Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 13.4s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 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-def 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. Final simplification 99.9%

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

Alternative 3: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \log y \cdot 0.5\\ t_1 := \log y \cdot -0.5 - z\\ \mathbf{if}\;y \leq 2.3 \cdot 10^{-185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+36}:\\ \;\;\;\;\left(x + y\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (* (log y) 0.5))) (t_1 (- (* (log y) -0.5) z)))
   (if (<= y 2.3e-185)
     t_0
     (if (<= y 3.5e-156)
       t_1
       (if (<= y 7e-93)
         t_0
         (if (<= y 7.6e-82)
           t_1
           (if (<= y 1.25e+36) (- (+ x y) z) (- (* y (- 1.0 (log y))) z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x - (log(y) * 0.5);
	double t_1 = (log(y) * -0.5) - z;
	double tmp;
	if (y <= 2.3e-185) {
		tmp = t_0;
	} else if (y <= 3.5e-156) {
		tmp = t_1;
	} else if (y <= 7e-93) {
		tmp = t_0;
	} else if (y <= 7.6e-82) {
		tmp = t_1;
	} else if (y <= 1.25e+36) {
		tmp = (x + y) - z;
	} else {
		tmp = (y * (1.0 - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x - (log(y) * 0.5d0)
    t_1 = (log(y) * (-0.5d0)) - z
    if (y <= 2.3d-185) then
        tmp = t_0
    else if (y <= 3.5d-156) then
        tmp = t_1
    else if (y <= 7d-93) then
        tmp = t_0
    else if (y <= 7.6d-82) then
        tmp = t_1
    else if (y <= 1.25d+36) then
        tmp = (x + y) - z
    else
        tmp = (y * (1.0d0 - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x - (Math.log(y) * 0.5);
	double t_1 = (Math.log(y) * -0.5) - z;
	double tmp;
	if (y <= 2.3e-185) {
		tmp = t_0;
	} else if (y <= 3.5e-156) {
		tmp = t_1;
	} else if (y <= 7e-93) {
		tmp = t_0;
	} else if (y <= 7.6e-82) {
		tmp = t_1;
	} else if (y <= 1.25e+36) {
		tmp = (x + y) - z;
	} else {
		tmp = (y * (1.0 - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (math.log(y) * 0.5)
	t_1 = (math.log(y) * -0.5) - z
	tmp = 0
	if y <= 2.3e-185:
		tmp = t_0
	elif y <= 3.5e-156:
		tmp = t_1
	elif y <= 7e-93:
		tmp = t_0
	elif y <= 7.6e-82:
		tmp = t_1
	elif y <= 1.25e+36:
		tmp = (x + y) - z
	else:
		tmp = (y * (1.0 - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(log(y) * 0.5))
	t_1 = Float64(Float64(log(y) * -0.5) - z)
	tmp = 0.0
	if (y <= 2.3e-185)
		tmp = t_0;
	elseif (y <= 3.5e-156)
		tmp = t_1;
	elseif (y <= 7e-93)
		tmp = t_0;
	elseif (y <= 7.6e-82)
		tmp = t_1;
	elseif (y <= 1.25e+36)
		tmp = Float64(Float64(x + y) - z);
	else
		tmp = Float64(Float64(y * Float64(1.0 - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (log(y) * 0.5);
	t_1 = (log(y) * -0.5) - z;
	tmp = 0.0;
	if (y <= 2.3e-185)
		tmp = t_0;
	elseif (y <= 3.5e-156)
		tmp = t_1;
	elseif (y <= 7e-93)
		tmp = t_0;
	elseif (y <= 7.6e-82)
		tmp = t_1;
	elseif (y <= 1.25e+36)
		tmp = (x + y) - z;
	else
		tmp = (y * (1.0 - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 2.3e-185], t$95$0, If[LessEqual[y, 3.5e-156], t$95$1, If[LessEqual[y, 7e-93], t$95$0, If[LessEqual[y, 7.6e-82], t$95$1, If[LessEqual[y, 1.25e+36], N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision], N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 2.3000000000000001e-185 or 3.4999999999999999e-156 < y < 7e-93

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around 0 77.1%

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

   if 2.3000000000000001e-185 < y < 3.4999999999999999e-156 or 7e-93 < y < 7.60000000000000041e-82

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in x around 0 95.2%

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

      1. *-commutative 95.2%

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

   6. Simplified 95.2%

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

   if 7.60000000000000041e-82 < y < 1.24999999999999994e36

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.7%

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

      2. pow3 99.6%

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

      3. *-commutative 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around inf 81.7%

