Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 15.6s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate--l+ 99.8%

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

   2. associate-+l- 99.8%

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

   3. fma-neg 99.9%

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

   4. sub-neg 99.9%

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

   5. +-commutative 99.9%

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

   6. distribute-neg-out 99.9%

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

   7. remove-double-neg 99.9%

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

   8. sub-neg 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-104}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-62}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+42}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.7e-104)
   (- x z)
   (if (<= y 2.1e-62)
     (- (* (log y) -0.5) z)
     (if (<= y 1.9e+42) (- x z) (+ x (* y (- 1.0 (log y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.7e-104) {
		tmp = x - z;
	} else if (y <= 2.1e-62) {
		tmp = (log(y) * -0.5) - z;
	} else if (y <= 1.9e+42) {
		tmp = x - z;
	} else {
		tmp = x + (y * (1.0 - log(y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.7d-104) then
        tmp = x - z
    else if (y <= 2.1d-62) then
        tmp = (log(y) * (-0.5d0)) - z
    else if (y <= 1.9d+42) then
        tmp = x - z
    else
        tmp = x + (y * (1.0d0 - log(y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.7e-104) {
		tmp = x - z;
	} else if (y <= 2.1e-62) {
		tmp = (Math.log(y) * -0.5) - z;
	} else if (y <= 1.9e+42) {
		tmp = x - z;
	} else {
		tmp = x + (y * (1.0 - Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.7e-104:
		tmp = x - z
	elif y <= 2.1e-62:
		tmp = (math.log(y) * -0.5) - z
	elif y <= 1.9e+42:
		tmp = x - z
	else:
		tmp = x + (y * (1.0 - math.log(y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.7e-104)
		tmp = Float64(x - z);
	elseif (y <= 2.1e-62)
		tmp = Float64(Float64(log(y) * -0.5) - z);
	elseif (y <= 1.9e+42)
		tmp = Float64(x - z);
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - log(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.7e-104)
		tmp = x - z;
	elseif (y <= 2.1e-62)
		tmp = (log(y) * -0.5) - z;
	elseif (y <= 1.9e+42)
		tmp = x - z;
	else
		tmp = x + (y * (1.0 - log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.7e-104], N[(x - z), $MachinePrecision], If[LessEqual[y, 2.1e-62], N[(N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[y, 1.9e+42], N[(x - z), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.6999999999999998e-104 or 2.0999999999999999e-62 < y < 1.8999999999999999e42

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+l- 100.0%

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

      3. fma-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-out 100.0%

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

      7. remove-double-neg 100.0%

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

      8. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 84.8%

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

   if 2.6999999999999998e-104 < y < 2.0999999999999999e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in x around 0 75.6%

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

      1. *-commutative 75.6%

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

   5. Simplified 75.6%

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

   if 1.8999999999999999e42 < 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. associate-+l- 99.6%

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

      3. fma-neg 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-neg-out 99.7%

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

      7. remove-double-neg 99.7%

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

      8. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 83.5%

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

      1. sub-neg 83.5%

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

      2. metadata-eval 83.5%

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

      3. +-commutative 83.5%

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

      4. log-rec 83.5%

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

      5. neg-mul-1 83.5%

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

      6. associate-*r* 83.5%

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

      7. metadata-eval 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in y around 0 83.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-104}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-62}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+42}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \]

