Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 3.1s

Alternatives: 7

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, 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]

Derivation

1. Initial program 99.7%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 66.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot \log t + \log z\\ \mathbf{if}\;a - 0.5 \leq -7.2 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a - 0.5 \leq 5.5 \cdot 10^{+57}:\\ \;\;\;\;\left(\log \left(x + y\right) + \log z\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* (- a 0.5) (log t)) (log z))))
   (if (<= (- a 0.5) -7.2e+22)
     t_1
     (if (<= (- a 0.5) 5.5e+57) (- (+ (log (+ x y)) (log z)) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((a - 0.5) * log(t)) + log(z);
	double tmp;
	if ((a - 0.5) <= -7.2e+22) {
		tmp = t_1;
	} else if ((a - 0.5) <= 5.5e+57) {
		tmp = (log((x + y)) + log(z)) - t;
	} 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 = ((a - 0.5d0) * log(t)) + log(z)
    if ((a - 0.5d0) <= (-7.2d+22)) then
        tmp = t_1
    else if ((a - 0.5d0) <= 5.5d+57) then
        tmp = (log((x + y)) + log(z)) - t
    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 = ((a - 0.5) * Math.log(t)) + Math.log(z);
	double tmp;
	if ((a - 0.5) <= -7.2e+22) {
		tmp = t_1;
	} else if ((a - 0.5) <= 5.5e+57) {
		tmp = (Math.log((x + y)) + Math.log(z)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((a - 0.5) * math.log(t)) + math.log(z)
	tmp = 0
	if (a - 0.5) <= -7.2e+22:
		tmp = t_1
	elif (a - 0.5) <= 5.5e+57:
		tmp = (math.log((x + y)) + math.log(z)) - t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(a - 0.5) * log(t)) + log(z))
	tmp = 0.0
	if (Float64(a - 0.5) <= -7.2e+22)
		tmp = t_1;
	elseif (Float64(a - 0.5) <= 5.5e+57)
		tmp = Float64(Float64(log(Float64(x + y)) + log(z)) - t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((a - 0.5) * log(t)) + log(z);
	tmp = 0.0;
	if ((a - 0.5) <= -7.2e+22)
		tmp = t_1;
	elseif ((a - 0.5) <= 5.5e+57)
		tmp = (log((x + y)) + log(z)) - t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a - 0.5), $MachinePrecision], -7.2e+22], t$95$1, If[LessEqual[N[(a - 0.5), $MachinePrecision], 5.5e+57], N[(N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -7.2e22 or 5.5000000000000002e57 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.7%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \left(x \cdot \left(\frac{-1}{2} \cdot \frac{x}{{y}^{2}} + \frac{1}{y}\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) - t} \]

   5. Applied rewrites 2.9%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \log z} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(\log y + x \cdot \left(\frac{-1}{2} \cdot \frac{x}{{y}^{2}} + \frac{1}{y}\right)\right) + \log \color{blue}{z} \]

   8. Applied rewrites 17.6%

      \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \color{blue}{z} \]

   9. Taylor expanded in x around 0

      \[\leadsto \log y + \log \color{blue}{z} \]

   11. Applied rewrites 20.9%

       \[\leadsto \left(\left(a - 0.5\right) - t\right) + \log \color{blue}{z} \]

   12. Taylor expanded in x around 0

       \[\leadsto \left(\left(\log y + \left(\log z + \frac{x}{y}\right)\right) - t\right) + \log z \]

   14. Applied rewrites 83.1%

       \[\leadsto \left(a - 0.5\right) \cdot \log t + \log z \]

   if -7.2e22 < (-.f64 a #s(literal 1/2 binary64)) < 5.5000000000000002e57

   1. Initial program 99.6%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \left(\log t \cdot \left(a - \frac{1}{2}\right) + \frac{x}{y}\right)\right)\right) - t} \]

   5. Applied rewrites 61.8%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 42.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 235:\\ \;\;\;\;\log \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a - 0.5\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 235.0) (log (+ x y)) (- (- a 0.5) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 235.0) {
		tmp = log((x + y));
	} else {
		tmp = (a - 0.5) - 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 <= 235.0d0) then
        tmp = log((x + y))
    else
        tmp = (a - 0.5d0) - 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 <= 235.0) {
		tmp = Math.log((x + y));
	} else {
		tmp = (a - 0.5) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 235.0:
		tmp = math.log((x + y))
	else:
		tmp = (a - 0.5) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 235.0)
		tmp = log(Float64(x + y));
	else
		tmp = Float64(Float64(a - 0.5) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 235.0)
		tmp = log((x + y));
	else
		tmp = (a - 0.5) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 235.0], N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision], N[(N[(a - 0.5), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 235

   1. Initial program 99.3%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \left(x \cdot \left(x \cdot \left(\frac{1}{3} \cdot \frac{x}{{y}^{3}} - \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right) + \frac{1}{y}\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) - t} \]