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

      1. +-commutative 81.7%

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

   7. Simplified 81.7%

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

   if 1.24999999999999994e36 < y

   1. Initial program 99.6%

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

      1. add-log-exp 6.0%

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

      2. *-commutative 6.0%

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

      3. exp-to-pow 6.0%

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

   4. Applied egg-rr 6.0%

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

      1. pow-to-exp 6.0%

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

      2. add-log-exp 99.6%

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

      3. flip-+ 54.7%

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

      4. associate-*r/ 54.6%

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

      5. fma-neg 54.6%

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

      6. metadata-eval 54.6%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, -\color{blue}{0.25}\right)}{y - 0.5}\right) + y\right) - z \]

      7. metadata-eval 54.6%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, \color{blue}{-0.25}\right)}{y - 0.5}\right) + y\right) - z \]

      8. sub-neg 54.6%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, -0.25\right)}{\color{blue}{y + \left(-0.5\right)}}\right) + y\right) - z \]

      9. metadata-eval 54.6%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, -0.25\right)}{y + \color{blue}{-0.5}}\right) + y\right) - z \]

   6. Applied egg-rr 54.6%

      \[\leadsto \left(\left(x - \color{blue}{\frac{\log y \cdot \mathsf{fma}\left(y, y, -0.25\right)}{y + -0.5}}\right) + y\right) - z \]
   7. Step-by-step derivation

      1. associate-/l* 54.7%

         \[\leadsto \left(\left(x - \color{blue}{\frac{\log y}{\frac{y + -0.5}{\mathsf{fma}\left(y, y, -0.25\right)}}}\right) + y\right) - z \]

   8. Simplified 54.7%

      \[\leadsto \left(\left(x - \color{blue}{\frac{\log y}{\frac{y + -0.5}{\mathsf{fma}\left(y, y, -0.25\right)}}}\right) + y\right) - z \]

   9. Taylor expanded in y around inf 86.6%

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

       1. neg-mul-1 86.6%

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

       2. log-rec 86.6%

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

       3. remove-double-neg 86.6%

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

   11. Simplified 86.6%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{-185}:\\ \;\;\;\;x - \log y \cdot 0.5\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-156}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-93}:\\ \;\;\;\;x - \log y \cdot 0.5\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-82}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+36}:\\ \;\;\;\;\left(x + y\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4400000000000 \lor \neg \left(z \leq 165\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x - \log y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4400000000000.0) (not (<= z 165.0)))
   (- x z)
   (- x (* (log y) 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4400000000000.0) || !(z <= 165.0)) {
		tmp = x - z;
	} else {
		tmp = x - (log(y) * 0.5);
	}
	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 <= (-4400000000000.0d0)) .or. (.not. (z <= 165.0d0))) then
        tmp = x - z
    else
        tmp = x - (log(y) * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4400000000000.0) || !(z <= 165.0)) {
		tmp = x - z;
	} else {
		tmp = x - (Math.log(y) * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4400000000000.0) or not (z <= 165.0):
		tmp = x - z
	else:
		tmp = x - (math.log(y) * 0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4400000000000.0) || !(z <= 165.0))
		tmp = Float64(x - z);
	else
		tmp = Float64(x - Float64(log(y) * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4400000000000.0) || ~((z <= 165.0)))
		tmp = x - z;
	else
		tmp = x - (log(y) * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4400000000000.0], N[Not[LessEqual[z, 165.0]], $MachinePrecision]], N[(x - z), $MachinePrecision], N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e12 or 165 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.7%

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

   if -4.4e12 < z < 165

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 67.1%

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

   4. Taylor expanded in z around 0 65.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4400000000000 \lor \neg \left(z \leq 165\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x - \log y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+20} \lor \neg \left(x \leq 7.5 \cdot 10^{-7}\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.5e+20) (not (<= x 7.5e-7))) (- x z) (- (* (log y) -0.5) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.5e+20) || !(x <= 7.5e-7)) {
		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 <= (-7.5d+20)) .or. (.not. (x <= 7.5d-7))) 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 <= -7.5e+20) || !(x <= 7.5e-7)) {
		tmp = x - z;
	} else {
		tmp = (Math.log(y) * -0.5) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.5e+20) or not (x <= 7.5e-7):
		tmp = x - z
	else:
		tmp = (math.log(y) * -0.5) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.5e+20) || !(x <= 7.5e-7))
		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 <= -7.5e+20) || ~((x <= 7.5e-7)))
		tmp = x - z;
	else
		tmp = (log(y) * -0.5) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.5e+20], N[Not[LessEqual[x, 7.5e-7]], $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 < -7.5e20 or 7.5000000000000002e-7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 80.1%