Alternative 3: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right)\\ t_1 := t_0 - z\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+91}:\\ \;\;\;\;x + t_0\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (log y)))) (t_1 (- t_0 z)))
   (if (<= z -3.4e+47)
     t_1
     (if (<= z 2.8e+91) (+ x t_0) (if (<= z 1.3e+134) t_1 (- x z))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - log(y));
	double t_1 = t_0 - z;
	double tmp;
	if (z <= -3.4e+47) {
		tmp = t_1;
	} else if (z <= 2.8e+91) {
		tmp = x + t_0;
	} else if (z <= 1.3e+134) {
		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 * (1.0d0 - log(y))
    t_1 = t_0 - z
    if (z <= (-3.4d+47)) then
        tmp = t_1
    else if (z <= 2.8d+91) then
        tmp = x + t_0
    else if (z <= 1.3d+134) 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 * (1.0 - Math.log(y));
	double t_1 = t_0 - z;
	double tmp;
	if (z <= -3.4e+47) {
		tmp = t_1;
	} else if (z <= 2.8e+91) {
		tmp = x + t_0;
	} else if (z <= 1.3e+134) {
		tmp = t_1;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - math.log(y))
	t_1 = t_0 - z
	tmp = 0
	if z <= -3.4e+47:
		tmp = t_1
	elif z <= 2.8e+91:
		tmp = x + t_0
	elif z <= 1.3e+134:
		tmp = t_1
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - log(y)))
	t_1 = Float64(t_0 - z)
	tmp = 0.0
	if (z <= -3.4e+47)
		tmp = t_1;
	elseif (z <= 2.8e+91)
		tmp = Float64(x + t_0);
	elseif (z <= 1.3e+134)
		tmp = t_1;
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - log(y));
	t_1 = t_0 - z;
	tmp = 0.0;
	if (z <= -3.4e+47)
		tmp = t_1;
	elseif (z <= 2.8e+91)
		tmp = x + t_0;
	elseif (z <= 1.3e+134)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(t$95$0 - z), $MachinePrecision]}, If[LessEqual[z, -3.4e+47], t$95$1, If[LessEqual[z, 2.8e+91], N[(x + t$95$0), $MachinePrecision], If[LessEqual[z, 1.3e+134], t$95$1, N[(x - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3999999999999998e47 or 2.7999999999999999e91 < z < 1.3000000000000001e134

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 86.6%

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

      1. log-rec 86.6%

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

   4. Simplified 86.6%

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

   5. Taylor expanded in y around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. log-rec 86.6%

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

      3. log-div 86.6%

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

      4. metadata-eval 86.6%

         \[\leadsto y \cdot \left(1 + \left(\color{blue}{0} - \log y\right)\right) - z \]

      5. associate-+r- 86.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + 0\right) - \log y\right)} - z \]

      6. metadata-eval 86.6%

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

   7. Simplified 86.6%

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

   if -3.3999999999999998e47 < z < 2.7999999999999999e91

   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. associate-+l- 99.8%

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

      3. fma-neg 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-neg-out 99.8%

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

      7. remove-double-neg 99.8%

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

      8. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 79.0%

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

      1. sub-neg 79.0%

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

      2. metadata-eval 79.0%

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

      3. +-commutative 79.0%

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

      4. log-rec 79.0%

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

      5. neg-mul-1 79.0%

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

      6. associate-*r* 79.0%

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

      7. metadata-eval 79.0%

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

   6. Simplified 79.0%

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

   7. Taylor expanded in y around 0 79.0%

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

   if 1.3000000000000001e134 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+l- 100.0%

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

      3. fma-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-out 100.0%

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

      7. remove-double-neg 100.0%

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

      8. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 96.2%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+91}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]

