Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 10.5s

Alternatives: 11

Speedup: 0.5×

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. associate-+l+ 99.8%

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

   4. associate-+r- 99.8%

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

   5. *-commutative 99.8%

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

   6. distribute-rgt-neg-in 99.8%

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

   7. fma-define 99.9%

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

   8. +-commutative 99.9%

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

   9. distribute-neg-in 99.9%

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

   10. unsub-neg 99.9%

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

   11. metadata-eval 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ \mathbf{if}\;y \leq 4.5 \cdot 10^{+28}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+139} \lor \neg \left(y \leq 6.4 \cdot 10^{+208}\right) \land y \leq 1.6 \cdot 10^{+256}:\\ \;\;\;\;\left(x + y\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(y - t\_0\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))))
   (if (<= y 4.5e+28)
     (- x (+ z (* (log y) 0.5)))
     (if (or (<= y 2.25e+139) (and (not (<= y 6.4e+208)) (<= y 1.6e+256)))
       (- (+ x y) t_0)
       (- (- y t_0) z)))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double tmp;
	if (y <= 4.5e+28) {
		tmp = x - (z + (log(y) * 0.5));
	} else if ((y <= 2.25e+139) || (!(y <= 6.4e+208) && (y <= 1.6e+256))) {
		tmp = (x + y) - t_0;
	} else {
		tmp = (y - t_0) - 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) :: tmp
    t_0 = y * log(y)
    if (y <= 4.5d+28) then
        tmp = x - (z + (log(y) * 0.5d0))
    else if ((y <= 2.25d+139) .or. (.not. (y <= 6.4d+208)) .and. (y <= 1.6d+256)) then
        tmp = (x + y) - t_0
    else
        tmp = (y - t_0) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.log(y);
	double tmp;
	if (y <= 4.5e+28) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else if ((y <= 2.25e+139) || (!(y <= 6.4e+208) && (y <= 1.6e+256))) {
		tmp = (x + y) - t_0;
	} else {
		tmp = (y - t_0) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	tmp = 0
	if y <= 4.5e+28:
		tmp = x - (z + (math.log(y) * 0.5))
	elif (y <= 2.25e+139) or (not (y <= 6.4e+208) and (y <= 1.6e+256)):
		tmp = (x + y) - t_0
	else:
		tmp = (y - t_0) - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	tmp = 0.0
	if (y <= 4.5e+28)
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	elseif ((y <= 2.25e+139) || (!(y <= 6.4e+208) && (y <= 1.6e+256)))
		tmp = Float64(Float64(x + y) - t_0);
	else
		tmp = Float64(Float64(y - t_0) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * log(y);
	tmp = 0.0;
	if (y <= 4.5e+28)
		tmp = x - (z + (log(y) * 0.5));
	elseif ((y <= 2.25e+139) || (~((y <= 6.4e+208)) && (y <= 1.6e+256)))
		tmp = (x + y) - t_0;
	else
		tmp = (y - t_0) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 4.5e+28], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.25e+139], And[N[Not[LessEqual[y, 6.4e+208]], $MachinePrecision], LessEqual[y, 1.6e+256]]], N[(N[(x + y), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(y - t$95$0), $MachinePrecision] - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 4.4999999999999997e28

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.5%

      \[\leadsto \color{blue}{x - \left(z + 0.5 \cdot \log y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   if 4.4999999999999997e28 < y < 2.25e139 or 6.4000000000000002e208 < y < 1.59999999999999998e256

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. distribute-rgt-neg-in 99.6%

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

      3. log-rec 99.6%

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

      4. remove-double-neg 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0 83.8%

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

      1. +-commutative 83.8%

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

   10. Simplified 83.8%

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

   if 2.25e139 < y < 6.4000000000000002e208 or 1.59999999999999998e256 < y

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 97.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}\right) \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}} \]

      2. pow3 97.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}\right)}^{3}} \]

   6. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\mathsf{fma}\left(\log y, -0.5 - y, y\right) - z\right)}\right)}^{3}} \]

   7. Taylor expanded in x around 0 94.4%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)\right) - z} \]
   8. Step-by-step derivation

