Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 8.4s

Alternatives: 12

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-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 3: 89.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right) - z\\ t_1 := \left(x - \log y \cdot 0.5\right) - z\\ \mathbf{if}\;y \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+151}:\\ \;\;\;\;x + \left(y - y \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* y (- 1.0 (log y))) z)) (t_1 (- (- x (* (log y) 0.5)) z)))
   (if (<= y 6.8e+43)
     t_1
     (if (<= y 1.05e+81)
       t_0
       (if (<= y 4.6e+115)
         t_1
         (if (<= y 1.4e+151) (+ x (- y (* y (log y)))) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * (1.0 - log(y))) - z;
	double t_1 = (x - (log(y) * 0.5)) - z;
	double tmp;
	if (y <= 6.8e+43) {
		tmp = t_1;
	} else if (y <= 1.05e+81) {
		tmp = t_0;
	} else if (y <= 4.6e+115) {
		tmp = t_1;
	} else if (y <= 1.4e+151) {
		tmp = x + (y - (y * log(y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (y * (1.0d0 - log(y))) - z
    t_1 = (x - (log(y) * 0.5d0)) - z
    if (y <= 6.8d+43) then
        tmp = t_1
    else if (y <= 1.05d+81) then
        tmp = t_0
    else if (y <= 4.6d+115) then
        tmp = t_1
    else if (y <= 1.4d+151) then
        tmp = x + (y - (y * log(y)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * (1.0 - Math.log(y))) - z;
	double t_1 = (x - (Math.log(y) * 0.5)) - z;
	double tmp;
	if (y <= 6.8e+43) {
		tmp = t_1;
	} else if (y <= 1.05e+81) {
		tmp = t_0;
	} else if (y <= 4.6e+115) {
		tmp = t_1;
	} else if (y <= 1.4e+151) {
		tmp = x + (y - (y * Math.log(y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * (1.0 - math.log(y))) - z
	t_1 = (x - (math.log(y) * 0.5)) - z
	tmp = 0
	if y <= 6.8e+43:
		tmp = t_1
	elif y <= 1.05e+81:
		tmp = t_0
	elif y <= 4.6e+115:
		tmp = t_1
	elif y <= 1.4e+151:
		tmp = x + (y - (y * math.log(y)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(1.0 - log(y))) - z)
	t_1 = Float64(Float64(x - Float64(log(y) * 0.5)) - z)
	tmp = 0.0
	if (y <= 6.8e+43)
		tmp = t_1;
	elseif (y <= 1.05e+81)
		tmp = t_0;
	elseif (y <= 4.6e+115)
		tmp = t_1;
	elseif (y <= 1.4e+151)
		tmp = Float64(x + Float64(y - Float64(y * log(y))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * (1.0 - log(y))) - z;
	t_1 = (x - (log(y) * 0.5)) - z;
	tmp = 0.0;
	if (y <= 6.8e+43)
		tmp = t_1;
	elseif (y <= 1.05e+81)
		tmp = t_0;
	elseif (y <= 4.6e+115)
		tmp = t_1;
	elseif (y <= 1.4e+151)
		tmp = x + (y - (y * log(y)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 6.8e+43], t$95$1, If[LessEqual[y, 1.05e+81], t$95$0, If[LessEqual[y, 4.6e+115], t$95$1, If[LessEqual[y, 1.4e+151], N[(x + N[(y - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.80000000000000024e43 or 1.0499999999999999e81 < y < 4.60000000000000007e115

   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 95.5%

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

   if 6.80000000000000024e43 < y < 1.0499999999999999e81 or 1.39999999999999994e151 < 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. Taylor expanded in y around 0 99.8%

