + Math.log(z)) - t) + (Math.log(t) * (a - 0.5));
}

Python

def code(x, y, z, t, a):
	return ((math.log((x + y)) + math.log(z)) - t) + (math.log(t) * (a - 0.5))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(log(Float64(x + y)) + log(z)) - t) + Float64(log(t) * Float64(a - 0.5)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((log((x + y)) + log(z)) - t) + (log(t) * (a - 0.5));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 3: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+23}:\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-13}:\\ \;\;\;\;\left(\log y + \log \left(z \cdot {t}^{-0.5}\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log t, a, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e+23)
   (- (* (log t) a) t)
   (if (<= a 1.08e-13)
     (- (+ (log y) (log (* z (pow t -0.5)))) t)
     (fma (log t) a (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+23) {
		tmp = (log(t) * a) - t;
	} else if (a <= 1.08e-13) {
		tmp = (log(y) + log((z * pow(t, -0.5)))) - t;
	} else {
		tmp = fma(log(t), a, -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e+23)
		tmp = Float64(Float64(log(t) * a) - t);
	elseif (a <= 1.08e-13)
		tmp = Float64(Float64(log(y) + log(Float64(z * (t ^ -0.5)))) - t);
	else
		tmp = fma(log(t), a, Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e+23], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[a, 1.08e-13], N[(N[(N[Log[y], $MachinePrecision] + N[Log[N[(z * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[t], $MachinePrecision] * a + (-t)), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 4: 81.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.8:\\ \;\;\;\;\log y + \left(\log z - \log t \cdot \left(0.5 - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log t, a, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 7.8)
   (+ (log y) (- (log z) (* (log t) (- 0.5 a))))
   (fma (log t) a (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 7.8) {
		tmp = log(y) + (log(z) - (log(t) * (0.5 - a)));
	} else {
		tmp = fma(log(t), a, -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 7.8)
		tmp = Float64(log(y) + Float64(log(z) - Float64(log(t) * Float64(0.5 - a))));
	else
		tmp = fma(log(t), a, Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 7.8], N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * N[(0.5 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] * a + (-t)), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 5: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\log y + \left(\log z - \log t \cdot \left(0.5 - a\right)\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- (+ (log y) (- (log z) (* (log t) (- 0.5 a)))) t))

C

double code(double x, double y, double z, double t, double a) {
	return (log(y) + (log(z) - (log(t) * (0.5 - a)))) - t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (log(y) + (log(z) - (log(t) * (0.5d0 - a)))) - t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (Math.log(y) + (Math.log(z) - (Math.log(t) * (0.5 - a)))) - t;
}

Python

def code(x, y, z, t, a):
	return (math.log(y) + (math.log(z) - (math.log(t) * (0.5 - a)))) - t

Julia

function code(x, y, z, t, a)
	return Float64(Float64(log(y) + Float64(log(z) - Float64(log(t) * Float64(0.5 - a)))) - t)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (log(y) + (log(z) - (log(t) * (0.5 - a)))) - t;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * N[(0.5 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 6: 87.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 54000000:\\ \;\;\;\;\left(\log \left(\left(x + y\right) \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log t, a, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 54000000.0)
   (- (+ (log (* (+ x y) z)) (* (log t) (- a 0.5))) t)
   (fma (log t) a (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 54000000.0) {
		tmp = (log(((x + y) * z)) + (log(t) * (a - 0.5))) - t;
	} else {
		tmp = fma(log(t), a, -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 54000000.0)
		tmp = Float64(Float64(log(Float64(Float64(x + y) * z)) + Float64(log(t) * Float64(a - 0.5))) - t);
	else
		tmp = fma(log(t), a, Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 54000000.0], N[(N[(N[Log[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[t], $MachinePrecision] * a + (-t)), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 86.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.9:\\ \;\;\;\;\log \left(\left(x + y\right) \cdot z\right) + \log t \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log t, a, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2.9)
   (+ (log (* (+ x y) z)) (* (log t) (- a 0.5)))
   (fma (log t) a (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.9) {
		tmp = log(((x + y) * z)) + (log(t) * (a - 0.5));
	} else {
		tmp = fma(log(t), a, -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.9)
		tmp = Float64(log(Float64(Float64(x + y) * z)) + Float64(log(t) * Float64(a - 0.5)));
	else
		tmp = fma(log(t), a, Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.9], N[(N[Log[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] * a + (-t)), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 8: 73.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 88000000:\\ \;\;\;\;\left(\log t \cdot \left(a - 0.5\right) + \log \left(y \cdot z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log t, a, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 88000000.0)
   (- (+ (* (log t) (- a 0.5)) (log (* y z))) t)
   (fma (log t) a (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 88000000.0) {
		tmp = ((log(t) * (a - 0.5)) + log((y * z))) - t;
	} else {
		tmp = fma(log(t), a, -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 88000000.0)
		tmp = Float64(Float64(Float64(log(t) * Float64(a - 0.5)) + log(Float64(y * z))) - t);
	else
		tmp = fma(log(t), a, Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 88000000.0], N[(N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[t], $MachinePrecision] * a + (-t)), $MachinePrecision]]