Alternative 4: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right)\\ t_1 := \left(x - 0.5 \cdot \log y\right) - z\\ \mathbf{if}\;y \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+113}:\\ \;\;\;\;x + t_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (log y)))) (t_1 (- (- x (* 0.5 (log y))) z)))
   (if (<= y 4.8e+42)
     t_1
     (if (<= y 1.7e+113) (+ x t_0) (if (<= y 2.2e+141) t_1 (- t_0 z))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - log(y));
	double t_1 = (x - (0.5 * log(y))) - z;
	double tmp;
	if (y <= 4.8e+42) {
		tmp = t_1;
	} else if (y <= 1.7e+113) {
		tmp = x + t_0;
	} else if (y <= 2.2e+141) {
		tmp = t_1;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (1.0d0 - log(y))
    t_1 = (x - (0.5d0 * log(y))) - z
    if (y <= 4.8d+42) then
        tmp = t_1
    else if (y <= 1.7d+113) then
        tmp = x + t_0
    else if (y <= 2.2d+141) then
        tmp = t_1
    else
        tmp = t_0 - 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 t_1 = (x - (0.5 * Math.log(y))) - z;
	double tmp;
	if (y <= 4.8e+42) {
		tmp = t_1;
	} else if (y <= 1.7e+113) {
		tmp = x + t_0;
	} else if (y <= 2.2e+141) {
		tmp = t_1;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - math.log(y))
	t_1 = (x - (0.5 * math.log(y))) - z
	tmp = 0
	if y <= 4.8e+42:
		tmp = t_1
	elif y <= 1.7e+113:
		tmp = x + t_0
	elif y <= 2.2e+141:
		tmp = t_1
	else:
		tmp = t_0 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - log(y)))
	t_1 = Float64(Float64(x - Float64(0.5 * log(y))) - z)
	tmp = 0.0
	if (y <= 4.8e+42)
		tmp = t_1;
	elseif (y <= 1.7e+113)
		tmp = Float64(x + t_0);
	elseif (y <= 2.2e+141)
		tmp = t_1;
	else
		tmp = Float64(t_0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - log(y));
	t_1 = (x - (0.5 * log(y))) - z;
	tmp = 0.0;
	if (y <= 4.8e+42)
		tmp = t_1;
	elseif (y <= 1.7e+113)
		tmp = x + t_0;
	elseif (y <= 2.2e+141)
		tmp = t_1;
	else
		tmp = t_0 - 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]}, Block[{t$95$1 = N[(N[(x - N[(0.5 * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 4.8e+42], t$95$1, If[LessEqual[y, 1.7e+113], N[(x + t$95$0), $MachinePrecision], If[LessEqual[y, 2.2e+141], t$95$1, N[(t$95$0 - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 4.7999999999999997e42 or 1.70000000000000009e113 < y < 2.2e141

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.2%

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

   if 4.7999999999999997e42 < y < 1.70000000000000009e113

   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. associate-+l- 99.8%

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

      3. fma-neg 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-neg-out 99.8%

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

      7. remove-double-neg 99.8%

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

      8. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 82.1%

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

      1. sub-neg 82.1%

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

      2. metadata-eval 82.1%

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

      3. +-commutative 82.1%

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

      4. log-rec 82.1%

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

      5. neg-mul-1 82.1%

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

      6. associate-*r* 82.1%

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

      7. metadata-eval 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in y around 0 82.1%

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

   if 2.2e141 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 90.0%

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

      1. log-rec 90.0%

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

   4. Simplified 90.0%

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

   5. Taylor expanded in y around 0 90.0%

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

      1. mul-1-neg 90.0%

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

      2. log-rec 90.0%

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

      3. log-div 90.0%

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

      4. metadata-eval 90.0%

         \[\leadsto y \cdot \left(1 + \left(\color{blue}{0} - \log y\right)\right) - z \]

      5. associate-+r- 90.0%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + 0\right) - \log y\right)} - z \]

      6. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;\left(x - 0.5 \cdot \log y\right) - z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+113}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+141}:\\ \;\;\;\;\left(x - 0.5 \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \]

Alternative 5: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 0.5 \cdot \log y\right) - z\\ \mathbf{if}\;y \leq 1.2 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+113}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+141}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- x (* 0.5 (log y))) z)))
   (if (<= y 1.2e+43)
     t_0
     (if (<= y 6e+113)
       (+ x (* y (- 1.0 (log y))))
       (if (<= y 1.6e+141) t_0 (- (- y (* y (log y))) z))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - (0.5 * log(y))) - z;
	double tmp;
	if (y <= 1.2e+43) {
		tmp = t_0;
	} else if (y <= 6e+113) {
		tmp = x + (y * (1.0 - log(y)));
	} else if (y <= 1.6e+141) {
		tmp = t_0;
	} else {
		tmp = (y - (y * log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - (0.5d0 * log(y))) - z
    if (y <= 1.2d+43) then
        tmp = t_0
    else if (y <= 6d+113) then
        tmp = x + (y * (1.0d0 - log(y)))
    else if (y <= 1.6d+141) then
        tmp = t_0
    else
        tmp = (y - (y * log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - (0.5 * Math.log(y))) - z;
	double tmp;
	if (y <= 1.2e+43) {
		tmp = t_0;
	} else if (y <= 6e+113) {
		tmp = x + (y * (1.0 - Math.log(y)));
	} else if (y <= 1.6e+141) {
		tmp = t_0;
	} else {
		tmp = (y - (y * Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - (0.5 * math.log(y))) - z
	tmp = 0
	if y <= 1.2e+43:
		tmp = t_0
	elif y <= 6e+113:
		tmp = x + (y * (1.0 - math.log(y)))
	elif y <= 1.6e+141:
		tmp = t_0
	else:
		tmp = (y - (y * math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - Float64(0.5 * log(y))) - z)
	tmp = 0.0
	if (y <= 1.2e+43)
		tmp = t_0;
	elseif (y <= 6e+113)
		tmp = Float64(x + Float64(y * Float64(1.0 - log(y))));
	elseif (y <= 1.6e+141)
		tmp = t_0;
	else
		tmp = Float64(Float64(y - Float64(y * log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - (0.5 * log(y))) - z;
	tmp = 0.0;
	if (y <= 1.2e+43)
		tmp = t_0;
	elseif (y <= 6e+113)
		tmp = x + (y * (1.0 - log(y)));
	elseif (y <= 1.6e+141)
		tmp = t_0;
	else
		tmp = (y - (y * log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - N[(0.5 * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 1.2e+43], t$95$0, If[LessEqual[y, 6e+113], N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+141], t$95$0, N[(N[(y - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.20000000000000012e43 or 6e113 < y < 1.60000000000000009e141