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

   4. Taylor expanded in x around 0 88.1%

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

   5. Taylor expanded in y around inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. log-rec 88.1%

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

      3. remove-double-neg 88.1%

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

   7. Simplified 88.1%

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

   if 4.60000000000000007e115 < y < 1.39999999999999994e151

   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%

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

      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- 99.6%

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

      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 99.6%

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

      8. +-commutative 99.6%

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

      9. distribute-neg-in 99.6%

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

      10. unsub-neg 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 83.5%

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

   6. Taylor expanded in z around 0 87.7%

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

      1. mul-1-neg 87.7%

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

      2. sub-neg 87.7%

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

      3. +-commutative 87.7%

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

   8. Simplified 87.7%

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

   9. Taylor expanded in y around inf 87.7%

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

       1. mul-1-neg 87.7%

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

       2. log-rec 87.7%

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

       3. distribute-rgt-neg-in 87.7%

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

       4. remove-double-neg 87.7%

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

   11. Simplified 87.7%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+81}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+115}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+151}:\\ \;\;\;\;x + \left(y - y \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+107}:\\ \;\;\;\;t\_0 - z\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-223}:\\ \;\;\;\;x + t\_0\\ \mathbf{elif}\;z \leq 245:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (log y)))))
   (if (<= z -2.4e+107)
     (- t_0 z)
     (if (<= z -2.05e-223)
       (+ x t_0)
       (if (<= z 245.0) (+ x (* (log y) -0.5)) (- x z))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - log(y));
	double tmp;
	if (z <= -2.4e+107) {
		tmp = t_0 - z;
	} else if (z <= -2.05e-223) {
		tmp = x + t_0;
	} else if (z <= 245.0) {
		tmp = x + (log(y) * -0.5);
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - log(y))
    if (z <= (-2.4d+107)) then
        tmp = t_0 - z
    else if (z <= (-2.05d-223)) then
        tmp = x + t_0
    else if (z <= 245.0d0) then
        tmp = x + (log(y) * (-0.5d0))
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - Math.log(y));
	double tmp;
	if (z <= -2.4e+107) {
		tmp = t_0 - z;
	} else if (z <= -2.05e-223) {
		tmp = x + t_0;
	} else if (z <= 245.0) {
		tmp = x + (Math.log(y) * -0.5);
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - math.log(y))
	tmp = 0
	if z <= -2.4e+107:
		tmp = t_0 - z
	elif z <= -2.05e-223:
		tmp = x + t_0
	elif z <= 245.0:
		tmp = x + (math.log(y) * -0.5)
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - log(y)))
	tmp = 0.0
	if (z <= -2.4e+107)
		tmp = Float64(t_0 - z);
	elseif (z <= -2.05e-223)
		tmp = Float64(x + t_0);
	elseif (z <= 245.0)
		tmp = Float64(x + Float64(log(y) * -0.5));
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - log(y));
	tmp = 0.0;
	if (z <= -2.4e+107)
		tmp = t_0 - z;
	elseif (z <= -2.05e-223)
		tmp = x + t_0;
	elseif (z <= 245.0)
		tmp = x + (log(y) * -0.5);
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+107], N[(t$95$0 - z), $MachinePrecision], If[LessEqual[z, -2.05e-223], N[(x + t$95$0), $MachinePrecision], If[LessEqual[z, 245.0], N[(x + N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], N[(x - z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4000000000000001e107

   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 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 x around 0 92.9%

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

   5. Taylor expanded in y around inf 92.9%

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

      1. mul-1-neg 92.9%

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

      2. log-rec 92.9%

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

      3. remove-double-neg 92.9%

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

   7. Simplified 92.9%

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

   if -2.4000000000000001e107 < z < -2.05000000000000007e-223

   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. Taylor expanded in z around inf 80.6%

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

   6. Taylor expanded in z around 0 96.9%

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

      1. mul-1-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. +-commutative 96.9%

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

   8. Simplified 96.9%

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

   9. Taylor expanded in y around inf 79.7%

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

       1. mul-1-neg 79.7%

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

       2. log-rec 79.7%

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

       3. remove-double-neg 79.7%

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

   11. Simplified 79.7%

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

   if -2.05000000000000007e-223 < z < 245

   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 99.8%

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

      8. +-commutative 99.8%

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

      9. distribute-neg-in 99.8%

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

      10. unsub-neg 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 77.9%

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

   6. Taylor expanded in z around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. sub-neg 99.5%

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

      3. +-commutative 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in y around 0 69.6%

