Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 13.9s

Alternatives: 14

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

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

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: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y - \log y \cdot \left(y + 0.5\right)\\ t_1 := x + y \cdot \left(1 - \log y\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+106}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-258}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-299}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-135}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- y (* (log y) (+ y 0.5)))) (t_1 (+ x (* y (- 1.0 (log y))))))
   (if (<= z -8.2e+106)
     (- x z)
     (if (<= z -2.7e-139)
       t_1
       (if (<= z -2.7e-258)
         t_0
         (if (<= z 1.6e-299)
           (+ x (* (log y) -0.5))
           (if (<= z 4.5e-135) t_0 (if (<= z 4e+48) t_1 (- x z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y - (log(y) * (y + 0.5));
	double t_1 = x + (y * (1.0 - log(y)));
	double tmp;
	if (z <= -8.2e+106) {
		tmp = x - z;
	} else if (z <= -2.7e-139) {
		tmp = t_1;
	} else if (z <= -2.7e-258) {
		tmp = t_0;
	} else if (z <= 1.6e-299) {
		tmp = x + (log(y) * -0.5);
	} else if (z <= 4.5e-135) {
		tmp = t_0;
	} else if (z <= 4e+48) {
		tmp = t_1;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y - (log(y) * (y + 0.5d0))
    t_1 = x + (y * (1.0d0 - log(y)))
    if (z <= (-8.2d+106)) then
        tmp = x - z
    else if (z <= (-2.7d-139)) then
        tmp = t_1
    else if (z <= (-2.7d-258)) then
        tmp = t_0
    else if (z <= 1.6d-299) then
        tmp = x + (log(y) * (-0.5d0))
    else if (z <= 4.5d-135) then
        tmp = t_0
    else if (z <= 4d+48) then
        tmp = t_1
    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 - (Math.log(y) * (y + 0.5));
	double t_1 = x + (y * (1.0 - Math.log(y)));
	double tmp;
	if (z <= -8.2e+106) {
		tmp = x - z;
	} else if (z <= -2.7e-139) {
		tmp = t_1;
	} else if (z <= -2.7e-258) {
		tmp = t_0;
	} else if (z <= 1.6e-299) {
		tmp = x + (Math.log(y) * -0.5);
	} else if (z <= 4.5e-135) {
		tmp = t_0;
	} else if (z <= 4e+48) {
		tmp = t_1;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y - (math.log(y) * (y + 0.5))
	t_1 = x + (y * (1.0 - math.log(y)))
	tmp = 0
	if z <= -8.2e+106:
		tmp = x - z
	elif z <= -2.7e-139:
		tmp = t_1
	elif z <= -2.7e-258:
		tmp = t_0
	elif z <= 1.6e-299:
		tmp = x + (math.log(y) * -0.5)
	elif z <= 4.5e-135:
		tmp = t_0
	elif z <= 4e+48:
		tmp = t_1
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y - Float64(log(y) * Float64(y + 0.5)))
	t_1 = Float64(x + Float64(y * Float64(1.0 - log(y))))
	tmp = 0.0
	if (z <= -8.2e+106)
		tmp = Float64(x - z);
	elseif (z <= -2.7e-139)
		tmp = t_1;
	elseif (z <= -2.7e-258)
		tmp = t_0;
	elseif (z <= 1.6e-299)
		tmp = Float64(x + Float64(log(y) * -0.5));
	elseif (z <= 4.5e-135)
		tmp = t_0;
	elseif (z <= 4e+48)
		tmp = t_1;
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y - (log(y) * (y + 0.5));
	t_1 = x + (y * (1.0 - log(y)));
	tmp = 0.0;
	if (z <= -8.2e+106)
		tmp = x - z;
	elseif (z <= -2.7e-139)
		tmp = t_1;
	elseif (z <= -2.7e-258)
		tmp = t_0;
	elseif (z <= 1.6e-299)
		tmp = x + (log(y) * -0.5);
	elseif (z <= 4.5e-135)
		tmp = t_0;
	elseif (z <= 4e+48)
		tmp = t_1;
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+106], N[(x - z), $MachinePrecision], If[LessEqual[z, -2.7e-139], t$95$1, If[LessEqual[z, -2.7e-258], t$95$0, If[LessEqual[z, 1.6e-299], N[(x + N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-135], t$95$0, If[LessEqual[z, 4e+48], t$95$1, N[(x - z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2000000000000005e106 or 4.00000000000000018e48 < 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 x around inf 87.0%