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.2%

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

   if 1.20000000000000012e43 < y < 6e113

   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. associate-+l- 99.8%

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

      3. fma-neg 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-neg-out 99.8%

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

      7. remove-double-neg 99.8%

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

      8. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 82.1%

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

      1. sub-neg 82.1%

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

      2. metadata-eval 82.1%

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

      3. +-commutative 82.1%

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

      4. log-rec 82.1%

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

      5. neg-mul-1 82.1%

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

      6. associate-*r* 82.1%

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

      7. metadata-eval 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in y around 0 82.1%

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

   if 1.60000000000000009e141 < y

   1. Initial program 99.6%

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

      1. flip3-- 0.3%

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

      2. clear-num 0.3%

         \[\leadsto \left(\color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(y + 0.5\right) \cdot \log y\right) \cdot \left(\left(y + 0.5\right) \cdot \log y\right) + x \cdot \left(\left(y + 0.5\right) \cdot \log y\right)\right)}{{x}^{3} - {\left(\left(y + 0.5\right) \cdot \log y\right)}^{3}}}} + y\right) - z \]

      3. *-un-lft-identity 0.3%

         \[\leadsto \left(\frac{1}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(\left(\left(y + 0.5\right) \cdot \log y\right) \cdot \left(\left(y + 0.5\right) \cdot \log y\right) + x \cdot \left(\left(y + 0.5\right) \cdot \log y\right)\right)\right)}}{{x}^{3} - {\left(\left(y + 0.5\right) \cdot \log y\right)}^{3}}} + y\right) - z \]

      4. associate-/l* 0.3%

         \[\leadsto \left(\frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} - {\left(\left(y + 0.5\right) \cdot \log y\right)}^{3}}{x \cdot x + \left(\left(\left(y + 0.5\right) \cdot \log y\right) \cdot \left(\left(y + 0.5\right) \cdot \log y\right) + x \cdot \left(\left(y + 0.5\right) \cdot \log y\right)\right)}}}} + y\right) - z \]

      5. flip3-- 99.4%

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

      6. cancel-sign-sub-inv 99.4%

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

      7. *-commutative 99.4%

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

      8. neg-sub0 99.4%

         \[\leadsto \left(\frac{1}{\frac{1}{x + \log y \cdot \color{blue}{\left(0 - \left(y + 0.5\right)\right)}}} + y\right) - z \]

      9. +-commutative 99.4%

         \[\leadsto \left(\frac{1}{\frac{1}{x + \log y \cdot \left(0 - \color{blue}{\left(0.5 + y\right)}\right)}} + y\right) - z \]

      10. associate--r+ 99.4%

          \[\leadsto \left(\frac{1}{\frac{1}{x + \log y \cdot \color{blue}{\left(\left(0 - 0.5\right) - y\right)}}} + y\right) - z \]

      11. metadata-eval 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in y around inf 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-/r* 89.8%