      \[\leadsto x + \color{blue}{-0.5 \cdot \log y} \]
   10. Step-by-step derivation

       1. *-commutative 69.6%

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

   11. Simplified 69.6%

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

   if 245 < 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 85.1%

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

Alternative 5: 71.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+106}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-223}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;z \leq 160:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.2e+106)
   (- x z)
   (if (<= z -3e-223)
     (+ x (* y (- 1.0 (log y))))
     (if (<= z 160.0) (+ x (* (log y) -0.5)) (- x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.2e+106) {
		tmp = x - z;
	} else if (z <= -3e-223) {
		tmp = x + (y * (1.0 - log(y)));
	} else if (z <= 160.0) {
		tmp = x + (log(y) * -0.5);
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-8.2d+106)) then
        tmp = x - z
    else if (z <= (-3d-223)) then
        tmp = x + (y * (1.0d0 - log(y)))
    else if (z <= 160.0d0) then
        tmp = x + (log(y) * (-0.5d0))
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.2e+106) {
		tmp = x - z;
	} else if (z <= -3e-223) {
		tmp = x + (y * (1.0 - Math.log(y)));
	} else if (z <= 160.0) {
		tmp = x + (Math.log(y) * -0.5);
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.2e+106:
		tmp = x - z
	elif z <= -3e-223:
		tmp = x + (y * (1.0 - math.log(y)))
	elif z <= 160.0:
		tmp = x + (math.log(y) * -0.5)
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.2e+106)
		tmp = Float64(x - z);
	elseif (z <= -3e-223)
		tmp = Float64(x + Float64(y * Float64(1.0 - log(y))));
	elseif (z <= 160.0)
		tmp = Float64(x + Float64(log(y) * -0.5));
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.2e+106)
		tmp = x - z;
	elseif (z <= -3e-223)
		tmp = x + (y * (1.0 - log(y)));
	elseif (z <= 160.0)
		tmp = x + (log(y) * -0.5);
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.2e+106], N[(x - z), $MachinePrecision], If[LessEqual[z, -3e-223], N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 160.0], N[(x + N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], N[(x - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2000000000000005e106 or 160 < 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 85.9%

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

   if -8.2000000000000005e106 < z < -2.99999999999999991e-223

   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. Taylor expanded in z around inf 80.6%

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

   6. Taylor expanded in z around 0 96.9%

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

      1. mul-1-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. +-commutative 96.9%

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

   8. Simplified 96.9%

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

   9. Taylor expanded in y around inf 79.7%

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

       1. mul-1-neg 79.7%

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

       2. log-rec 79.7%

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

       3. remove-double-neg 79.7%

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

   11. Simplified 79.7%

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

   if -2.99999999999999991e-223 < z < 160

   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 99.8%

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

      8. +-commutative 99.8%

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

      9. distribute-neg-in 99.8%

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

      10. unsub-neg 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 77.9%

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

   6. Taylor expanded in z around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. sub-neg 99.5%

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

      3. +-commutative 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in y around 0 69.6%

      \[\leadsto x + \color{blue}{-0.5 \cdot \log y} \]
   10. Step-by-step derivation

       1. *-commutative 69.6%

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

   11. Simplified 69.6%

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

Alternative 6: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+47}:\\ \;\;\;\;x + \left(y - \log y \cdot \left(y + 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.8e+98)
   (- (* y (- 1.0 (log y))) z)
   (if (<= z 3.2e+47) (+ x (- y (* (log y) (+ y 0.5)))) (- x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.8e+98) {
		tmp = (y * (1.0 - log(y))) - z;
	} else if (z <= 3.2e+47) {
		tmp = x + (y - (log(y) * (y + 0.5)));
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-6.8d+98)) then
        tmp = (y * (1.0d0 - log(y))) - z
    else if (z <= 3.2d+47) then
        tmp = x + (y - (log(y) * (y + 0.5d0)))
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.8e+98) {
		tmp = (y * (1.0 - Math.log(y))) - z;
	} else if (z <= 3.2e+47) {
		tmp = x + (y - (Math.log(y) * (y + 0.5)));
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.8e+98:
		tmp = (y * (1.0 - math.log(y))) - z
	elif z <= 3.2e+47:
		tmp = x + (y - (math.log(y) * (y + 0.5)))
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.8e+98)
		tmp = Float64(Float64(y * Float64(1.0 - log(y))) - z);
	elseif (z <= 3.2e+47)
		tmp = Float64(x + Float64(y - Float64(log(y) * Float64(y + 0.5))));
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.8e+98)
		tmp = (y * (1.0 - log(y))) - z;
	elseif (z <= 3.2e+47)
		tmp = x + (y - (log(y) * (y + 0.5)));
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.8e+98], N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[z, 3.2e+47], N[(x + N[(y - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999944e98

   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 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 x around 0 93.0%

