Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 17.6s

Alternatives: 19

Speedup: 0.8×

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: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{elif}\;a - 0.5 \leq -0.4:\\ \;\;\;\;\left(\log y + \left(\log z + \log t \cdot -0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a + -0.5, \log t, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- a 0.5) -2e+19)
   (- (* (log t) a) t)
   (if (<= (- a 0.5) -0.4)
     (- (+ (log y) (+ (log z) (* (log t) -0.5))) t)
     (fma (+ a -0.5) (log t) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a - 0.5) <= -2e+19) {
		tmp = (log(t) * a) - t;
	} else if ((a - 0.5) <= -0.4) {
		tmp = (log(y) + (log(z) + (log(t) * -0.5))) - t;
	} else {
		tmp = fma((a + -0.5), log(t), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a - 0.5) <= -2e+19)
		tmp = Float64(Float64(log(t) * a) - t);
	elseif (Float64(a - 0.5) <= -0.4)
		tmp = Float64(Float64(log(y) + Float64(log(z) + Float64(log(t) * -0.5))) - t);
	else
		tmp = fma(Float64(a + -0.5), log(t), Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a - 0.5), $MachinePrecision], -2e+19], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[N[(a - 0.5), $MachinePrecision], -0.4], N[(N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 3: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 410:\\ \;\;\;\;\log z + \left(\log \left(x + y\right) + \log t \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a + -0.5, \log t, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 410.0)
   (+ (log z) (+ (log (+ x y)) (* (log t) (- a 0.5))))
   (fma (+ a -0.5) (log t) (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 410.0) {
		tmp = log(z) + (log((x + y)) + (log(t) * (a - 0.5)));
	} else {
		tmp = fma((a + -0.5), log(t), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 410.0)
		tmp = Float64(log(z) + Float64(log(Float64(x + y)) + Float64(log(t) * Float64(a - 0.5))));
	else
		tmp = fma(Float64(a + -0.5), log(t), Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 410.0], N[(N[Log[z], $MachinePrecision] + N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 4: 99.6% accurate, 1.0× speedup

Math

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

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(log(Float64(x + y)) + Float64(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[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 5: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1200000000:\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{elif}\;a \leq 0.0018:\\ \;\;\;\;\left(\log y + \log \left(z \cdot {t}^{-0.5}\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a + -0.5, \log t, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1200000000.0)
   (- (* (log t) a) t)
   (if (<= a 0.0018)
     (- (+ (log y) (log (* z (pow t -0.5)))) t)
     (fma (+ a -0.5) (log t) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1200000000.0) {
		tmp = (log(t) * a) - t;
	} else if (a <= 0.0018) {
		tmp = (log(y) + log((z * pow(t, -0.5)))) - t;
	} else {
		tmp = fma((a + -0.5), log(t), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1200000000.0)
		tmp = Float64(Float64(log(t) * a) - t);
	elseif (a <= 0.0018)
		tmp = Float64(Float64(log(y) + log(Float64(z * (t ^ -0.5)))) - t);
	else
		tmp = fma(Float64(a + -0.5), log(t), Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1200000000.0], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[a, 0.0018], N[(N[(N[Log[y], $MachinePrecision] + N[Log[N[(z * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 6: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t \leq 4.2 \cdot 10^{-215}:\\ \;\;\;\;\log \left(\left(x + y\right) \cdot z\right) + t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-182}:\\ \;\;\;\;\log z + \left(\log y + \log t \cdot -0.5\right)\\ \mathbf{elif}\;t \leq 2900:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + t_1\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a + -0.5, \log t, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) (- a 0.5))))
   (if (<= t 4.2e-215)
     (+ (log (* (+ x y) z)) t_1)
     (if (<= t 2.7e-182)
       (+ (log z) (+ (log y) (* (log t) -0.5)))
       (if (<= t 2900.0)
         (- (+ (log (* y z)) t_1) t)
         (fma (+ a -0.5) (log t) (- t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * (a - 0.5);
	double tmp;
	if (t <= 4.2e-215) {
		tmp = log(((x + y) * z)) + t_1;
	} else if (t <= 2.7e-182) {
		tmp = log(z) + (log(y) + (log(t) * -0.5));
	} else if (t <= 2900.0) {
		tmp = (log((y * z)) + t_1) - t;
	} else {
		tmp = fma((a + -0.5), log(t), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * Float64(a - 0.5))
	tmp = 0.0
	if (t <= 4.2e-215)
		tmp = Float64(log(Float64(Float64(x + y) * z)) + t_1);
	elseif (t <= 2.7e-182)
		tmp = Float64(log(z) + Float64(log(y) + Float64(log(t) * -0.5)));
	elseif (t <= 2900.0)
		tmp = Float64(Float64(log(Float64(y * z)) + t_1) - t);
	else
		tmp = fma(Float64(a + -0.5), log(t), Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 4.2e-215], N[(N[Log[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 2.7e-182], N[(N[Log[z], $MachinePrecision] + N[(N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2900.0], N[(N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + t$95$1), $MachinePrecision] - t), $MachinePrecision], N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision]]]]]

