Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 8.6s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y \cdot \left(1 - \log y\right)\right) - \log y \cdot 0.5\right) - z \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (- (+ x (* y (- 1.0 (log y)))) (* (log y) 0.5)) z))

C

double code(double x, double y, double z) {
	return ((x + (y * (1.0 - log(y)))) - (log(y) * 0.5)) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x + (y * (1.0d0 - log(y)))) - (log(y) * 0.5d0)) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x + (y * (1.0 - Math.log(y)))) - (Math.log(y) * 0.5)) - z;
}

Python

def code(x, y, z):
	return ((x + (y * (1.0 - math.log(y)))) - (math.log(y) * 0.5)) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x + Float64(y * Float64(1.0 - log(y)))) - Float64(log(y) * 0.5)) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x + (y * (1.0 - log(y)))) - (log(y) * 0.5)) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

2. Taylor expanded in y around 0 99.9%

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

3. Final simplification 99.9%

   \[\leadsto \left(\left(x + y \cdot \left(1 - \log y\right)\right) - \log y \cdot 0.5\right) - z \]

Alternative 2: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate--l+ 99.9%

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

   2. sub-neg 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. *-commutative 99.9%

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

   6. distribute-rgt-neg-in 99.9%

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

   7. fma-def 99.9%

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

   8. neg-sub0 99.9%

      \[\leadsto \mathsf{fma}\left(\log y, \color{blue}{0 - \left(y + 0.5\right)}, x + \left(y - z\right)\right) \]

   9. +-commutative 99.9%

      \[\leadsto \mathsf{fma}\left(\log y, 0 - \color{blue}{\left(0.5 + y\right)}, x + \left(y - z\right)\right) \]

   10. associate--r+ 99.9%

       \[\leadsto \mathsf{fma}\left(\log y, \color{blue}{\left(0 - 0.5\right) - y}, x + \left(y - z\right)\right) \]

   11. metadata-eval 99.9%

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

   12. associate-+r- 99.9%

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

   13. +-commutative 99.9%

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

   14. associate-+r- 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right) - z\\ t_1 := y + \log y \cdot \left(-0.5 - y\right)\\ \mathbf{if}\;x \leq -16500000:\\ \;\;\;\;x - z\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-280}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* y (- 1.0 (log y))) z)) (t_1 (+ y (* (log y) (- -0.5 y)))))
   (if (<= x -16500000.0)
     (- x z)
     (if (<= x -1.55e-117)
       t_1
       (if (<= x -2.05e-197)
         t_0
         (if (<= x -5.8e-307)
           t_1
           (if (<= x 9e-280)
             t_0
             (if (<= x 8.5e-182) t_1 (if (<= x 2e+85) t_0 (- x z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * (1.0 - log(y))) - z;
	double t_1 = y + (log(y) * (-0.5 - y));
	double tmp;
	if (x <= -16500000.0) {
		tmp = x - z;
	} else if (x <= -1.55e-117) {
		tmp = t_1;
	} else if (x <= -2.05e-197) {
		tmp = t_0;
	} else if (x <= -5.8e-307) {
		tmp = t_1;
	} else if (x <= 9e-280) {
		tmp = t_0;
	} else if (x <= 8.5e-182) {
		tmp = t_1;
	} else if (x <= 2e+85) {
		tmp = t_0;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (y * (1.0d0 - log(y))) - z
    t_1 = y + (log(y) * ((-0.5d0) - y))
    if (x <= (-16500000.0d0)) then
        tmp = x - z
    else if (x <= (-1.55d-117)) then
        tmp = t_1
    else if (x <= (-2.05d-197)) then
        tmp = t_0
    else if (x <= (-5.8d-307)) then
        tmp = t_1
    else if (x <= 9d-280) then
        tmp = t_0
    else if (x <= 8.5d-182) then
        tmp = t_1
    else if (x <= 2d+85) then
        tmp = t_0
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * (1.0 - Math.log(y))) - z;
	double t_1 = y + (Math.log(y) * (-0.5 - y));
	double tmp;
	if (x <= -16500000.0) {
		tmp = x - z;
	} else if (x <= -1.55e-117) {
		tmp = t_1;
	} else if (x <= -2.05e-197) {
		tmp = t_0;
	} else if (x <= -5.8e-307) {
		tmp = t_1;
	} else if (x <= 9e-280) {
		tmp = t_0;
	} else if (x <= 8.5e-182) {
		tmp = t_1;
	} else if (x <= 2e+85) {
		tmp = t_0;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * (1.0 - math.log(y))) - z
	t_1 = y + (math.log(y) * (-0.5 - y))
	tmp = 0
	if x <= -16500000.0:
		tmp = x - z
	elif x <= -1.55e-117:
		tmp = t_1
	elif x <= -2.05e-197:
		tmp = t_0
	elif x <= -5.8e-307:
		tmp = t_1
	elif x <= 9e-280:
		tmp = t_0
	elif x <= 8.5e-182:
		tmp = t_1
	elif x <= 2e+85:
		tmp = t_0
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(1.0 - log(y))) - z)
	t_1 = Float64(y + Float64(log(y) * Float64(-0.5 - y)))
	tmp = 0.0
	if (x <= -16500000.0)
		tmp = Float64(x - z);
	elseif (x <= -1.55e-117)
		tmp = t_1;
	elseif (x <= -2.05e-197)
		tmp = t_0;
	elseif (x <= -5.8e-307)
		tmp = t_1;
	elseif (x <= 9e-280)
		tmp = t_0;
	elseif (x <= 8.5e-182)
		tmp = t_1;
	elseif (x <= 2e+85)
		tmp = t_0;
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * (1.0 - log(y))) - z;
	t_1 = y + (log(y) * (-0.5 - y));
	tmp = 0.0;
	if (x <= -16500000.0)
		tmp = x - z;
	elseif (x <= -1.55e-117)
		tmp = t_1;
	elseif (x <= -2.05e-197)
		tmp = t_0;
	elseif (x <= -5.8e-307)
		tmp = t_1;
	elseif (x <= 9e-280)
		tmp = t_0;
	elseif (x <= 8.5e-182)
		tmp = t_1;
	elseif (x <= 2e+85)
		tmp = t_0;
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$1 = N[(y + N[(N[Log[y], $MachinePrecision] * N[(-0.5 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -16500000.0], N[(x - z), $MachinePrecision], If[LessEqual[x, -1.55e-117], t$95$1, If[LessEqual[x, -2.05e-197], t$95$0, If[LessEqual[x, -5.8e-307], t$95$1, If[LessEqual[x, 9e-280], t$95$0, If[LessEqual[x, 8.5e-182], t$95$1, If[LessEqual[x, 2e+85], t$95$0, N[(x - z), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e7 or 2e85 < x