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

   if -7.5e20 < x < 7.5000000000000002e-7

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 65.2%

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

   4. Taylor expanded in x around 0 65.0%

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

      1. *-commutative 65.0%

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

   6. Simplified 65.0%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+20} \lor \neg \left(x \leq 7.5 \cdot 10^{-7}\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.28) {
		tmp = (x - (log(y) * 0.5)) - z;
	} 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 - (log(y) * 0.5d0)) - z
    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 - (Math.log(y) * 0.5)) - z;
	} 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 - (math.log(y) * 0.5)) - z
	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(Float64(x - Float64(log(y) * 0.5)) - z);
	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 - (log(y) * 0.5)) - z;
	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[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $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. Add Preprocessing

   3. Taylor expanded in y around 0 99.0%

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

   if 0.28000000000000003 < y

   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+ 99.6%

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

      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+ 99.7%

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

      4. associate-+r- 99.7%

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

      5. *-commutative 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. fma-def 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 99.3%

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

      1. log-rec 99.3%

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

      2. sub-neg 99.3%

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

   7. Simplified 99.3%

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

4. Final simplification 99.1%

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

Alternative 7: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.06 \cdot 10^{+36}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.06e+36) (- (- x (* (log y) 0.5)) z) (- (* y (- 1.0 (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.06e+36) {
		tmp = (x - (log(y) * 0.5)) - z;
	} else {
		tmp = (y * (1.0 - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.06d+36) then
        tmp = (x - (log(y) * 0.5d0)) - z
    else
        tmp = (y * (1.0d0 - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.06e+36) {
		tmp = (x - (Math.log(y) * 0.5)) - z;
	} else {
		tmp = (y * (1.0 - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.06e+36:
		tmp = (x - (math.log(y) * 0.5)) - z
	else:
		tmp = (y * (1.0 - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.06e+36)
		tmp = Float64(Float64(x - Float64(log(y) * 0.5)) - z);
	else
		tmp = Float64(Float64(y * Float64(1.0 - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.06e+36)
		tmp = (x - (log(y) * 0.5)) - z;
	else
		tmp = (y * (1.0 - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.06e+36], N[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.06000000000000002e36

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.8%

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

   if 1.06000000000000002e36 < y

   1. Initial program 99.6%

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

      1. add-log-exp 6.0%

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

      2. *-commutative 6.0%

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

      3. exp-to-pow 6.0%

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

   4. Applied egg-rr 6.0%

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

      1. pow-to-exp 6.0%

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

      2. add-log-exp 99.6%

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

      3. flip-+ 54.7%

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

      4. associate-*r/ 54.6%

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

      5. fma-neg 54.6%

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

      6. metadata-eval 54.6%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, -\color{blue}{0.25}\right)}{y - 0.5}\right) + y\right) - z \]

      7. metadata-eval 54.6%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, \color{blue}{-0.25}\right)}{y - 0.5}\right) + y\right) - z \]

      8. sub-neg 54.6%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, -0.25\right)}{\color{blue}{y + \left(-0.5\right)}}\right) + y\right) - z \]

      9. metadata-eval 54.6%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, -0.25\right)}{y + \color{blue}{-0.5}}\right) + y\right) - z \]

   6. Applied egg-rr 54.6%

      \[\leadsto \left(\left(x - \color{blue}{\frac{\log y \cdot \mathsf{fma}\left(y, y, -0.25\right)}{y + -0.5}}\right) + y\right) - z \]
   7. Step-by-step derivation

      1. associate-/l* 54.7%

         \[\leadsto \left(\left(x - \color{blue}{\frac{\log y}{\frac{y + -0.5}{\mathsf{fma}\left(y, y, -0.25\right)}}}\right) + y\right) - z \]

   8. Simplified 54.7%

      \[\leadsto \left(\left(x - \color{blue}{\frac{\log y}{\frac{y + -0.5}{\mathsf{fma}\left(y, y, -0.25\right)}}}\right) + y\right) - z \]

   9. Taylor expanded in y around inf 86.6%

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

       1. neg-mul-1 86.6%

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

       2. log-rec 86.6%

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

       3. remove-double-neg 86.6%

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

   11. Simplified 86.6%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.06 \cdot 10^{+36}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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. Add Preprocessing

3. Final simplification 99.8%

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

Alternative 9: 58.3% 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. Add Preprocessing

3. Taylor expanded in x around inf 55.6%

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

4. Final simplification 55.6%

   \[\leadsto x - z \]
5. Add Preprocessing

Alternative 10: 29.8% accurate, 55.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 99.9%

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

4. Taylor expanded in z around inf 29.8%

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

   1. neg-mul-1 29.8%

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

6. Simplified 29.8%

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

7. Final simplification 29.8%

   \[\leadsto -z \]
8. 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 2024018 
(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))