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

      3. log-rec 89.8%

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

      4. mul-1-neg 89.8%

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

      5. associate-/r* 89.8%

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

      6. metadata-eval 89.8%

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

   6. Simplified 89.8%

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

      1. associate-/r/ 89.9%

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

      2. distribute-lft1-in 89.9%

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

      3. +-commutative 89.9%

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

      4. associate-/r/ 90.0%

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

      5. metadata-eval 90.0%

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

      6. metadata-eval 90.0%

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

      7. cancel-sign-sub-inv 90.0%

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

      8. *-un-lft-identity 90.0%

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

   8. Applied egg-rr 90.0%

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

      1. *-commutative 90.0%

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

      2. distribute-rgt-out-- 90.0%

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

      3. *-un-lft-identity 90.0%

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

      4. *-commutative 90.0%

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

   10. Applied egg-rr 90.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+43}:\\ \;\;\;\;\left(x - 0.5 \cdot \log y\right) - z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+113}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+141}:\\ \;\;\;\;\left(x - 0.5 \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \end{array} \]

Alternative 6: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - y \cdot \log y\right) - z\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+91}:\\ \;\;\;\;y + \left(x - \left(y + 0.5\right) \cdot \log y\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+133}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- y (* y (log y))) z)))
   (if (<= z -7.2e+60)
     t_0
     (if (<= z 1.5e+91)
       (+ y (- x (* (+ y 0.5) (log y))))
       (if (<= z 1.9e+133) t_0 (- x z))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - (y * log(y))) - z;
	double tmp;
	if (z <= -7.2e+60) {
		tmp = t_0;
	} else if (z <= 1.5e+91) {
		tmp = y + (x - ((y + 0.5) * log(y)));
	} else if (z <= 1.9e+133) {
		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 = (y - (y * log(y))) - z
    if (z <= (-7.2d+60)) then
        tmp = t_0
    else if (z <= 1.5d+91) then
        tmp = y + (x - ((y + 0.5d0) * log(y)))
    else if (z <= 1.9d+133) 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 = (y - (y * Math.log(y))) - z;
	double tmp;
	if (z <= -7.2e+60) {
		tmp = t_0;
	} else if (z <= 1.5e+91) {
		tmp = y + (x - ((y + 0.5) * Math.log(y)));
	} else if (z <= 1.9e+133) {
		tmp = t_0;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - (y * math.log(y))) - z
	tmp = 0
	if z <= -7.2e+60:
		tmp = t_0
	elif z <= 1.5e+91:
		tmp = y + (x - ((y + 0.5) * math.log(y)))
	elif z <= 1.9e+133:
		tmp = t_0
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - Float64(y * log(y))) - z)
	tmp = 0.0
	if (z <= -7.2e+60)
		tmp = t_0;
	elseif (z <= 1.5e+91)
		tmp = Float64(y + Float64(x - Float64(Float64(y + 0.5) * log(y))));
	elseif (z <= 1.9e+133)
		tmp = t_0;
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - (y * log(y))) - z;
	tmp = 0.0;
	if (z <= -7.2e+60)
		tmp = t_0;
	elseif (z <= 1.5e+91)
		tmp = y + (x - ((y + 0.5) * log(y)));
	elseif (z <= 1.9e+133)
		tmp = t_0;
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[z, -7.2e+60], t$95$0, If[LessEqual[z, 1.5e+91], N[(y + N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+133], t$95$0, N[(x - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999935e60 or 1.50000000000000003e91 < z < 1.9000000000000001e133

   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. flip3-- 41.8%

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

      2. clear-num 41.8%

         \[\leadsto \left(\color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(y + 0.5\right) \cdot \log y\right) \cdot \left(\left(y + 0.5\right) \cdot \log y\right) + x \cdot \left(\left(y + 0.5\right) \cdot \log y\right)\right)}{{x}^{3} - {\left(\left(y + 0.5\right) \cdot \log y\right)}^{3}}}} + y\right) - z \]

      3. *-un-lft-identity 41.8%

         \[\leadsto \left(\frac{1}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(\left(\left(y + 0.5\right) \cdot \log y\right) \cdot \left(\left(y + 0.5\right) \cdot \log y\right) + x \cdot \left(\left(y + 0.5\right) \cdot \log y\right)\right)\right)}}{{x}^{3} - {\left(\left(y + 0.5\right) \cdot \log y\right)}^{3}}} + y\right) - z \]