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

   if -8.2000000000000005e106 < z < -2.6999999999999998e-139 or 4.49999999999999987e-135 < z < 4.00000000000000018e48

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 94.9%

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

   6. Taylor expanded in y around inf 81.2%

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

      1. mul-1-neg 81.2%

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

      2. log-rec 81.2%

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

      3. distribute-rgt-neg-out 81.2%

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

      4. remove-double-neg 81.2%

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

   8. Simplified 81.2%

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

      1. sub-neg 81.2%

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

      2. associate-+l+ 81.2%

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

      3. sub-neg 81.2%

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

      4. *-un-lft-identity 81.2%

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

      5. *-commutative 81.2%

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

      6. distribute-rgt-out-- 81.3%

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

      7. +-commutative 81.3%

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

   10. Applied egg-rr 81.3%

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

   if -2.6999999999999998e-139 < z < -2.69999999999999996e-258 or 1.60000000000000004e-299 < z < 4.49999999999999987e-135

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in x around 0 81.9%

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

   if -2.69999999999999996e-258 < z < 1.60000000000000004e-299

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. rem-cube-cbrt 98.7%

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

   7. Applied egg-rr 98.7%

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

   8. Taylor expanded in y around 0 83.5%

      \[\leadsto \color{blue}{x - 0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)} \]
   9. Step-by-step derivation

      1. sub-neg 83.5%

         \[\leadsto \color{blue}{x + \left(-0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)\right)} \]

      2. *-commutative 83.5%

         \[\leadsto x + \left(-\color{blue}{\left({1}^{0.3333333333333333} \cdot \log y\right) \cdot 0.5}\right) \]