      1. associate-*r* 94.4%

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

      2. neg-mul-1 94.4%

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

      3. +-commutative 94.4%

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

      4. cancel-sign-sub-inv 94.4%

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

   9. Simplified 94.4%

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

   10. Taylor expanded in y around inf 94.4%

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

       1. mul-1-neg 94.4%

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

       2. distribute-rgt-neg-in 94.4%

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

       3. log-rec 94.4%

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

       4. remove-double-neg 94.4%

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

   12. Simplified 94.4%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{+28}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+139} \lor \neg \left(y \leq 6.4 \cdot 10^{+208}\right) \land y \leq 1.6 \cdot 10^{+256}:\\ \;\;\;\;\left(x + y\right) - y \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+31}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+140} \lor \neg \left(y \leq 5 \cdot 10^{+208}\right):\\ \;\;\;\;y \cdot \left(1 + \left(\frac{x}{y} - \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.6e+31)
   (- x (+ z (* (log y) 0.5)))
   (if (or (<= y 1.4e+140) (not (<= y 5e+208)))
     (* y (+ 1.0 (- (/ x y) (log y))))
     (- (- y (* y (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.6e+31) {
		tmp = x - (z + (log(y) * 0.5));
	} else if ((y <= 1.4e+140) || !(y <= 5e+208)) {
		tmp = y * (1.0 + ((x / y) - log(y)));
	} else {
		tmp = (y - (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 <= 2.6d+31) then
        tmp = x - (z + (log(y) * 0.5d0))
    else if ((y <= 1.4d+140) .or. (.not. (y <= 5d+208))) then
        tmp = y * (1.0d0 + ((x / y) - log(y)))
    else
        tmp = (y - (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 <= 2.6e+31) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else if ((y <= 1.4e+140) || !(y <= 5e+208)) {
		tmp = y * (1.0 + ((x / y) - Math.log(y)));
	} else {
		tmp = (y - (y * Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.6e+31:
		tmp = x - (z + (math.log(y) * 0.5))
	elif (y <= 1.4e+140) or not (y <= 5e+208):
		tmp = y * (1.0 + ((x / y) - math.log(y)))
	else:
		tmp = (y - (y * math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.6e+31)
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	elseif ((y <= 1.4e+140) || !(y <= 5e+208))
		tmp = Float64(y * Float64(1.0 + Float64(Float64(x / y) - log(y))));
	else
		tmp = Float64(Float64(y - Float64(y * log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.6e+31)
		tmp = x - (z + (log(y) * 0.5));
	elseif ((y <= 1.4e+140) || ~((y <= 5e+208)))
		tmp = y * (1.0 + ((x / y) - log(y)));
	else
		tmp = (y - (y * log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.6e+31], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.4e+140], N[Not[LessEqual[y, 5e+208]], $MachinePrecision]], N[(y * N[(1.0 + N[(N[(x / y), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.6e31

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.5%

      \[\leadsto \color{blue}{x - \left(z + 0.5 \cdot \log y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   if 2.6e31 < y < 1.39999999999999991e140 or 5.0000000000000004e208 < y

   1. Initial program 99.5%

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

      1. associate--l+ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 99.7%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \left(-1 \cdot \log \left(\frac{1}{y}\right) + \left(-0.5 \cdot \frac{\log \left(\frac{1}{y}\right)}{y} + \frac{z}{y}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. mul-1-neg 99.7%

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

      4. log-rec 99.7%

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

      5. remove-double-neg 99.7%

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

      6. associate-+l+ 99.7%

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

      7. associate-*r/ 99.7%

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

      8. log-rec 99.7%

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

      9. mul-1-neg 99.7%

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

      10. associate-*r* 99.7%

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

      11. metadata-eval 99.7%

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

      12. *-lft-identity 99.7%

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

      13. times-frac 99.7%

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

      14. metadata-eval 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. log-rec 87.1%

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

      3. remove-double-neg 87.1%

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

   10. Simplified 87.1%

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

   if 1.39999999999999991e140 < y < 5.0000000000000004e208

   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%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 97.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}\right) \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}} \]

      2. pow3 98.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}\right)}^{3}} \]

   6. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\mathsf{fma}\left(\log y, -0.5 - y, y\right) - z\right)}\right)}^{3}} \]

   7. Taylor expanded in x around 0 92.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)\right) - z} \]
   8. Step-by-step derivation

