Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.8s

Alternatives: 13

Speedup: 1.0×

• Could not converge on a ground truth

  1. x = 4.824803338075312e+215
  2. y = 3.123614889168347e+268
  3. z = -2.2153380412476877e+148

• 59.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[e^{\left(x + y \cdot \log y\right) - z} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 73.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-79}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 1250000000:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 5e-79) (exp x) (if (<= y 1250000000.0) (exp (- z)) (pow y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5e-79) {
		tmp = exp(x);
	} else if (y <= 1250000000.0) {
		tmp = exp(-z);
	} else {
		tmp = pow(y, 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 <= 5d-79) then
        tmp = exp(x)
    else if (y <= 1250000000.0d0) then
        tmp = exp(-z)
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 5e-79) {
		tmp = Math.exp(x);
	} else if (y <= 1250000000.0) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5e-79:
		tmp = math.exp(x)
	elif y <= 1250000000.0:
		tmp = math.exp(-z)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5e-79)
		tmp = exp(x);
	elseif (y <= 1250000000.0)
		tmp = exp(Float64(-z));
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5e-79)
		tmp = exp(x);
	elseif (y <= 1250000000.0)
		tmp = exp(-z);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5e-79], N[Exp[x], $MachinePrecision], If[LessEqual[y, 1250000000.0], N[Exp[(-z)], $MachinePrecision], N[Power[y, y], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 4.99999999999999999e-79

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.4%

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

   if 4.99999999999999999e-79 < y < 1.25e9

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.4%

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

      1. neg-mul-1 83.4%

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

   5. Simplified 83.4%

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

   if 1.25e9 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 69.8%

         \[\leadsto \color{blue}{e^{y \cdot \log y} \cdot e^{x - z}} \]

      4. *-commutative 69.8%

         \[\leadsto e^{\color{blue}{\log y \cdot y}} \cdot e^{x - z} \]

      5. exp-to-pow 69.8%

         \[\leadsto \color{blue}{{y}^{y}} \cdot e^{x - z} \]

   3. Simplified 69.8%

      \[\leadsto \color{blue}{{y}^{y} \cdot e^{x - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 80.3%

      \[\leadsto {y}^{y} \cdot \color{blue}{e^{x}} \]

   6. Taylor expanded in x around 0 85.6%

      \[\leadsto \color{blue}{{y}^{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 72.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+106}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-23}:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.2e+106) 0.0 (if (<= x 8.2e-23) (exp (- z)) (exp x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.2e+106) {
		tmp = 0.0;
	} else if (x <= 8.2e-23) {
		tmp = exp(-z);
	} else {
		tmp = exp(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-9.2d+106)) then
        tmp = 0.0d0
    else if (x <= 8.2d-23) then
        tmp = exp(-z)
    else
        tmp = exp(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.2e+106) {
		tmp = 0.0;
	} else if (x <= 8.2e-23) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.2e+106:
		tmp = 0.0
	elif x <= 8.2e-23:
		tmp = math.exp(-z)
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.2e+106)
		tmp = 0.0;
	elseif (x <= 8.2e-23)
		tmp = exp(Float64(-z));
	else
		tmp = exp(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.2e+106)
		tmp = 0.0;
	elseif (x <= 8.2e-23)
		tmp = exp(-z);
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.2e+106], 0.0, If[LessEqual[x, 8.2e-23], N[Exp[(-z)], $MachinePrecision], N[Exp[x], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.2000000000000008e106

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 54.6%

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

      1. neg-mul-1 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in z around 0 2.7%

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

      1. mul-1-neg 2.7%

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

      2. unsub-neg 2.7%

         \[\leadsto \color{blue}{1 - z} \]

   8. Simplified 2.7%

      \[\leadsto \color{blue}{1 - z} \]

   9. Taylor expanded in z around inf 3.4%

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

       1. neg-mul-1 3.4%

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

   11. Simplified 3.4%

       \[\leadsto \color{blue}{-z} \]
   12. Step-by-step derivation

       1. add-log-exp 31.3%

          \[\leadsto \color{blue}{\log \left(e^{-z}\right)} \]

       2. exp-neg 31.3%

          \[\leadsto \log \color{blue}{\left(\frac{1}{e^{z}}\right)} \]

       3. add-sqr-sqrt 31.3%

          \[\leadsto \log \left(\frac{1}{\color{blue}{\sqrt{e^{z}} \cdot \sqrt{e^{z}}}}\right) \]

       4. associate-/r* 31.3%

          \[\leadsto \log \color{blue}{\left(\frac{\frac{1}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right)} \]

       5. metadata-eval 31.3%

          \[\leadsto \log \left(\frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       6. sqrt-div 31.3%

          \[\leadsto \log \left(\frac{\color{blue}{\sqrt{\frac{1}{e^{z}}}}}{\sqrt{e^{z}}}\right) \]

       7. exp-neg 31.3%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       8. pow1 31.3%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{-z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       9. pow1 31.3%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       10. add-sqr-sqrt 18.9%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}}}{\sqrt{e^{z}}}\right) \]

       11. sqrt-unprod 30.6%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}}}{\sqrt{e^{z}}}\right) \]

       12. sqr-neg 30.6%

           \[\leadsto \log \left(\frac{\sqrt{e^{\sqrt{\color{blue}{z \cdot z}}}}}{\sqrt{e^{z}}}\right) \]