      3. pow-base-1 83.5%

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

      4. *-lft-identity 83.5%

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

      5. distribute-rgt-neg-in 83.5%

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

      6. metadata-eval 83.5%

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

   10. Simplified 83.5%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+106}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-139}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-258}:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-299}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-135}:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y - \log y \cdot \left(y + 0.5\right)\\ t_1 := y \cdot \left(1 - \log y\right)\\ t_2 := x + t\_1\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+107}:\\ \;\;\;\;t\_1 - z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-139}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-258}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-299}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-135}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- y (* (log y) (+ y 0.5))))
        (t_1 (* y (- 1.0 (log y))))
        (t_2 (+ x t_1)))
   (if (<= z -2.4e+107)
     (- t_1 z)
     (if (<= z -3.1e-139)
       t_2
       (if (<= z -1.6e-258)
         t_0
         (if (<= z 1.65e-299)
           (+ x (* (log y) -0.5))
           (if (<= z 1.3e-135) t_0 (if (<= z 1.65e+48) t_2 (- x z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y - (log(y) * (y + 0.5));
	double t_1 = y * (1.0 - log(y));
	double t_2 = x + t_1;
	double tmp;
	if (z <= -2.4e+107) {
		tmp = t_1 - z;
	} else if (z <= -3.1e-139) {
		tmp = t_2;
	} else if (z <= -1.6e-258) {
		tmp = t_0;
	} else if (z <= 1.65e-299) {
		tmp = x + (log(y) * -0.5);
	} else if (z <= 1.3e-135) {
		tmp = t_0;
	} else if (z <= 1.65e+48) {
		tmp = t_2;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = y - (log(y) * (y + 0.5d0))
    t_1 = y * (1.0d0 - log(y))
    t_2 = x + t_1
    if (z <= (-2.4d+107)) then
        tmp = t_1 - z
    else if (z <= (-3.1d-139)) then
        tmp = t_2
    else if (z <= (-1.6d-258)) then
        tmp = t_0
    else if (z <= 1.65d-299) then
        tmp = x + (log(y) * (-0.5d0))
    else if (z <= 1.3d-135) then
        tmp = t_0
    else if (z <= 1.65d+48) then
        tmp = t_2
    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 - (Math.log(y) * (y + 0.5));
	double t_1 = y * (1.0 - Math.log(y));
	double t_2 = x + t_1;
	double tmp;
	if (z <= -2.4e+107) {
		tmp = t_1 - z;
	} else if (z <= -3.1e-139) {
		tmp = t_2;
	} else if (z <= -1.6e-258) {
		tmp = t_0;
	} else if (z <= 1.65e-299) {
		tmp = x + (Math.log(y) * -0.5);
	} else if (z <= 1.3e-135) {
		tmp = t_0;
	} else if (z <= 1.65e+48) {
		tmp = t_2;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y - (math.log(y) * (y + 0.5))
	t_1 = y * (1.0 - math.log(y))
	t_2 = x + t_1
	tmp = 0
	if z <= -2.4e+107:
		tmp = t_1 - z
	elif z <= -3.1e-139:
		tmp = t_2
	elif z <= -1.6e-258:
		tmp = t_0
	elif z <= 1.65e-299:
		tmp = x + (math.log(y) * -0.5)
	elif z <= 1.3e-135:
		tmp = t_0
	elif z <= 1.65e+48:
		tmp = t_2
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y - Float64(log(y) * Float64(y + 0.5)))
	t_1 = Float64(y * Float64(1.0 - log(y)))
	t_2 = Float64(x + t_1)
	tmp = 0.0
	if (z <= -2.4e+107)
		tmp = Float64(t_1 - z);
	elseif (z <= -3.1e-139)
		tmp = t_2;
	elseif (z <= -1.6e-258)
		tmp = t_0;
	elseif (z <= 1.65e-299)
		tmp = Float64(x + Float64(log(y) * -0.5));
	elseif (z <= 1.3e-135)
		tmp = t_0;
	elseif (z <= 1.65e+48)
		tmp = t_2;
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y - (log(y) * (y + 0.5));
	t_1 = y * (1.0 - log(y));
	t_2 = x + t_1;
	tmp = 0.0;
	if (z <= -2.4e+107)
		tmp = t_1 - z;
	elseif (z <= -3.1e-139)
		tmp = t_2;
	elseif (z <= -1.6e-258)
		tmp = t_0;
	elseif (z <= 1.65e-299)
		tmp = x + (log(y) * -0.5);
	elseif (z <= 1.3e-135)
		tmp = t_0;
	elseif (z <= 1.65e+48)
		tmp = t_2;
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + t$95$1), $MachinePrecision]}, If[LessEqual[z, -2.4e+107], N[(t$95$1 - z), $MachinePrecision], If[LessEqual[z, -3.1e-139], t$95$2, If[LessEqual[z, -1.6e-258], t$95$0, If[LessEqual[z, 1.65e-299], N[(x + N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-135], t$95$0, If[LessEqual[z, 1.65e+48], t$95$2, N[(x - z), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 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. Step-by-step derivation

      1. flip-+ 73.3%

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

      2. associate-*l/ 73.3%

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

      3. fma-neg 73.3%

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

      4. metadata-eval 73.3%

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

      5. metadata-eval 73.3%

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

      6. sub-neg 73.3%

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

      7. metadata-eval 73.3%

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

   4. Applied egg-rr 73.3%

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

   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 < -3.0999999999999999e-139 or 1.30000000000000002e-135 < z < 1.65000000000000011e48

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 94.9%

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

   6. Taylor expanded in y around inf 81.2%

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

      1. mul-1-neg 81.2%

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

      2. log-rec 81.2%

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

      3. distribute-rgt-neg-out 81.2%

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

      4. remove-double-neg 81.2%

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

   8. Simplified 81.2%

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

      1. sub-neg 81.2%

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

      2. associate-+l+ 81.2%

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

      3. sub-neg 81.2%

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

      4. *-un-lft-identity 81.2%

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

      5. *-commutative 81.2%

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

      6. distribute-rgt-out-- 81.3%

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

      7. +-commutative 81.3%

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

   10. Applied egg-rr 81.3%

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

   if -3.0999999999999999e-139 < z < -1.6000000000000001e-258 or 1.6500000000000001e-299 < z < 1.30000000000000002e-135