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

   5. Taylor expanded in y around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. log-rec 93.0%

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

      3. remove-double-neg 93.0%

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

   7. Simplified 93.0%

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

   if -6.79999999999999944e98 < z < 3.2e47

   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. Taylor expanded in z around inf 80.5%

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

   6. Taylor expanded in z around 0 97.2%

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

      1. mul-1-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. +-commutative 97.2%

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

   8. Simplified 97.2%

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

   if 3.2e47 < 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 87.1%

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

Alternative 7: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+34} \lor \neg \left(z \leq 255\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e+34) (not (<= z 255.0))) (- x z) (+ x (* (log y) -0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e+34) || !(z <= 255.0)) {
		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 <= (-3d+34)) .or. (.not. (z <= 255.0d0))) 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 <= -3e+34) || !(z <= 255.0)) {
		tmp = x - z;
	} else {
		tmp = x + (Math.log(y) * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e+34) or not (z <= 255.0):
		tmp = x - z
	else:
		tmp = x + (math.log(y) * -0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e+34) || !(z <= 255.0))
		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 <= -3e+34) || ~((z <= 255.0)))
		tmp = x - z;
	else
		tmp = x + (log(y) * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e+34], N[Not[LessEqual[z, 255.0]], $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 < -3.00000000000000018e34 or 255 < 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 82.7%

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

   if -3.00000000000000018e34 < z < 255

   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. Taylor expanded in z around inf 77.1%

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

   6. Taylor expanded in z around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

   8. Simplified 99.2%

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

   9. Taylor expanded in y around 0 64.5%

      \[\leadsto x + \color{blue}{-0.5 \cdot \log y} \]
   10. Step-by-step derivation

       1. *-commutative 64.5%

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

   11. Simplified 64.5%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+34} \lor \neg \left(z \leq 255\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.4% 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 99.4%

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

   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+ 99.7%

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

      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- 99.7%

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

      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-define 99.8%

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

      8. +-commutative 99.8%

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

      9. distribute-neg-in 99.8%

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

      10. unsub-neg 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.4%

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

      1. log-rec 99.4%

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

      2. sub-neg 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 99.4%

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

Alternative 9: 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 10: 47.5% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+107} \lor \neg \left(z \leq 1.3 \cdot 10^{+39}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.6e+107) (not (<= z 1.3e+39))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.6e+107) || !(z <= 1.3e+39)) {
		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 ((z <= (-6.6d+107)) .or. (.not. (z <= 1.3d+39))) 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 ((z <= -6.6e+107) || !(z <= 1.3e+39)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.6e+107) or not (z <= 1.3e+39):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.6e+107) || !(z <= 1.3e+39))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.6e+107) || ~((z <= 1.3e+39)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.6e+107], N[Not[LessEqual[z, 1.3e+39]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if z < -6.60000000000000064e107 or 1.3e39 < 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 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 73.2%

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

      1. neg-mul-1 73.2%

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

   6. Simplified 73.2%

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

   if -6.60000000000000064e107 < z < 1.3e39

   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. Taylor expanded in z around inf 80.1%

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

   6. Taylor expanded in z around 0 98.6%

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

      1. mul-1-neg 98.6%

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

      2. sub-neg 98.6%

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

      3. +-commutative 98.6%

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

   8. Simplified 98.6%

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

   9. Taylor expanded in y around 0 63.9%

      \[\leadsto x + \color{blue}{-0.5 \cdot \log y} \]
   10. Step-by-step derivation

       1. *-commutative 63.9%

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

   11. Simplified 63.9%

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

   12. Taylor expanded in x around inf 36.0%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+107} \lor \neg \left(z \leq 1.3 \cdot 10^{+39}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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. Add Preprocessing

3. Taylor expanded in x around inf 58.6%

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

Alternative 12: 29.4% 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+ 99.8%

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

   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. Taylor expanded in z around inf 88.9%

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

6. Taylor expanded in z around 0 67.1%

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

   1. mul-1-neg 67.1%

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

   2. sub-neg 67.1%

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

   3. +-commutative 67.1%

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

8. Simplified 67.1%

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

9. Taylor expanded in y around 0 42.0%

   \[\leadsto x + \color{blue}{-0.5 \cdot \log y} \]
10. Step-by-step derivation

    1. *-commutative 42.0%

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

11. Simplified 42.0%

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

12. Taylor expanded in x around inf 26.4%

    \[\leadsto \color{blue}{x} \]
13. 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 2024096 
(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))