Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 10.8s

Alternatives: 11

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

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

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 + fma(log(y), Float64(-0.5 - y), Float64(y - z)))
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[Log[y], $MachinePrecision] * N[(-0.5 - y), $MachinePrecision] + N[(y - z), $MachinePrecision]), $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+ 99.9%

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

   4. *-commutative 99.9%

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

   5. distribute-rgt-neg-in 99.9%

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

   6. fma-def 99.9%

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

   7. +-commutative 99.9%

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

   8. distribute-neg-in 99.9%

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

   9. unsub-neg 99.9%

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

   10. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 87.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{+81} \lor \neg \left(y \leq 8 \cdot 10^{+100}\right) \land y \leq 4 \cdot 10^{+149}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 3e+81) (and (not (<= y 8e+100)) (<= y 4e+149)))
   (- x (+ z (* (log y) 0.5)))
   (+ x (* y (- 1.0 (log y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 3e+81) || (!(y <= 8e+100) && (y <= 4e+149))) {
		tmp = x - (z + (log(y) * 0.5));
	} else {
		tmp = x + (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 <= 3d+81) .or. (.not. (y <= 8d+100)) .and. (y <= 4d+149)) then
        tmp = x - (z + (log(y) * 0.5d0))
    else
        tmp = x + (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 <= 3e+81) || (!(y <= 8e+100) && (y <= 4e+149))) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else {
		tmp = x + (y * (1.0 - Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 3e+81) or (not (y <= 8e+100) and (y <= 4e+149)):
		tmp = x - (z + (math.log(y) * 0.5))
	else:
		tmp = x + (y * (1.0 - math.log(y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 3e+81) || (!(y <= 8e+100) && (y <= 4e+149)))
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - log(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= 3e+81) || (~((y <= 8e+100)) && (y <= 4e+149)))
		tmp = x - (z + (log(y) * 0.5));
	else
		tmp = x + (y * (1.0 - log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 3e+81], And[N[Not[LessEqual[y, 8e+100]], $MachinePrecision], LessEqual[y, 4e+149]]], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.99999999999999997e81 or 8.00000000000000013e100 < y < 4.0000000000000002e149

   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 94.6%

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

   if 2.99999999999999997e81 < y < 8.00000000000000013e100 or 4.0000000000000002e149 < 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%

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

      2. sub-neg 99.6%

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

      3. associate-+l+ 99.6%

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

      4. *-commutative 99.6%

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

      5. distribute-rgt-neg-in 99.6%

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

      6. fma-def 99.6%

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

      7. +-commutative 99.6%

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

      8. distribute-neg-in 99.6%

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

      9. unsub-neg 99.6%

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

      10. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. log-rec 87.5%

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

      2. sub-neg 87.5%

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

   6. Simplified 87.5%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{+81} \lor \neg \left(y \leq 8 \cdot 10^{+100}\right) \land y \leq 4 \cdot 10^{+149}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \]

Alternative 3: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 6.8 \cdot 10^{+41}\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -26000.0) (not (<= z 6.8e+41)))
   (- x z)
   (+ x (* y (- 1.0 (log y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -26000.0) || !(z <= 6.8e+41)) {
		tmp = x - z;
	} else {
		tmp = x + (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 ((z <= (-26000.0d0)) .or. (.not. (z <= 6.8d+41))) then
        tmp = x - z
    else
        tmp = x + (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 ((z <= -26000.0) || !(z <= 6.8e+41)) {
		tmp = x - z;
	} else {
		tmp = x + (y * (1.0 - Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -26000.0) or not (z <= 6.8e+41):
		tmp = x - z
	else:
		tmp = x + (y * (1.0 - math.log(y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -26000.0) || !(z <= 6.8e+41))
		tmp = Float64(x - z);
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - log(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -26000.0) || ~((z <= 6.8e+41)))
		tmp = x - z;
	else
		tmp = x + (y * (1.0 - log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -26000.0], N[Not[LessEqual[z, 6.8e+41]], $MachinePrecision]], N[(x - z), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -26000 or 6.79999999999999996e41 < z

   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%

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

   3. Taylor expanded in x around inf 85.0%

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

   if -26000 < z < 6.79999999999999996e41

   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. *-commutative 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. unsub-neg 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 68.0%

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

      1. log-rec 68.0%

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

      2. sub-neg 68.0%

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

   6. Simplified 68.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 6.8 \cdot 10^{+41}\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \]

Alternative 4: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+80}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - \log y \cdot \left(y + 0.5\right)\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.3e+80)
   (- x (+ z (* (log y) 0.5)))
   (- (- y (* (log y) (+ y 0.5))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.3e+80) {
		tmp = x - (z + (log(y) * 0.5));
	} else {
		tmp = (y - (log(y) * (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 (y <= 1.3d+80) then
        tmp = x - (z + (log(y) * 0.5d0))
    else
        tmp = (y - (log(y) * (y + 0.5d0))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.3e+80) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else {
		tmp = (y - (Math.log(y) * (y + 0.5))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.3e+80:
		tmp = x - (z + (math.log(y) * 0.5))
	else:
		tmp = (y - (math.log(y) * (y + 0.5))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.3e+80)
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	else
		tmp = Float64(Float64(y - Float64(log(y) * Float64(y + 0.5))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.3e+80)
		tmp = x - (z + (log(y) * 0.5));
	else
		tmp = (y - (log(y) * (y + 0.5))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.3e+80], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.29999999999999991e80