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in x around 0 81.9%

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

   if -1.6000000000000001e-258 < z < 1.6500000000000001e-299

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. rem-cube-cbrt 98.7%

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

   7. Applied egg-rr 98.7%

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

   8. Taylor expanded in y around 0 83.5%

      \[\leadsto \color{blue}{x - 0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)} \]
   9. Step-by-step derivation

      1. sub-neg 83.5%

         \[\leadsto \color{blue}{x + \left(-0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)\right)} \]

      2. *-commutative 83.5%

         \[\leadsto x + \left(-\color{blue}{\left({1}^{0.3333333333333333} \cdot \log y\right) \cdot 0.5}\right) \]

      3. pow-base-1 83.5%

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

      4. *-lft-identity 83.5%

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

      5. distribute-rgt-neg-in 83.5%

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

      6. metadata-eval 83.5%

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

   10. Simplified 83.5%

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

   if 1.65000000000000011e48 < 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 x around inf 87.1%

      \[\leadsto \color{blue}{x} - z \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-139}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-258}:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-299}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-135}:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right) - z\\ t_1 := \left(x - \log y \cdot 0.5\right) - z\\ \mathbf{if}\;y \leq 9 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+79}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+151}:\\ \;\;\;\;\left(x + y\right) - y \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 9e+43)
     t_1
     (if (<= y 3.2e+79)
       t_0
       (if (<= y 1.32e+116)
         t_1
         (if (<= y 6.8e+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 <= 9e+43) {
		tmp = t_1;
	} else if (y <= 3.2e+79) {
		tmp = t_0;
	} else if (y <= 1.32e+116) {
		tmp = t_1;
	} else if (y <= 6.8e+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 <= 9d+43) then
        tmp = t_1
    else if (y <= 3.2d+79) then
        tmp = t_0
    else if (y <= 1.32d+116) then
        tmp = t_1
    else if (y <= 6.8d+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 <= 9e+43) {
		tmp = t_1;
	} else if (y <= 3.2e+79) {
		tmp = t_0;
	} else if (y <= 1.32e+116) {
		tmp = t_1;
	} else if (y <= 6.8e+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 <= 9e+43:
		tmp = t_1
	elif y <= 3.2e+79:
		tmp = t_0
	elif y <= 1.32e+116:
		tmp = t_1
	elif y <= 6.8e+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 <= 9e+43)
		tmp = t_1;
	elseif (y <= 3.2e+79)
		tmp = t_0;
	elseif (y <= 1.32e+116)
		tmp = t_1;
	elseif (y <= 6.8e+151)
		tmp = Float64(Float64(x + 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 <= 9e+43)
		tmp = t_1;
	elseif (y <= 3.2e+79)
		tmp = t_0;
	elseif (y <= 1.32e+116)
		tmp = t_1;
	elseif (y <= 6.8e+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, 9e+43], t$95$1, If[LessEqual[y, 3.2e+79], t$95$0, If[LessEqual[y, 1.32e+116], t$95$1, If[LessEqual[y, 6.8e+151], N[(N[(x + y), $MachinePrecision] - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 9e43 or 3.20000000000000003e79 < y < 1.32000000000000002e116

   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 9e43 < y < 3.20000000000000003e79 or 6.7999999999999999e151 < 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. flip-+ 29.0%

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

      2. associate-*l/ 29.1%

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

      3. fma-neg 29.1%

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

      4. metadata-eval 29.1%

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

      5. metadata-eval 29.1%

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

      6. sub-neg 29.1%

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

      7. metadata-eval 29.1%

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

   4. Applied egg-rr 29.1%

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

   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 1.32000000000000002e116 < y < 6.7999999999999999e151