Derivation

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1. Add Preprocessing

Alternative 7: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t \leq 1.4 \cdot 10^{-214}:\\ \;\;\;\;\log \left(\left(x + y\right) \cdot z\right) + t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-182}:\\ \;\;\;\;\left(\log z + \log y\right) - \log t \cdot 0.5\\ \mathbf{elif}\;t \leq 2500:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + t_1\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a + -0.5, \log t, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) (- a 0.5))))
   (if (<= t 1.4e-214)
     (+ (log (* (+ x y) z)) t_1)
     (if (<= t 6e-182)
       (- (+ (log z) (log y)) (* (log t) 0.5))
       (if (<= t 2500.0)
         (- (+ (log (* y z)) t_1) t)
         (fma (+ a -0.5) (log t) (- t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * (a - 0.5);
	double tmp;
	if (t <= 1.4e-214) {
		tmp = log(((x + y) * z)) + t_1;
	} else if (t <= 6e-182) {
		tmp = (log(z) + log(y)) - (log(t) * 0.5);
	} else if (t <= 2500.0) {
		tmp = (log((y * z)) + t_1) - t;
	} else {
		tmp = fma((a + -0.5), log(t), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * Float64(a - 0.5))
	tmp = 0.0
	if (t <= 1.4e-214)
		tmp = Float64(log(Float64(Float64(x + y) * z)) + t_1);
	elseif (t <= 6e-182)
		tmp = Float64(Float64(log(z) + log(y)) - Float64(log(t) * 0.5));
	elseif (t <= 2500.0)
		tmp = Float64(Float64(log(Float64(y * z)) + t_1) - t);
	else
		tmp = fma(Float64(a + -0.5), log(t), Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 1.4e-214], N[(N[Log[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 6e-182], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2500.0], N[(N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + t$95$1), $MachinePrecision] - t), $MachinePrecision], N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision]]]]]

Derivation

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1. Add Preprocessing

Alternative 8: 68.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (log(y) + (log(z) + (log(t) * (a - 0.5)))) - 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) * (a - 0.5d0)))) - 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) * (a - 0.5)))) - t;
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (log(y) + (log(z) + (log(t) * (a - 0.5)))) - 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[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 9: 87.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2900:\\ \;\;\;\;\left(\log \left(\left(x + y\right) \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a + -0.5, \log t, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2900.0)
   (- (+ (log (* (+ x y) z)) (* (log t) (- a 0.5))) t)
   (fma (+ a -0.5) (log t) (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2900.0) {
		tmp = (log(((x + y) * z)) + (log(t) * (a - 0.5))) - t;
	} else {
		tmp = fma((a + -0.5), log(t), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2900.0)
		tmp = Float64(Float64(log(Float64(Float64(x + y) * z)) + Float64(log(t) * Float64(a - 0.5))) - t);
	else
		tmp = fma(Float64(a + -0.5), log(t), Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2900.0], 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[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision]]

Derivation

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

Alternative 10: 87.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3:\\ \;\;\;\;\log \left(\left(x + y\right) \cdot z\right) + \log t \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a + -0.5, \log t, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 3.0)
   (+ (log (* (+ x y) z)) (* (log t) (- a 0.5)))
   (fma (+ a -0.5) (log t) (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 3.0) {
		tmp = log(((x + y) * z)) + (log(t) * (a - 0.5));
	} else {
		tmp = fma((a + -0.5), log(t), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 3.0)
		tmp = Float64(log(Float64(Float64(x + y) * z)) + Float64(log(t) * Float64(a - 0.5)));
	else
		tmp = fma(Float64(a + -0.5), log(t), Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 3.0], 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[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision]]

Derivation

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

Alternative 11: 73.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2700:\\ \;\;\;\;\left(\log t \cdot \left(a - 0.5\right) + \log \left(y \cdot z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a + -0.5, \log t, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2700.0)
   (- (+ (* (log t) (- a 0.5)) (log (* y z))) t)
   (fma (+ a -0.5) (log t) (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2700.0) {
		tmp = ((log(t) * (a - 0.5)) + log((y * z))) - t;
	} else {
		tmp = fma((a + -0.5), log(t), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2700.0)
		tmp = Float64(Float64(Float64(log(t) * Float64(a - 0.5)) + log(Float64(y * z))) - t);
	else
		tmp = fma(Float64(a + -0.5), log(t), Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2700.0], 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[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision]]

Derivation

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

Alternative 12: 72.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-30} \lor \neg \left(a \leq 1.08 \cdot 10^{-16}\right):\\ \;\;\;\;\mathsf{fma}\left(a + -0.5, \log t, -t\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{-0.5}\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1e-30) (not (<= a 1.08e-16)))
   (fma (+ a -0.5) (log t) (- t))
   (- (log (* y (* z (pow t -0.5)))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1e-30) || !(a <= 1.08e-16)) {
		tmp = fma((a + -0.5), log(t), -t);
	} else {
		tmp = log((y * (z * pow(t, -0.5)))) - t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1e-30) || !(a <= 1.08e-16))
		tmp = fma(Float64(a + -0.5), log(t), Float64(-t));
	else
		tmp = Float64(log(Float64(y * Float64(z * (t ^ -0.5)))) - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1e-30], N[Not[LessEqual[a, 1.08e-16]], $MachinePrecision]], N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision], N[(N[Log[N[(y * N[(z * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]]