   5. Applied rewrites 10.0%

      \[\leadsto \color{blue}{\log \left(x + y\right)} \]

   if 235 < t

   1. Initial program 99.9%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \left(\log t \cdot \left(a - \frac{1}{2}\right) + \frac{x}{y}\right)\right)\right) - t} \]

   5. Applied rewrites 68.6%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - t} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(\log y + \log z\right) - t \]

   8. Applied rewrites 71.8%

      \[\leadsto \left(a - 0.5\right) - t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 41.8% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

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 = ((a - 0.5d0) - t) + log(z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(\log y + \left(\log z + \left(x \cdot \left(\frac{-1}{2} \cdot \frac{x}{{y}^{2}} + \frac{1}{y}\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) - t} \]

5. Applied rewrites 6.3%

   \[\leadsto \color{blue}{\log \left(x + y\right) + \log z} \]

6. Taylor expanded in x around 0

   \[\leadsto \left(\log y + x \cdot \left(\frac{-1}{2} \cdot \frac{x}{{y}^{2}} + \frac{1}{y}\right)\right) + \log \color{blue}{z} \]

8. Applied rewrites 42.5%

   \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \color{blue}{z} \]

9. Taylor expanded in x around 0

   \[\leadsto \log y + \log \color{blue}{z} \]

11. Applied rewrites 43.2%

    \[\leadsto \left(\left(a - 0.5\right) - t\right) + \log \color{blue}{z} \]
12. Add Preprocessing

Alternative 5: 42.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1:\\ \;\;\;\;\log z\\ \mathbf{else}:\\ \;\;\;\;\left(a - 0.5\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.0) (log z) (- (- a 0.5) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.0) {
		tmp = log(z);
	} else {
		tmp = (a - 0.5) - 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 <= 1.0d0) then
        tmp = log(z)
    else
        tmp = (a - 0.5d0) - 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 <= 1.0) {
		tmp = Math.log(z);
	} else {
		tmp = (a - 0.5) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.0:
		tmp = math.log(z)
	else:
		tmp = (a - 0.5) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.0)
		tmp = log(z);
	else
		tmp = Float64(Float64(a - 0.5) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.0)
		tmp = log(z);
	else
		tmp = (a - 0.5) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.0], N[Log[z], $MachinePrecision], N[(N[(a - 0.5), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1

   1. Initial program 99.3%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \left(x \cdot \left(\frac{-1}{2} \cdot \frac{x}{{y}^{2}} + \frac{1}{y}\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) - t} \]

   5. Applied rewrites 11.0%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \log z} \]

   6. Taylor expanded in x around 0

      \[\leadsto \log y + \color{blue}{\left(\log z + \frac{x}{y}\right)} \]

   8. Applied rewrites 8.9%

      \[\leadsto \log z \]

   if 1 < t

   1. Initial program 99.9%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \left(\log t \cdot \left(a - \frac{1}{2}\right) + \frac{x}{y}\right)\right)\right) - t} \]

   5. Applied rewrites 67.8%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - t} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(\log y + \log z\right) - t \]

   8. Applied rewrites 71.0%

      \[\leadsto \left(a - 0.5\right) - t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 39.6% accurate, 45.9× speedup

Math

\[\begin{array}{l} \\ \left(a - 0.5\right) - t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (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 = (a - 0.5d0) - t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (a - 0.5) - t;
}

Python

def code(x, y, z, t, a):
	return (a - 0.5) - t

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(\log y + \left(\log z + \left(\log t \cdot \left(a - \frac{1}{2}\right) + \frac{x}{y}\right)\right)\right) - t} \]

5. Applied rewrites 43.0%

   \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - t} \]

6. Taylor expanded in x around 0

   \[\leadsto \left(\log y + \log z\right) - t \]

8. Applied rewrites 41.1%

   \[\leadsto \left(a - 0.5\right) - t \]
9. Add Preprocessing

Alternative 7: 4.8% accurate, 80.3× speedup

Math

\[\begin{array}{l} \\ a - 0.5 \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return 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 = a - 0.5d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return a - 0.5;
}

Python

def code(x, y, z, t, a):
	return a - 0.5

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(\log y + \left(\log z + \left(x \cdot \left(\frac{-1}{2} \cdot \frac{x}{{y}^{2}} + \frac{1}{y}\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) - t} \]

5. Applied rewrites 6.3%

   \[\leadsto \color{blue}{\log \left(x + y\right) + \log z} \]

6. Taylor expanded in x around 0

   \[\leadsto \log y + \color{blue}{\log z} \]

8. Applied rewrites 5.6%

   \[\leadsto a - \color{blue}{0.5} \]
9. Add Preprocessing

Developer Target 1: 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 2024313 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (log (+ x y)) (+ (- (log z) t) (* (- a 1/2) (log t)))))

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