      4. associate-/l* 41.8%

         \[\leadsto \left(\frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} - {\left(\left(y + 0.5\right) \cdot \log y\right)}^{3}}{x \cdot x + \left(\left(\left(y + 0.5\right) \cdot \log y\right) \cdot \left(\left(y + 0.5\right) \cdot \log y\right) + x \cdot \left(\left(y + 0.5\right) \cdot \log y\right)\right)}}}} + y\right) - z \]

      5. flip3-- 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. neg-sub0 99.8%

         \[\leadsto \left(\frac{1}{\frac{1}{x + \log y \cdot \color{blue}{\left(0 - \left(y + 0.5\right)\right)}}} + y\right) - z \]

      9. +-commutative 99.8%

         \[\leadsto \left(\frac{1}{\frac{1}{x + \log y \cdot \left(0 - \color{blue}{\left(0.5 + y\right)}\right)}} + y\right) - z \]

      10. associate--r+ 99.8%

          \[\leadsto \left(\frac{1}{\frac{1}{x + \log y \cdot \color{blue}{\left(\left(0 - 0.5\right) - y\right)}}} + y\right) - z \]

      11. metadata-eval 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around inf 87.6%

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

      1. *-commutative 87.6%

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

      2. associate-/r* 87.6%

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

      3. log-rec 87.6%

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

      4. mul-1-neg 87.6%

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

      5. associate-/r* 87.6%

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

      6. metadata-eval 87.6%

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

   6. Simplified 87.6%

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

      1. associate-/r/ 87.6%

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

      2. distribute-lft1-in 87.6%

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

      3. +-commutative 87.6%

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

      4. associate-/r/ 87.6%

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

      5. metadata-eval 87.6%

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

      6. metadata-eval 87.6%

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

      7. cancel-sign-sub-inv 87.6%

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

      8. *-un-lft-identity 87.6%

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

   8. Applied egg-rr 87.6%

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

      1. *-commutative 87.6%

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

      2. distribute-rgt-out-- 87.7%

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

      3. *-un-lft-identity 87.7%

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

      4. *-commutative 87.7%

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

   10. Applied egg-rr 87.7%

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

   if -7.19999999999999935e60 < z < 1.50000000000000003e91

   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. associate-+l- 99.8%

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

      3. fma-neg 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-neg-out 99.8%

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

      7. remove-double-neg 99.8%

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

      8. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 95.5%

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

      1. +-commutative 95.5%

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

      2. +-commutative 95.5%

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

      3. *-commutative 95.5%

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

      4. associate--l+ 95.5%

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

      5. *-commutative 95.5%

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

      6. +-commutative 95.5%

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

   6. Simplified 95.5%

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

   if 1.9000000000000001e133 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+l- 100.0%

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

      3. fma-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-out 100.0%

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

      7. remove-double-neg 100.0%

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

      8. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 96.2%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+60}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+91}:\\ \;\;\;\;y + \left(x - \left(y + 0.5\right) \cdot \log y\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+133}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]