      1. associate-*r* 92.0%

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

      2. neg-mul-1 92.0%

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

      3. +-commutative 92.0%

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

      4. cancel-sign-sub-inv 92.0%

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

   9. Simplified 92.0%

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

   10. Taylor expanded in y around inf 92.0%

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

       1. mul-1-neg 92.0%

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

       2. distribute-rgt-neg-in 92.0%

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

       3. log-rec 92.0%

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

       4. remove-double-neg 92.0%

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

   12. Simplified 92.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+31}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+140} \lor \neg \left(y \leq 5 \cdot 10^{+208}\right):\\ \;\;\;\;y \cdot \left(1 + \left(\frac{x}{y} - \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{+83} \lor \neg \left(y \leq 3.1 \cdot 10^{+187}\right) \land y \leq 1.15 \cdot 10^{+194}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 3.5e+83) (and (not (<= y 3.1e+187)) (<= y 1.15e+194)))
   (- x (+ z (* (log y) 0.5)))
   (* y (- 1.0 (log y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 3.5e+83) || (!(y <= 3.1e+187) && (y <= 1.15e+194))) {
		tmp = x - (z + (log(y) * 0.5));
	} else {
		tmp = y * (1.0 - log(y));
	}
	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 <= 3.5d+83) .or. (.not. (y <= 3.1d+187)) .and. (y <= 1.15d+194)) then
        tmp = x - (z + (log(y) * 0.5d0))
    else
        tmp = y * (1.0d0 - log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= 3.5e+83) || (!(y <= 3.1e+187) && (y <= 1.15e+194))) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else {
		tmp = y * (1.0 - Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 3.5e+83) or (not (y <= 3.1e+187) and (y <= 1.15e+194)):
		tmp = x - (z + (math.log(y) * 0.5))
	else:
		tmp = y * (1.0 - math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 3.5e+83) || (!(y <= 3.1e+187) && (y <= 1.15e+194)))
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	else
		tmp = Float64(y * Float64(1.0 - log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= 3.5e+83) || (~((y <= 3.1e+187)) && (y <= 1.15e+194)))
		tmp = x - (z + (log(y) * 0.5));
	else
		tmp = y * (1.0 - log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 3.5e+83], And[N[Not[LessEqual[y, 3.1e+187]], $MachinePrecision], LessEqual[y, 1.15e+194]]], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.49999999999999977e83 or 3.10000000000000012e187 < y < 1.15000000000000003e194

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 95.0%

      \[\leadsto \color{blue}{x - \left(z + 0.5 \cdot \log y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 95.0%

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

   7. Simplified 95.0%

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

   if 3.49999999999999977e83 < y < 3.10000000000000012e187 or 1.15000000000000003e194 < y

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 97.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}\right) \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}} \]

      2. pow3 97.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}\right)}^{3}} \]

   6. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\mathsf{fma}\left(\log y, -0.5 - y, y\right) - z\right)}\right)}^{3}} \]

   7. Taylor expanded in y around inf 73.4%

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

      1. log-rec 73.4%

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

      2. sub-neg 73.4%

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

   9. Simplified 73.4%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{+83} \lor \neg \left(y \leq 3.1 \cdot 10^{+187}\right) \land y \leq 1.15 \cdot 10^{+194}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.25 \cdot 10^{+83} \lor \neg \left(y \leq 3.1 \cdot 10^{+187}\right) \land y \leq 1.2 \cdot 10^{+194}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 4.25e+83) (and (not (<= y 3.1e+187)) (<= y 1.2e+194)))
   (- x z)
   (* y (- 1.0 (log y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 4.25e+83) || (!(y <= 3.1e+187) && (y <= 1.2e+194))) {
		tmp = x - z;
	} else {
		tmp = y * (1.0 - log(y));
	}
	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 <= 4.25d+83) .or. (.not. (y <= 3.1d+187)) .and. (y <= 1.2d+194)) then
        tmp = x - z
    else
        tmp = y * (1.0d0 - log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= 4.25e+83) || (!(y <= 3.1e+187) && (y <= 1.2e+194))) {
		tmp = x - z;
	} else {
		tmp = y * (1.0 - Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 4.25e+83) or (not (y <= 3.1e+187) and (y <= 1.2e+194)):
		tmp = x - z
	else:
		tmp = y * (1.0 - math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 4.25e+83) || (!(y <= 3.1e+187) && (y <= 1.2e+194)))
		tmp = Float64(x - z);
	else
		tmp = Float64(y * Float64(1.0 - log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= 4.25e+83) || (~((y <= 3.1e+187)) && (y <= 1.2e+194)))
		tmp = x - z;
	else
		tmp = y * (1.0 - log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 4.25e+83], And[N[Not[LessEqual[y, 3.1e+187]], $MachinePrecision], LessEqual[y, 1.2e+194]]], N[(x - z), $MachinePrecision], N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.2499999999999998e83 or 3.10000000000000012e187 < y < 1.2e194

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. distribute-rgt-neg-in 80.0%

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

      3. log-rec 80.0%

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

      4. remove-double-neg 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in y around 0 75.1%

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

   if 4.2499999999999998e83 < y < 3.10000000000000012e187 or 1.2e194 < y

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 97.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}\right) \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}} \]

      2. pow3 97.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}\right)}^{3}} \]

   6. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\mathsf{fma}\left(\log y, -0.5 - y, y\right) - z\right)}\right)}^{3}} \]