Derivation

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

Alternative 13: 69.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot a - t\\ \mathbf{if}\;a \leq -1200000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-52}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-22}:\\ \;\;\;\;\log \left(\frac{y}{\frac{\sqrt{t}}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (log t) a) t)))
   (if (<= a -1200000000.0)
     t_1
     (if (<= a 5.8e-52)
       (- (+ (log z) (log y)) t)
       (if (<= a 1.05e-22) (log (/ y (/ (sqrt t) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (log(t) * a) - t;
	double tmp;
	if (a <= -1200000000.0) {
		tmp = t_1;
	} else if (a <= 5.8e-52) {
		tmp = (log(z) + log(y)) - t;
	} else if (a <= 1.05e-22) {
		tmp = log((y / (sqrt(t) / z)));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (log(t) * a) - t
    if (a <= (-1200000000.0d0)) then
        tmp = t_1
    else if (a <= 5.8d-52) then
        tmp = (log(z) + log(y)) - t
    else if (a <= 1.05d-22) then
        tmp = log((y / (sqrt(t) / z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (Math.log(t) * a) - t;
	double tmp;
	if (a <= -1200000000.0) {
		tmp = t_1;
	} else if (a <= 5.8e-52) {
		tmp = (Math.log(z) + Math.log(y)) - t;
	} else if (a <= 1.05e-22) {
		tmp = Math.log((y / (Math.sqrt(t) / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (math.log(t) * a) - t
	tmp = 0
	if a <= -1200000000.0:
		tmp = t_1
	elif a <= 5.8e-52:
		tmp = (math.log(z) + math.log(y)) - t
	elif a <= 1.05e-22:
		tmp = math.log((y / (math.sqrt(t) / z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(log(t) * a) - t)
	tmp = 0.0
	if (a <= -1200000000.0)
		tmp = t_1;
	elseif (a <= 5.8e-52)
		tmp = Float64(Float64(log(z) + log(y)) - t);
	elseif (a <= 1.05e-22)
		tmp = log(Float64(y / Float64(sqrt(t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (log(t) * a) - t;
	tmp = 0.0;
	if (a <= -1200000000.0)
		tmp = t_1;
	elseif (a <= 5.8e-52)
		tmp = (log(z) + log(y)) - t;
	elseif (a <= 1.05e-22)
		tmp = log((y / (sqrt(t) / z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[a, -1200000000.0], t$95$1, If[LessEqual[a, 5.8e-52], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[a, 1.05e-22], N[Log[N[(y / N[(N[Sqrt[t], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], t$95$1]]]]

Derivation

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

Alternative 14: 73.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 9.2 \cdot 10^{-5}:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \log \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a + -0.5, \log t, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 9.2e-5)
   (+ (* (log t) (- a 0.5)) (log (* y z)))
   (fma (+ a -0.5) (log t) (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 9.2e-5) {
		tmp = (log(t) * (a - 0.5)) + log((y * z));
	} else {
		tmp = fma((a + -0.5), log(t), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 9.2e-5)
		tmp = Float64(Float64(log(t) * Float64(a - 0.5)) + log(Float64(y * z)));
	else
		tmp = fma(Float64(a + -0.5), log(t), Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 9.2e-5], N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision]]

Derivation

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

Alternative 15: 76.8% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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

Alternative 16: 62.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+33} \lor \neg \left(a \leq 7.2 \cdot 10^{+37}\right):\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.5e+33) (not (<= a 7.2e+37))) (* (log t) a) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.5e+33) || !(a <= 7.2e+37)) {
		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 ((a <= (-6.5d+33)) .or. (.not. (a <= 7.2d+37))) 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 ((a <= -6.5e+33) || !(a <= 7.2e+37)) {
		tmp = Math.log(t) * a;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.5e+33) or not (a <= 7.2e+37):
		tmp = math.log(t) * a
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.5e+33) || !(a <= 7.2e+37))
		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 ((a <= -6.5e+33) || ~((a <= 7.2e+37)))
		tmp = log(t) * a;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.5e+33], N[Not[LessEqual[a, 7.2e+37]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision], (-t)]

Derivation

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

Alternative 17: 39.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 350:\\ \;\;\;\;\log \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 350.0) (log (* y z)) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 350.0) {
		tmp = log((y * z));
	} 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 <= 350.0d0) then
        tmp = log((y * z))
    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 <= 350.0) {
		tmp = Math.log((y * z));
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 350.0:
		tmp = math.log((y * z))
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 350.0)
		tmp = log(Float64(y * z));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 350.0)
		tmp = log((y * z));
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 350.0], N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision], (-t)]

Derivation

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

Alternative 18: 74.2% 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 19: 37.8% 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 2023350 
(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))))