   1. Initial program 99.5%

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

      1. associate--l+ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 87.6%

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

   6. Taylor expanded in y around inf 87.6%

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

      1. mul-1-neg 87.6%

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

      2. log-rec 87.6%

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

      3. distribute-rgt-neg-out 87.6%

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

      4. remove-double-neg 87.6%

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

   8. Simplified 87.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+43}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+116}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+151}:\\ \;\;\;\;\left(x + y\right) - y \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log y \cdot -0.5\\ \mathbf{if}\;z \leq -3 \cdot 10^{-139}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-244}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{-137}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log y) -0.5)))
   (if (<= z -3e-139)
     (- x z)
     (if (<= z -2.5e-244)
       t_0
       (if (<= z -3.4e-296) x (if (<= z 6.7e-137) t_0 (- x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = log(y) * -0.5;
	double tmp;
	if (z <= -3e-139) {
		tmp = x - z;
	} else if (z <= -2.5e-244) {
		tmp = t_0;
	} else if (z <= -3.4e-296) {
		tmp = x;
	} else if (z <= 6.7e-137) {
		tmp = t_0;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = log(y) * (-0.5d0)
    if (z <= (-3d-139)) then
        tmp = x - z
    else if (z <= (-2.5d-244)) then
        tmp = t_0
    else if (z <= (-3.4d-296)) then
        tmp = x
    else if (z <= 6.7d-137) then
        tmp = t_0
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log(y) * -0.5;
	double tmp;
	if (z <= -3e-139) {
		tmp = x - z;
	} else if (z <= -2.5e-244) {
		tmp = t_0;
	} else if (z <= -3.4e-296) {
		tmp = x;
	} else if (z <= 6.7e-137) {
		tmp = t_0;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(y) * -0.5
	tmp = 0
	if z <= -3e-139:
		tmp = x - z
	elif z <= -2.5e-244:
		tmp = t_0
	elif z <= -3.4e-296:
		tmp = x
	elif z <= 6.7e-137:
		tmp = t_0
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(y) * -0.5)
	tmp = 0.0
	if (z <= -3e-139)
		tmp = Float64(x - z);
	elseif (z <= -2.5e-244)
		tmp = t_0;
	elseif (z <= -3.4e-296)
		tmp = x;
	elseif (z <= 6.7e-137)
		tmp = t_0;
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log(y) * -0.5;
	tmp = 0.0;
	if (z <= -3e-139)
		tmp = x - z;
	elseif (z <= -2.5e-244)
		tmp = t_0;
	elseif (z <= -3.4e-296)
		tmp = x;
	elseif (z <= 6.7e-137)
		tmp = t_0;
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision]}, If[LessEqual[z, -3e-139], N[(x - z), $MachinePrecision], If[LessEqual[z, -2.5e-244], t$95$0, If[LessEqual[z, -3.4e-296], x, If[LessEqual[z, 6.7e-137], t$95$0, N[(x - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9999999999999999e-139 or 6.6999999999999998e-137 < z

   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 x around inf 70.7%

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

   if -2.9999999999999999e-139 < z < -2.49999999999999999e-244 or -3.39999999999999997e-296 < z < 6.6999999999999998e-137

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. rem-cube-cbrt 98.4%

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

   7. Applied egg-rr 98.4%

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

   8. Taylor expanded in y around 0 66.9%

      \[\leadsto \color{blue}{x - 0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)} \]
   9. Step-by-step derivation

      1. sub-neg 66.9%

         \[\leadsto \color{blue}{x + \left(-0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)\right)} \]

      2. *-commutative 66.9%

         \[\leadsto x + \left(-\color{blue}{\left({1}^{0.3333333333333333} \cdot \log y\right) \cdot 0.5}\right) \]

