Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 17.9s

Alternatives: 15

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 99.6%

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

Alternative 2: 92.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\log \left(y + x\right) + \log z\right) - t\right) - \left(0.5 - a\right) \cdot \log t\\ \mathbf{if}\;t\_1 \leq -50000000000:\\ \;\;\;\;\left(-t\right) - \frac{\log t}{\frac{-1}{a - 0.5}}\\ \mathbf{elif}\;t\_1 \leq 850:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, \log t, \log \left(z \cdot \left(y + x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, \log t, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (- (+ (log (+ y x)) (log z)) t) (* (- 0.5 a) (log t)))))
   (if (<= t_1 -50000000000.0)
     (- (- t) (/ (log t) (/ -1.0 (- a 0.5))))
     (if (<= t_1 850.0)
       (fma (- a 0.5) (log t) (log (* z (+ y x))))
       (fma (- a 0.5) (log t) (- t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((log((y + x)) + log(z)) - t) - ((0.5 - a) * log(t));
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = -t - (log(t) / (-1.0 / (a - 0.5)));
	} else if (t_1 <= 850.0) {
		tmp = fma((a - 0.5), log(t), log((z * (y + x))));
	} else {
		tmp = fma((a - 0.5), log(t), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(log(Float64(y + x)) + log(z)) - t) - Float64(Float64(0.5 - a) * log(t)))
	tmp = 0.0
	if (t_1 <= -50000000000.0)
		tmp = Float64(Float64(-t) - Float64(log(t) / Float64(-1.0 / Float64(a - 0.5))));
	elseif (t_1 <= 850.0)
		tmp = fma(Float64(a - 0.5), log(t), log(Float64(z * Float64(y + x))));
	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[(N[(N[Log[N[(y + x), $MachinePrecision]], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000.0], N[((-t) - N[(N[Log[t], $MachinePrecision] / N[(-1.0 / N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 850.0], N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + N[Log[N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a #s(literal 1/2 binary64)) (log.f64 t))) < -5e10

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. flip3-- N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. lower-/.f64 N/A

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 99.8

          \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \frac{\log t}{\color{blue}{\frac{1}{a - 0.5}}} \]

   4. Applied rewrites 99.8%

      \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\frac{\log t}{\frac{1}{a - 0.5}}} \]

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot t} + \frac{\log t}{\frac{1}{a - \frac{1}{2}}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} + \frac{\log t}{\frac{1}{a - \frac{1}{2}}} \]

      2. lower-neg.f64 99.4

         \[\leadsto \color{blue}{\left(-t\right)} + \frac{\log t}{\frac{1}{a - 0.5}} \]

   7. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\left(-t\right)} + \frac{\log t}{\frac{1}{a - 0.5}} \]

   if -5e10 < (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a #s(literal 1/2 binary64)) (log.f64 t))) < 850

   1. Initial program 98.9%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

   4. Applied rewrites 92.5%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(\log t, a - 0.5, \log \left(z \cdot \left(y + x\right)\right) - t\right)}}} \]

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 89.0

         \[\leadsto \mathsf{fma}\left(a - 0.5, \log t, \log \left(\color{blue}{\left(x + y\right)} \cdot z\right)\right) \]

   7. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a - 0.5, \log t, \log \left(\left(x + y\right) \cdot z\right)\right)} \]

   if 850 < (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a #s(literal 1/2 binary64)) (log.f64 t)))

   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

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - \frac{1}{2}\right)\right)\right) - t} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. associate-+r- N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. associate-+r- N/A

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

      11. +-commutative N/A

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

      12. lower--.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 N/A

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

      15. lower-log.f64 N/A

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

      16. lower-log.f64 70.0

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

   5. Applied rewrites 70.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, -1 \cdot t\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 79.1%

      \[\leadsto \mathsf{fma}\left(a - 0.5, \log t, -t\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\log \left(y + x\right) + \log z\right) - t\right) - \left(0.5 - a\right) \cdot \log t \leq -50000000000:\\ \;\;\;\;\left(-t\right) - \frac{\log t}{\frac{-1}{a - 0.5}}\\ \mathbf{elif}\;\left(\left(\log \left(y + x\right) + \log z\right) - t\right) - \left(0.5 - a\right) \cdot \log t \leq 850:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, \log t, \log \left(z \cdot \left(y + x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, \log t, -t\right)\\ \end{array} \]
5. 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 2024230 
(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))))