Derivation

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

Alternative 9: 71.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-13}:\\ \;\;\;\;\log \left(z \cdot \left(y \cdot {t}^{-0.5}\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log t, a, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e-6)
   (- (* (log t) a) t)
   (if (<= a 1.08e-13)
     (- (log (* z (* y (pow t -0.5)))) t)
     (fma (log t) a (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e-6) {
		tmp = (log(t) * a) - t;
	} else if (a <= 1.08e-13) {
		tmp = log((z * (y * pow(t, -0.5)))) - t;
	} else {
		tmp = fma(log(t), a, -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e-6)
		tmp = Float64(Float64(log(t) * a) - t);
	elseif (a <= 1.08e-13)
		tmp = Float64(log(Float64(z * Float64(y * (t ^ -0.5)))) - t);
	else
		tmp = fma(log(t), a, Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e-6], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[a, 1.08e-13], N[(N[Log[N[(z * N[(y * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision], N[(N[Log[t], $MachinePrecision] * a + (-t)), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 10: 73.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.1:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \log \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log t, a, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2.1) (+ (* (log t) (- a 0.5)) (log (* y z))) (fma (log t) a (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.1) {
		tmp = (log(t) * (a - 0.5)) + log((y * z));
	} else {
		tmp = fma(log(t), a, -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.1)
		tmp = Float64(Float64(log(t) * Float64(a - 0.5)) + log(Float64(y * z)));
	else
		tmp = fma(log(t), a, Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.1], N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] * a + (-t)), $MachinePrecision]]

Derivation

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

Alternative 11: 75.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\log t, a, -t\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma (log t) a (- t)))

C

double code(double x, double y, double z, double t, double a) {
	return fma(log(t), a, -t);
}

Julia

function code(x, y, z, t, a)
	return fma(log(t), a, Float64(-t))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[Log[t], $MachinePrecision] * a + (-t)), $MachinePrecision]

Derivation

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

Alternative 12: 63.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.05 \cdot 10^{+44}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2.05e+44) (* (log t) a) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.05e+44) {
		tmp = log(t) * a;
	} else {
		tmp = -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 2.05d+44) then
        tmp = log(t) * a
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.05e+44) {
		tmp = Math.log(t) * a;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.05e+44:
		tmp = math.log(t) * a
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.05e+44)
		tmp = Float64(log(t) * a);
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 2.05e+44)
		tmp = log(t) * a;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.05e+44], N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision], (-t)]

Derivation

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

Alternative 13: 75.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \log t \cdot a - t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- (* (log t) a) t))

C

double code(double x, double y, double z, double t, double a) {
	return (log(t) * a) - t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (log(t) * a) - t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (Math.log(t) * a) - t;
}

Python

def code(x, y, z, t, a):
	return (math.log(t) * a) - t

Julia

function code(x, y, z, t, a)
	return Float64(Float64(log(t) * a) - t)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (log(t) * a) - t;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision]

Derivation

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

Alternative 14: 38.5% accurate, 156.5× speedup

Math

\[\begin{array}{l} \\ -t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- t))

C

double code(double x, double y, double z, double t, double a) {
	return -t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = -t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -t;
}

Python

def code(x, y, z, t, a):
	return -t

Julia

function code(x, y, z, t, a)
	return Float64(-t)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -t;
end

Wolfram

code[x_, y_, z_, t_, a_] := (-t)

Derivation

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

Developer target: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t)))))

C

double code(double x, double y, double z, double t, double a) {
	return log((x + y)) + ((log(z) - t) + ((a - 0.5) * log(t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = log((x + y)) + ((log(z) - t) + ((a - 0.5d0) * log(t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return Math.log((x + y)) + ((Math.log(z) - t) + ((a - 0.5) * Math.log(t)));
}

Python

def code(x, y, z, t, a):
	return math.log((x + y)) + ((math.log(z) - t) + ((a - 0.5) * math.log(t)))

Julia

function code(x, y, z, t, a)
	return Float64(log(Float64(x + y)) + Float64(Float64(log(z) - t) + Float64(Float64(a - 0.5) * log(t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = log((x + y)) + ((log(z) - t) + ((a - 0.5) * log(t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023343 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))