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in x around inf 88.7%

      \[\leadsto \color{blue}{x} - z \]

   if -1.65e7 < x < -1.55000000000000005e-117 or -2.05e-197 < x < -5.8000000000000001e-307 or 8.9999999999999991e-280 < x < 8.5000000000000001e-182

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. *-commutative 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. fma-def 99.8%

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

      8. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(\log y, \color{blue}{0 - \left(y + 0.5\right)}, x + \left(y - z\right)\right) \]

      9. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(\log y, 0 - \color{blue}{\left(0.5 + y\right)}, x + \left(y - z\right)\right) \]

      10. associate--r+ 99.8%

          \[\leadsto \mathsf{fma}\left(\log y, \color{blue}{\left(0 - 0.5\right) - y}, x + \left(y - z\right)\right) \]

      11. metadata-eval 99.8%

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

      12. associate-+r- 99.8%

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

      13. +-commutative 99.8%

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

      14. associate-+r- 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 80.6%

      \[\leadsto \mathsf{fma}\left(\log y, -0.5 - y, \color{blue}{y}\right) \]
   5. Step-by-step derivation

      1. fma-udef 80.5%

         \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   6. Applied egg-rr 80.5%

      \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   if -1.55000000000000005e-117 < x < -2.05e-197 or -5.8000000000000001e-307 < x < 8.9999999999999991e-280 or 8.5000000000000001e-182 < x < 2e85

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in y around inf 86.1%

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

      1. *-commutative 86.1%

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

      2. log-rec 86.1%

         \[\leadsto y \cdot \left(1 - \color{blue}{\left(-\log y\right)} \cdot -1\right) - z \]

      3. cancel-sign-sub 86.1%

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

      4. *-commutative 86.1%

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

      5. mul-1-neg 86.1%

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

      6. sub-neg 86.1%

         \[\leadsto y \cdot \color{blue}{\left(1 - \log y\right)} - z \]

   4. Simplified 86.1%

      \[\leadsto \color{blue}{y \cdot \left(1 - \log y\right)} - z \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16500000:\\ \;\;\;\;x - z\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-117}:\\ \;\;\;\;y + \log y \cdot \left(-0.5 - y\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-307}:\\ \;\;\;\;y + \log y \cdot \left(-0.5 - y\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-182}:\\ \;\;\;\;y + \log y \cdot \left(-0.5 - y\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]