      3. pow-base-1 66.9%

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

      4. *-lft-identity 66.9%

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

      5. distribute-rgt-neg-in 66.9%

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

      6. metadata-eval 66.9%

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

   10. Simplified 66.9%

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

   11. Taylor expanded in x around 0 48.1%

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

       1. *-commutative 48.1%

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

   13. Simplified 48.1%

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

   if -2.49999999999999999e-244 < z < -3.39999999999999997e-296

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 58.4%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-139}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-244}:\\ \;\;\;\;\log y \cdot -0.5\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{-137}:\\ \;\;\;\;\log y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-84}:\\ \;\;\;\;y - y \cdot \log y\\ \mathbf{elif}\;z \leq 104:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.8e+19)
   (- x z)
   (if (<= z -2.7e-84)
     (- y (* y (log y)))
     (if (<= z 104.0) (+ x (* (log y) -0.5)) (- x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e+19) {
		tmp = x - z;
	} else if (z <= -2.7e-84) {
		tmp = y - (y * log(y));
	} else if (z <= 104.0) {
		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 <= (-3.8d+19)) then
        tmp = x - z
    else if (z <= (-2.7d-84)) then
        tmp = y - (y * log(y))
    else if (z <= 104.0d0) 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 <= -3.8e+19) {
		tmp = x - z;
	} else if (z <= -2.7e-84) {
		tmp = y - (y * Math.log(y));
	} else if (z <= 104.0) {
		tmp = x + (Math.log(y) * -0.5);
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.8e+19:
		tmp = x - z
	elif z <= -2.7e-84:
		tmp = y - (y * math.log(y))
	elif z <= 104.0:
		tmp = x + (math.log(y) * -0.5)
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.8e+19)
		tmp = Float64(x - z);
	elseif (z <= -2.7e-84)
		tmp = Float64(y - Float64(y * log(y)));
	elseif (z <= 104.0)
		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 <= -3.8e+19)
		tmp = x - z;
	elseif (z <= -2.7e-84)
		tmp = y - (y * log(y));
	elseif (z <= 104.0)
		tmp = x + (log(y) * -0.5);
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.8e+19], N[(x - z), $MachinePrecision], If[LessEqual[z, -2.7e-84], N[(y - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 104.0], 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 < -3.8e19 or 104 < 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 x around inf 83.0%

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

   if -3.8e19 < z < -2.6999999999999999e-84

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 96.2%

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

   6. Taylor expanded in y around inf 72.5%

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

      1. mul-1-neg 72.5%

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

      2. log-rec 72.5%

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

      3. distribute-rgt-neg-out 72.5%

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

      4. remove-double-neg 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in x around 0 65.6%

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

   if -2.6999999999999999e-84 < z < 104

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.5%

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

      1. +-commutative 99.5%

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

      2. rem-cube-cbrt 98.4%

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

   7. Applied egg-rr 98.4%

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

   8. Taylor expanded in y around 0 67.4%

      \[\leadsto \color{blue}{x - 0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)} \]
   9. Step-by-step derivation

      1. sub-neg 67.4%

         \[\leadsto \color{blue}{x + \left(-0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)\right)} \]

      2. *-commutative 67.4%

         \[\leadsto x + \left(-\color{blue}{\left({1}^{0.3333333333333333} \cdot \log y\right) \cdot 0.5}\right) \]

      3. pow-base-1 67.4%

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

      4. *-lft-identity 67.4%

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

      5. distribute-rgt-neg-in 67.4%

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

      6. metadata-eval 67.4%

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

   10. Simplified 67.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-84}:\\ \;\;\;\;y - y \cdot \log y\\ \mathbf{elif}\;z \leq 104:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+107}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-223}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;z \leq 180:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7e+107)
   (- x z)
   (if (<= z -1.65e-223)
     (+ x (* y (- 1.0 (log y))))
     (if (<= z 180.0) (+ x (* (log y) -0.5)) (- x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7e+107) {
		tmp = x - z;
	} else if (z <= -1.65e-223) {
		tmp = x + (y * (1.0 - log(y)));
	} else if (z <= 180.0) {
		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 <= (-7d+107)) then
        tmp = x - z
    else if (z <= (-1.65d-223)) then
        tmp = x + (y * (1.0d0 - log(y)))
    else if (z <= 180.0d0) 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 <= -7e+107) {
		tmp = x - z;
	} else if (z <= -1.65e-223) {
		tmp = x + (y * (1.0 - Math.log(y)));
	} else if (z <= 180.0) {
		tmp = x + (Math.log(y) * -0.5);
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7e+107:
		tmp = x - z
	elif z <= -1.65e-223:
		tmp = x + (y * (1.0 - math.log(y)))
	elif z <= 180.0:
		tmp = x + (math.log(y) * -0.5)
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7e+107)
		tmp = Float64(x - z);
	elseif (z <= -1.65e-223)
		tmp = Float64(x + Float64(y * Float64(1.0 - log(y))));
	elseif (z <= 180.0)
		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 <= -7e+107)
		tmp = x - z;
	elseif (z <= -1.65e-223)
		tmp = x + (y * (1.0 - log(y)));
	elseif (z <= 180.0)
		tmp = x + (log(y) * -0.5);
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7e+107], N[(x - z), $MachinePrecision], If[LessEqual[z, -1.65e-223], N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 180.0], 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 < -6.9999999999999995e107 or 180 < 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 x around inf 85.9%