Alternative 7: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-104}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-62}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+146}:\\ \;\;\;\;\left(x + -1\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.4e-104)
   (- x z)
   (if (<= y 5.4e-62)
     (- (* (log y) -0.5) z)
     (if (<= y 2.45e+146) (- (+ x -1.0) z) (* y (- 1.0 (log y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.4e-104) {
		tmp = x - z;
	} else if (y <= 5.4e-62) {
		tmp = (log(y) * -0.5) - z;
	} else if (y <= 2.45e+146) {
		tmp = (x + -1.0) - z;
	} else {
		tmp = y * (1.0 - log(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.4d-104) then
        tmp = x - z
    else if (y <= 5.4d-62) then
        tmp = (log(y) * (-0.5d0)) - z
    else if (y <= 2.45d+146) then
        tmp = (x + (-1.0d0)) - z
    else
        tmp = y * (1.0d0 - log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.4e-104) {
		tmp = x - z;
	} else if (y <= 5.4e-62) {
		tmp = (Math.log(y) * -0.5) - z;
	} else if (y <= 2.45e+146) {
		tmp = (x + -1.0) - z;
	} else {
		tmp = y * (1.0 - Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.4e-104:
		tmp = x - z
	elif y <= 5.4e-62:
		tmp = (math.log(y) * -0.5) - z
	elif y <= 2.45e+146:
		tmp = (x + -1.0) - z
	else:
		tmp = y * (1.0 - math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.4e-104)
		tmp = Float64(x - z);
	elseif (y <= 5.4e-62)
		tmp = Float64(Float64(log(y) * -0.5) - z);
	elseif (y <= 2.45e+146)
		tmp = Float64(Float64(x + -1.0) - z);
	else
		tmp = Float64(y * Float64(1.0 - log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.4e-104)
		tmp = x - z;
	elseif (y <= 5.4e-62)
		tmp = (log(y) * -0.5) - z;
	elseif (y <= 2.45e+146)
		tmp = (x + -1.0) - z;
	else
		tmp = y * (1.0 - log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.4e-104], N[(x - z), $MachinePrecision], If[LessEqual[y, 5.4e-62], N[(N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[y, 2.45e+146], N[(N[(x + -1.0), $MachinePrecision] - z), $MachinePrecision], N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 2.4000000000000001e-104

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+l- 100.0%

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

      3. fma-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-out 100.0%

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

      7. remove-double-neg 100.0%

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

      8. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 83.5%

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

   if 2.4000000000000001e-104 < y < 5.40000000000000039e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in x around 0 75.6%

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

      1. *-commutative 75.6%

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

   5. Simplified 75.6%

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

   if 5.40000000000000039e-62 < y < 2.4500000000000001e146

   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. expm1-log1p-u 99.9%

         \[\leadsto \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y\right)\right)}\right) - z \]

      2. expm1-udef 99.9%

         \[\leadsto \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + \color{blue}{\left(e^{\mathsf{log1p}\left(y\right)} - 1\right)}\right) - z \]

      3. associate-+r- 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + e^{\mathsf{log1p}\left(y\right)}\right) - 1\right)} - z \]

      4. cancel-sign-sub-inv 99.9%

         \[\leadsto \left(\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right)\right) \cdot \log y\right)} + e^{\mathsf{log1p}\left(y\right)}\right) - 1\right) - z \]

      5. *-commutative 99.9%

         \[\leadsto \left(\left(\left(x + \color{blue}{\log y \cdot \left(-\left(y + 0.5\right)\right)}\right) + e^{\mathsf{log1p}\left(y\right)}\right) - 1\right) - z \]

      6. neg-sub0 99.9%

         \[\leadsto \left(\left(\left(x + \log y \cdot \color{blue}{\left(0 - \left(y + 0.5\right)\right)}\right) + e^{\mathsf{log1p}\left(y\right)}\right) - 1\right) - z \]

      7. +-commutative 99.9%

         \[\leadsto \left(\left(\left(x + \log y \cdot \left(0 - \color{blue}{\left(0.5 + y\right)}\right)\right) + e^{\mathsf{log1p}\left(y\right)}\right) - 1\right) - z \]

      8. associate--r+ 99.9%

         \[\leadsto \left(\left(\left(x + \log y \cdot \color{blue}{\left(\left(0 - 0.5\right) - y\right)}\right) + e^{\mathsf{log1p}\left(y\right)}\right) - 1\right) - z \]

      9. metadata-eval 99.9%

         \[\leadsto \left(\left(\left(x + \log y \cdot \left(\color{blue}{-0.5} - y\right)\right) + e^{\mathsf{log1p}\left(y\right)}\right) - 1\right) - z \]

   3. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(\left(\left(x + \log y \cdot \left(-0.5 - y\right)\right) + e^{\mathsf{log1p}\left(y\right)}\right) - 1\right)} - z \]