Alternative 4: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -18500000:\\ \;\;\;\;x - z\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-164}:\\ \;\;\;\;y + \log y \cdot \left(-0.5 - y\right)\\ \mathbf{elif}\;x \leq 125:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -18500000.0)
   (- x z)
   (if (<= x 3e-164)
     (+ y (* (log y) (- -0.5 y)))
     (if (<= x 125.0) (- (* (log y) -0.5) z) (- x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -18500000.0) {
		tmp = x - z;
	} else if (x <= 3e-164) {
		tmp = y + (log(y) * (-0.5 - y));
	} else if (x <= 125.0) {
		tmp = (log(y) * -0.5) - z;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-18500000.0d0)) then
        tmp = x - z
    else if (x <= 3d-164) then
        tmp = y + (log(y) * ((-0.5d0) - y))
    else if (x <= 125.0d0) then
        tmp = (log(y) * (-0.5d0)) - z
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -18500000.0) {
		tmp = x - z;
	} else if (x <= 3e-164) {
		tmp = y + (Math.log(y) * (-0.5 - y));
	} else if (x <= 125.0) {
		tmp = (Math.log(y) * -0.5) - z;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -18500000.0:
		tmp = x - z
	elif x <= 3e-164:
		tmp = y + (math.log(y) * (-0.5 - y))
	elif x <= 125.0:
		tmp = (math.log(y) * -0.5) - z
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -18500000.0)
		tmp = Float64(x - z);
	elseif (x <= 3e-164)
		tmp = Float64(y + Float64(log(y) * Float64(-0.5 - y)));
	elseif (x <= 125.0)
		tmp = Float64(Float64(log(y) * -0.5) - z);
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -18500000.0)
		tmp = x - z;
	elseif (x <= 3e-164)
		tmp = y + (log(y) * (-0.5 - y));
	elseif (x <= 125.0)
		tmp = (log(y) * -0.5) - z;
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -18500000.0], N[(x - z), $MachinePrecision], If[LessEqual[x, 3e-164], N[(y + N[(N[Log[y], $MachinePrecision] * N[(-0.5 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 125.0], N[(N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision] - z), $MachinePrecision], N[(x - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85e7 or 125 < x

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in x around inf 87.0%

      \[\leadsto \color{blue}{x} - z \]

   if -1.85e7 < x < 3.0000000000000001e-164

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. fma-def 99.9%

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

      8. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(\log y, \color{blue}{0 - \left(y + 0.5\right)}, x + \left(y - z\right)\right) \]

      9. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(\log y, 0 - \color{blue}{\left(0.5 + y\right)}, x + \left(y - z\right)\right) \]

      10. associate--r+ 99.9%

          \[\leadsto \mathsf{fma}\left(\log y, \color{blue}{\left(0 - 0.5\right) - y}, x + \left(y - z\right)\right) \]

      11. metadata-eval 99.9%

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

      12. associate-+r- 99.9%

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

      13. +-commutative 99.9%

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

      14. associate-+r- 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 68.8%

      \[\leadsto \mathsf{fma}\left(\log y, -0.5 - y, \color{blue}{y}\right) \]
   5. Step-by-step derivation

      1. fma-udef 68.8%

         \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   6. Applied egg-rr 68.8%

      \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   if 3.0000000000000001e-164 < x < 125

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in y around 0 71.2%

      \[\leadsto \color{blue}{\left(x - 0.5 \cdot \log y\right)} - z \]

   3. Taylor expanded in x around 0 71.2%

      \[\leadsto \color{blue}{-0.5 \cdot \log y} - z \]
   4. Step-by-step derivation

      1. *-commutative 71.2%

         \[\leadsto \color{blue}{\log y \cdot -0.5} - z \]

   5. Simplified 71.2%

      \[\leadsto \color{blue}{\log y \cdot -0.5} - z \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -18500000:\\ \;\;\;\;x - z\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-164}:\\ \;\;\;\;y + \log y \cdot \left(-0.5 - y\right)\\ \mathbf{elif}\;x \leq 125:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]

Alternative 5: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.00315:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(x - y \cdot \log y\right)\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 0.00315)
   (- (- x (* (log y) 0.5)) z)
   (- (+ y (- x (* y (log y)))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.00315) {
		tmp = (x - (log(y) * 0.5)) - z;
	} else {
		tmp = (y + (x - (y * log(y)))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 0.00315d0) then
        tmp = (x - (log(y) * 0.5d0)) - z
    else
        tmp = (y + (x - (y * log(y)))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.00315) {
		tmp = (x - (Math.log(y) * 0.5)) - z;
	} else {
		tmp = (y + (x - (y * Math.log(y)))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 0.00315:
		tmp = (x - (math.log(y) * 0.5)) - z
	else:
		tmp = (y + (x - (y * math.log(y)))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 0.00315)
		tmp = Float64(Float64(x - Float64(log(y) * 0.5)) - z);
	else
		tmp = Float64(Float64(y + Float64(x - Float64(y * log(y)))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 0.00315)
		tmp = (x - (log(y) * 0.5)) - z;
	else
		tmp = (y + (x - (y * log(y)))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 0.00315], N[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(y + N[(x - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.00315