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

   if -6.9999999999999995e107 < z < -1.64999999999999997e-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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 96.9%

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

   6. Taylor expanded in y around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. log-rec 79.5%

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

      3. distribute-rgt-neg-out 79.5%

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

      4. remove-double-neg 79.5%

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

   8. Simplified 79.5%

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

      1. sub-neg 79.5%

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

      2. associate-+l+ 79.5%

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

      3. sub-neg 79.5%

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

      4. *-un-lft-identity 79.5%

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

      5. *-commutative 79.5%

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

      6. distribute-rgt-out-- 79.7%

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

      7. +-commutative 79.7%

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

   10. Applied egg-rr 79.7%

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

   if -1.64999999999999997e-223 < z < 180

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.5%

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

      1. +-commutative 99.5%

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

      2. rem-cube-cbrt 98.3%

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

   7. Applied egg-rr 98.3%

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

   8. Taylor expanded in y around 0 69.6%

      \[\leadsto \color{blue}{x - 0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)} \]
   9. Step-by-step derivation

      1. sub-neg 69.6%

         \[\leadsto \color{blue}{x + \left(-0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)\right)} \]

      2. *-commutative 69.6%

         \[\leadsto x + \left(-\color{blue}{\left({1}^{0.3333333333333333} \cdot \log y\right) \cdot 0.5}\right) \]

      3. pow-base-1 69.6%

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

      4. *-lft-identity 69.6%

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

      5. distribute-rgt-neg-in 69.6%

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

      6. metadata-eval 69.6%

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

   10. Simplified 69.6%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+107}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-223}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;z \leq 180:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+34} \lor \neg \left(z \leq 104\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e+34) (not (<= z 104.0))) (- x z) (+ x (* (log y) -0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e+34) || !(z <= 104.0)) {
		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 <= 104.0d0))) 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 <= 104.0)) {
		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 <= 104.0):
		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 <= 104.0))
		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 <= 104.0)))
		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, 104.0]], $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 104 < 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 x around inf 82.7%

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

   if -3.00000000000000018e34 < z < 104

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.2%

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

      1. +-commutative 99.2%

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

      2. rem-cube-cbrt 98.0%

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

   7. Applied egg-rr 98.0%

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

   8. Taylor expanded in y around 0 64.5%

      \[\leadsto \color{blue}{x - 0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)} \]
   9. Step-by-step derivation

      1. sub-neg 64.5%

         \[\leadsto \color{blue}{x + \left(-0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log y\right)\right)} \]

      2. *-commutative 64.5%

         \[\leadsto x + \left(-\color{blue}{\left({1}^{0.3333333333333333} \cdot \log y\right) \cdot 0.5}\right) \]

      3. pow-base-1 64.5%

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

      4. *-lft-identity 64.5%

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

      5. distribute-rgt-neg-in 64.5%

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

      6. metadata-eval 64.5%

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

   10. Simplified 64.5%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+34} \lor \neg \left(z \leq 104\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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-def 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 11: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate--l+ 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 12: 47.6% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+107} \lor \neg \left(z \leq 3.7 \cdot 10^{+33}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e+107) (not (<= z 3.7e+33))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e+107) || !(z <= 3.7e+33)) {
		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 <= (-2.4d+107)) .or. (.not. (z <= 3.7d+33))) 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 <= -2.4e+107) || !(z <= 3.7e+33)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e+107) or not (z <= 3.7e+33):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e+107) || !(z <= 3.7e+33))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.4e+107) || ~((z <= 3.7e+33)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e+107], N[Not[LessEqual[z, 3.7e+33]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e107 or 3.6999999999999999e33 < 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 -2.4000000000000001e107 < z < 3.6999999999999999e33

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 36.0%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+107} \lor \neg \left(z \leq 3.7 \cdot 10^{+33}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 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 inf 58.6%

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

5. Final simplification 58.6%

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

Alternative 14: 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%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around inf 26.4%

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

6. Final simplification 26.4%

   \[\leadsto x \]
7. 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

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

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