   4. Taylor expanded in x around inf 75.9%

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

   if 2.4500000000000001e146 < y

   1. Initial program 99.6%

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

      1. associate--l+ 99.5%

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

      2. associate-+l- 99.5%

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

      3. fma-neg 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-neg-out 99.6%

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

      7. remove-double-neg 99.6%

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

      8. sub-neg 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 80.0%

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

      1. cancel-sign-sub-inv 80.0%

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

      2. metadata-eval 80.0%

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

      3. log-rec 80.0%

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

      4. neg-mul-1 80.0%

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

      5. associate-*r* 80.0%

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

      6. metadata-eval 80.0%

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

      7. neg-mul-1 80.0%

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

      8. sub-neg 80.0%

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

   6. Simplified 80.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-104}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-62}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+146}:\\ \;\;\;\;\left(x + -1\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \]

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 9: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{+146}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.85e+146) (- x z) (* y (- 1.0 (log y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.85e+146) {
		tmp = x - z;
	} else {
		tmp = y * (1.0 - log(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.85d+146) then
        tmp = x - z
    else
        tmp = y * (1.0d0 - log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.85e+146) {
		tmp = x - z;
	} else {
		tmp = y * (1.0 - Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.85e+146:
		tmp = x - z
	else:
		tmp = y * (1.0 - math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.85e+146)
		tmp = Float64(x - z);
	else
		tmp = Float64(y * Float64(1.0 - log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.85e+146)
		tmp = x - z;
	else
		tmp = y * (1.0 - log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.85e+146], N[(x - z), $MachinePrecision], N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.85000000000000002e146

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-+l- 99.9%

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

      3. fma-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-neg-out 99.9%

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

      7. remove-double-neg 99.9%

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

      8. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.9%

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

   if 1.85000000000000002e146 < y

   1. Initial program 99.6%

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

      1. associate--l+ 99.5%

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

      2. associate-+l- 99.5%

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

      3. fma-neg 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-neg-out 99.6%

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

      7. remove-double-neg 99.6%

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

      8. sub-neg 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 80.0%

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

      1. cancel-sign-sub-inv 80.0%

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

      2. metadata-eval 80.0%

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

      3. log-rec 80.0%

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

      4. neg-mul-1 80.0%

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

      5. associate-*r* 80.0%

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

      6. metadata-eval 80.0%

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

      7. neg-mul-1 80.0%

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

      8. sub-neg 80.0%

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

   6. Simplified 80.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{+146}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \]

Alternative 10: 48.2% accurate, 18.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+17} \lor \neg \left(z \leq 1.9 \cdot 10^{+89}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.8e+17) (not (<= z 1.9e+89))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.8e+17) || !(z <= 1.9e+89)) {
		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 <= (-9.8d+17)) .or. (.not. (z <= 1.9d+89))) 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 <= -9.8e+17) || !(z <= 1.9e+89)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.8e+17) or not (z <= 1.9e+89):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.8e+17) || !(z <= 1.9e+89))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.8e+17) || ~((z <= 1.9e+89)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.8e+17], N[Not[LessEqual[z, 1.9e+89]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if z < -9.8e17 or 1.90000000000000012e89 < z

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-+l- 99.9%

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

      3. fma-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-neg-out 99.9%

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

      7. remove-double-neg 99.9%

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

      8. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 63.9%

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

      1. mul-1-neg 63.9%

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

   6. Simplified 63.9%

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

   if -9.8e17 < z < 1.90000000000000012e89

   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. associate-+l- 99.8%

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

      3. fma-neg 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-neg-out 99.8%

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

      7. remove-double-neg 99.8%

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

      8. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 42.1%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+17} \lor \neg \left(z \leq 1.9 \cdot 10^{+89}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 58.1% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. associate--l+ 99.8%

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

   2. associate-+l- 99.8%

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

   3. fma-neg 99.9%

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

   4. sub-neg 99.9%

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

   5. +-commutative 99.9%

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

   6. distribute-neg-out 99.9%

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

   7. remove-double-neg 99.9%

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

   8. sub-neg 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in z around inf 60.3%

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

5. Final simplification 60.3%

   \[\leadsto x - z \]

Alternative 12: 29.7% 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. associate-+l- 99.8%

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

   3. fma-neg 99.9%

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

   4. sub-neg 99.9%

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

   5. +-commutative 99.9%

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

   6. distribute-neg-out 99.9%

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

   7. remove-double-neg 99.9%

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

   8. sub-neg 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 31.0%

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

5. Final simplification 31.0%

   \[\leadsto x \]

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023301 
(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))