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in y around 0 99.0%

      \[\leadsto \color{blue}{\left(x - 0.5 \cdot \log y\right)} - z \]

   if 0.00315 < y

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in y around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. log-rec 99.8%

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

      4. remove-double-neg 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.00315:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(x - y \cdot \log y\right)\right) - z\\ \end{array} \]

Alternative 6: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

2. Final simplification 99.9%

   \[\leadsto \left(y + \left(x - \log y \cdot \left(y + 0.5\right)\right)\right) - z \]

Alternative 7: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -118 \lor \neg \left(x \leq 125\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -118.0) (not (<= x 125.0))) (- x z) (- (* (log y) -0.5) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -118.0) || !(x <= 125.0)) {
		tmp = x - z;
	} else {
		tmp = (log(y) * -0.5) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-118.0d0)) .or. (.not. (x <= 125.0d0))) then
        tmp = x - z
    else
        tmp = (log(y) * (-0.5d0)) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -118.0) || !(x <= 125.0)) {
		tmp = x - z;
	} else {
		tmp = (Math.log(y) * -0.5) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -118.0) or not (x <= 125.0):
		tmp = x - z
	else:
		tmp = (math.log(y) * -0.5) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -118.0) || !(x <= 125.0))
		tmp = Float64(x - z);
	else
		tmp = Float64(Float64(log(y) * -0.5) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -118.0) || ~((x <= 125.0)))
		tmp = x - z;
	else
		tmp = (log(y) * -0.5) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -118.0], N[Not[LessEqual[x, 125.0]], $MachinePrecision]], N[(x - z), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -118 or 125 < x

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in x around inf 86.4%

      \[\leadsto \color{blue}{x} - z \]

   if -118 < x < 125

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in y around 0 66.5%

      \[\leadsto \color{blue}{\left(x - 0.5 \cdot \log y\right)} - z \]

   3. Taylor expanded in x around 0 65.9%

      \[\leadsto \color{blue}{-0.5 \cdot \log y} - z \]
   4. Step-by-step derivation

      1. *-commutative 65.9%

         \[\leadsto \color{blue}{\log y \cdot -0.5} - z \]

   5. Simplified 65.9%

      \[\leadsto \color{blue}{\log y \cdot -0.5} - z \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -118 \lor \neg \left(x \leq 125\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \end{array} \]

Alternative 8: 90.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{+62}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.85e+62) (- (- x (* (log y) 0.5)) z) (- (* y (- 1.0 (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.85e+62) {
		tmp = (x - (log(y) * 0.5)) - z;
	} else {
		tmp = (y * (1.0 - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.85d+62) then
        tmp = (x - (log(y) * 0.5d0)) - z
    else
        tmp = (y * (1.0d0 - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.85e+62) {
		tmp = (x - (Math.log(y) * 0.5)) - z;
	} else {
		tmp = (y * (1.0 - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.85e+62:
		tmp = (x - (math.log(y) * 0.5)) - z
	else:
		tmp = (y * (1.0 - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.85e+62)
		tmp = Float64(Float64(x - Float64(log(y) * 0.5)) - z);
	else
		tmp = Float64(Float64(y * Float64(1.0 - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.85e+62)
		tmp = (x - (log(y) * 0.5)) - z;
	else
		tmp = (y * (1.0 - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.85e+62], N[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.85000000000000007e62

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in y around 0 94.8%

      \[\leadsto \color{blue}{\left(x - 0.5 \cdot \log y\right)} - z \]

   if 1.85000000000000007e62 < y

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in y around inf 80.5%

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

      1. *-commutative 80.5%

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

      2. log-rec 80.5%

         \[\leadsto y \cdot \left(1 - \color{blue}{\left(-\log y\right)} \cdot -1\right) - z \]

      3. cancel-sign-sub 80.5%

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

      4. *-commutative 80.5%

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

      5. mul-1-neg 80.5%

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

      6. sub-neg 80.5%

         \[\leadsto y \cdot \color{blue}{\left(1 - \log y\right)} - z \]

   4. Simplified 80.5%

      \[\leadsto \color{blue}{y \cdot \left(1 - \log y\right)} - z \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{+62}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \]

Alternative 9: 57.5% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x - z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x - z), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

2. Taylor expanded in x around inf 62.7%

   \[\leadsto \color{blue}{x} - z \]

3. Final simplification 62.7%

   \[\leadsto x - z \]

Alternative 10: 29.9% accurate, 55.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 99.9%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

2. Taylor expanded in z around inf 30.3%

   \[\leadsto \color{blue}{-1 \cdot z} \]
3. Step-by-step derivation

   1. neg-mul-1 30.3%

      \[\leadsto \color{blue}{-z} \]

4. Simplified 30.3%

   \[\leadsto \color{blue}{-z} \]

5. Final simplification 30.3%

   \[\leadsto -z \]

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

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

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