   7. Taylor expanded in y around inf 73.4%

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

      1. log-rec 73.4%

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

      2. sub-neg 73.4%

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

   9. Simplified 73.4%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.25 \cdot 10^{+83} \lor \neg \left(y \leq 3.1 \cdot 10^{+187}\right) \land y \leq 1.2 \cdot 10^{+194}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.28:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(1 - \log y\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 0.28)
   (- x (+ z (* (log y) 0.5)))
   (+ x (- (* y (- 1.0 (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.28) {
		tmp = x - (z + (log(y) * 0.5));
	} else {
		tmp = x + ((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 <= 0.28d0) then
        tmp = x - (z + (log(y) * 0.5d0))
    else
        tmp = x + ((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 <= 0.28) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else {
		tmp = x + ((y * (1.0 - Math.log(y))) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 0.28:
		tmp = x - (z + (math.log(y) * 0.5))
	else:
		tmp = x + ((y * (1.0 - math.log(y))) - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 0.28)
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	else
		tmp = Float64(x + 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 <= 0.28)
		tmp = x - (z + (log(y) * 0.5));
	else
		tmp = x + ((y * (1.0 - log(y))) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 0.28], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.28000000000000003

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.4%

      \[\leadsto \color{blue}{x - \left(z + 0.5 \cdot \log y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 99.4%

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

   7. Simplified 99.4%

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

   if 0.28000000000000003 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   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. associate-+l+ 99.7%

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

      4. associate-+r- 99.6%

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

      5. *-commutative 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. fma-define 99.7%

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

      8. +-commutative 99.7%

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

      9. distribute-neg-in 99.7%

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

      10. unsub-neg 99.7%

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

      11. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 99.7%

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

      1. log-rec 99.7%

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

      2. sub-neg 99.7%

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

   7. Simplified 99.7%

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

Alternative 7: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 4.6e+33) (- x (+ z (* (log y) 0.5))) (- (+ x y) (* y (log y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.6e+33) {
		tmp = x - (z + (log(y) * 0.5));
	} else {
		tmp = (x + y) - (y * log(y));
	}
	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 <= 4.6d+33) then
        tmp = x - (z + (log(y) * 0.5d0))
    else
        tmp = (x + y) - (y * log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.6e+33) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else {
		tmp = (x + y) - (y * Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.6e+33:
		tmp = x - (z + (math.log(y) * 0.5))
	else:
		tmp = (x + y) - (y * math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.6e+33)
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	else
		tmp = Float64(Float64(x + y) - Float64(y * log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.6e+33)
		tmp = x - (z + (log(y) * 0.5));
	else
		tmp = (x + y) - (y * log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.6e+33], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.60000000000000021e33

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.5%

      \[\leadsto \color{blue}{x - \left(z + 0.5 \cdot \log y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   if 4.60000000000000021e33 < y

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. distribute-rgt-neg-in 99.6%

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

      3. log-rec 99.6%

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

      4. remove-double-neg 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0 82.1%

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

      1. +-commutative 82.1%

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

   10. Simplified 82.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 9: 47.7% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+103}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.2e+26) x (if (<= x 3.6e+103) (- z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.2e+26) {
		tmp = x;
	} else if (x <= 3.6e+103) {
		tmp = -z;
	} else {
		tmp = x;
	}
	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 <= (-9.2d+26)) then
        tmp = x
    else if (x <= 3.6d+103) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.2e+26) {
		tmp = x;
	} else if (x <= 3.6e+103) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.2e+26:
		tmp = x
	elif x <= 3.6e+103:
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.2e+26)
		tmp = x;
	elseif (x <= 3.6e+103)
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.2e+26)
		tmp = x;
	elseif (x <= 3.6e+103)
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.2e+26], x, If[LessEqual[x, 3.6e+103], (-z), x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.2000000000000002e26 or 3.60000000000000017e103 < x

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 66.1%

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

   if -9.2000000000000002e26 < x < 3.60000000000000017e103

   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%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 97.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}\right) \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}} \]

      2. pow3 98.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)}\right)}^{3}} \]

   6. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\mathsf{fma}\left(\log y, -0.5 - y, y\right) - z\right)}\right)}^{3}} \]

   7. Taylor expanded in z around inf 37.2%

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

      1. neg-mul-1 37.2%

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

   9. Simplified 37.2%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 57.2% 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 99.8%

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

   1. associate--l+ 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 87.7%

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

   1. mul-1-neg 87.7%

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

   2. distribute-rgt-neg-in 87.7%

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

   3. log-rec 87.7%

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

   4. remove-double-neg 87.7%

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

7. Simplified 87.7%

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

8. Taylor expanded in y around 0 56.2%

   \[\leadsto \color{blue}{x - z} \]
9. Add Preprocessing

Alternative 11: 29.5% accurate, 111.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

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%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around inf 29.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

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 2024093 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

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

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