   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 97.7%

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

   if 1.29999999999999991e80 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 88.2%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+80}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - \log y \cdot \left(y + 0.5\right)\right) - z\\ \end{array} \]

Alternative 5: 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 99.8%

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

2. Final simplification 99.8%

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

Alternative 6: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7000 \lor \neg \left(x \leq 250\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7000.0) (not (<= x 250.0))) (- x z) (- (* (log y) -0.5) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7000.0) || !(x <= 250.0)) {
		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 <= (-7000.0d0)) .or. (.not. (x <= 250.0d0))) 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 <= -7000.0) || !(x <= 250.0)) {
		tmp = x - z;
	} else {
		tmp = (Math.log(y) * -0.5) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7000.0) or not (x <= 250.0):
		tmp = x - z
	else:
		tmp = (math.log(y) * -0.5) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7000.0) || !(x <= 250.0))
		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 <= -7000.0) || ~((x <= 250.0)))
		tmp = x - z;
	else
		tmp = (log(y) * -0.5) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7000.0], N[Not[LessEqual[x, 250.0]], $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 < -7e3 or 250 < x

   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 99.8%

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

   3. Taylor expanded in x around inf 74.8%

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

   if -7e3 < x < 250

   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 0 98.9%

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

   3. Taylor expanded in y around 0 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7000 \lor \neg \left(x \leq 250\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \end{array} \]

Alternative 7: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+80}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 4.6e+80) (- x (+ z (* (log y) 0.5))) (- (* y (- 1.0 (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.6e+80) {
		tmp = x - (z + (log(y) * 0.5));
	} 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 <= 4.6d+80) then
        tmp = x - (z + (log(y) * 0.5d0))
    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 <= 4.6e+80) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else {
		tmp = (y * (1.0 - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.6e+80:
		tmp = x - (z + (math.log(y) * 0.5))
	else:
		tmp = (y * (1.0 - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.6e+80)
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	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 <= 4.6e+80)
		tmp = x - (z + (log(y) * 0.5));
	else
		tmp = (y * (1.0 - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.6e+80], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $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 < 4.60000000000000008e80

   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 97.7%

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

   if 4.60000000000000008e80 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 88.2%

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

   3. Taylor expanded in y around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. log-rec 88.2%

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

      3. distribute-rgt-neg-out 88.2%

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

      4. remove-double-neg 88.2%

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

   5. Simplified 88.2%

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

      1. *-commutative 88.2%

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

      2. *-un-lft-identity 88.2%

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

      3. distribute-rgt-out-- 88.2%

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

      4. *-commutative 88.2%

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

   7. Applied egg-rr 88.2%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+80}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \]

Alternative 8: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+79}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 8e+79) (- x (+ z (* (log y) 0.5))) (- (- y (* y (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8e+79) {
		tmp = x - (z + (log(y) * 0.5));
	} 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 <= 8d+79) then
        tmp = x - (z + (log(y) * 0.5d0))
    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 <= 8e+79) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else {
		tmp = (y - (y * Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8e+79:
		tmp = x - (z + (math.log(y) * 0.5))
	else:
		tmp = (y - (y * math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8e+79)
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	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 <= 8e+79)
		tmp = x - (z + (log(y) * 0.5));
	else
		tmp = (y - (y * log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8e+79], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.99999999999999974e79

   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 97.7%

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

   if 7.99999999999999974e79 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 88.2%

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

   3. Taylor expanded in y around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. log-rec 88.2%

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

      3. distribute-rgt-neg-out 88.2%

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

      4. remove-double-neg 88.2%

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

   5. Simplified 88.2%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+79}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \end{array} \]

Alternative 9: 46.7% accurate, 18.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+120}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.5e+154) x (if (<= x 3.2e+120) (- z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.5e+154) {
		tmp = x;
	} else if (x <= 3.2e+120) {
		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 <= (-8.5d+154)) then
        tmp = x
    else if (x <= 3.2d+120) 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 <= -8.5e+154) {
		tmp = x;
	} else if (x <= 3.2e+120) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.5e+154:
		tmp = x
	elif x <= 3.2e+120:
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.5e+154)
		tmp = x;
	elseif (x <= 3.2e+120)
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.5e+154)
		tmp = x;
	elseif (x <= 3.2e+120)
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.5e+154], x, If[LessEqual[x, 3.2e+120], (-z), x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000002e154 or 3.19999999999999982e120 < 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%

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

      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. associate-+l+ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. distribute-neg-in 99.9%

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

      9. unsub-neg 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 73.3%

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

   if -8.5000000000000002e154 < x < 3.19999999999999982e120

   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 99.8%

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

   3. Taylor expanded in z around inf 42.6%

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

      1. neg-mul-1 42.6%

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

   5. Simplified 42.6%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+120}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 58.0% 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. Taylor expanded in y around 0 99.9%

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

3. Taylor expanded in x around inf 57.5%

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

4. Final simplification 57.5%

   \[\leadsto x - z \]

Alternative 11: 30.4% 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%

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

   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+ 99.9%

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

   4. *-commutative 99.9%

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

   5. distribute-rgt-neg-in 99.9%

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

   6. fma-def 99.9%

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

   7. +-commutative 99.9%

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

   8. distribute-neg-in 99.9%

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

   9. unsub-neg 99.9%

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

   10. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 25.7%

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

5. Final simplification 25.7%

   \[\leadsto x \]

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 2023320 
(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))