       13. sqrt-unprod 11.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}}{\sqrt{e^{z}}}\right) \]

       14. add-sqr-sqrt 23.3%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{z}}}}{\sqrt{e^{z}}}\right) \]

       15. pow1 23.3%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       16. pow1 23.3%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       17. log-div 23.3%

           \[\leadsto \color{blue}{\log \left(\sqrt{e^{z}}\right) - \log \left(\sqrt{e^{z}}\right)} \]

   13. Applied egg-rr 90.8%

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

       1. +-inverses 90.8%

          \[\leadsto \color{blue}{0} \]

   15. Simplified 90.8%

       \[\leadsto \color{blue}{0} \]

   if -9.2000000000000008e106 < x < 8.20000000000000059e-23

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.0%

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

      1. neg-mul-1 64.0%

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

   5. Simplified 64.0%

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

   if 8.20000000000000059e-23 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.7%

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

Alternative 4: 69.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+104}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+125}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5e+104)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (<= z 3.35e+125) (exp x) 0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+104) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 3.35e+125) {
		tmp = exp(x);
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= (-9.5d+104)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if (z <= 3.35d+125) then
        tmp = exp(x)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+104) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 3.35e+125) {
		tmp = Math.exp(x);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.5e+104:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif z <= 3.35e+125:
		tmp = math.exp(x)
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5e+104)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif (z <= 3.35e+125)
		tmp = exp(x);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.5e+104)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif (z <= 3.35e+125)
		tmp = exp(x);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.5e+104], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.35e+125], N[Exp[x], $MachinePrecision], 0.0]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5e104

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 86.5%

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

      1. neg-mul-1 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in z around 0 86.5%

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(0.5 + -0.16666666666666666 \cdot z\right) - 1\right)} \]

   7. Taylor expanded in z around inf 86.5%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(-0.16666666666666666 \cdot z\right)} - 1\right) \]
   8. Step-by-step derivation

      1. *-commutative 86.5%

         \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   9. Simplified 86.5%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   if -9.5e104 < z < 3.3500000000000002e125

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.7%

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

   if 3.3500000000000002e125 < z

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 82.9%

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

      1. neg-mul-1 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in z around 0 1.6%

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

      1. mul-1-neg 1.6%

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

      2. unsub-neg 1.6%

         \[\leadsto \color{blue}{1 - z} \]

   8. Simplified 1.6%

      \[\leadsto \color{blue}{1 - z} \]

   9. Taylor expanded in z around inf 1.6%

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

       1. neg-mul-1 1.6%

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

   11. Simplified 1.6%

       \[\leadsto \color{blue}{-z} \]
   12. Step-by-step derivation

       1. add-log-exp 1.3%

          \[\leadsto \color{blue}{\log \left(e^{-z}\right)} \]

       2. exp-neg 1.3%

          \[\leadsto \log \color{blue}{\left(\frac{1}{e^{z}}\right)} \]

       3. add-sqr-sqrt 1.3%

          \[\leadsto \log \left(\frac{1}{\color{blue}{\sqrt{e^{z}} \cdot \sqrt{e^{z}}}}\right) \]

       4. associate-/r* 1.3%

          \[\leadsto \log \color{blue}{\left(\frac{\frac{1}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right)} \]

       5. metadata-eval 1.3%

          \[\leadsto \log \left(\frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       6. sqrt-div 1.3%

          \[\leadsto \log \left(\frac{\color{blue}{\sqrt{\frac{1}{e^{z}}}}}{\sqrt{e^{z}}}\right) \]

       7. exp-neg 1.3%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       8. pow1 1.3%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{-z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       9. pow1 1.3%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       10. add-sqr-sqrt 0.0%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}}}{\sqrt{e^{z}}}\right) \]

       11. sqrt-unprod 0.0%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}}}{\sqrt{e^{z}}}\right) \]

       12. sqr-neg 0.0%

           \[\leadsto \log \left(\frac{\sqrt{e^{\sqrt{\color{blue}{z \cdot z}}}}}{\sqrt{e^{z}}}\right) \]

       13. sqrt-unprod 0.0%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}}{\sqrt{e^{z}}}\right) \]

       14. add-sqr-sqrt 0.0%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{z}}}}{\sqrt{e^{z}}}\right) \]

       15. pow1 0.0%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       16. pow1 0.0%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       17. log-div 0.0%

           \[\leadsto \color{blue}{\log \left(\sqrt{e^{z}}\right) - \log \left(\sqrt{e^{z}}\right)} \]

   13. Applied egg-rr 82.9%

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

       1. +-inverses 82.9%

          \[\leadsto \color{blue}{0} \]

   15. Simplified 82.9%

       \[\leadsto \color{blue}{0} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+104}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+125}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.6 \cdot 10^{+24}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 7.6e+24) (exp (- x z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.6e+24) {
		tmp = exp((x - z));
	} else {
		tmp = pow(y, 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 <= 7.6d+24) then
        tmp = exp((x - z))
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.6e+24) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7.6e+24:
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7.6e+24)
		tmp = exp(Float64(x - z));
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7.6e+24)
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7.6e+24], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.6000000000000003e24

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.9%

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

   if 7.6000000000000003e24 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 69.4%

         \[\leadsto \color{blue}{e^{y \cdot \log y} \cdot e^{x - z}} \]

      4. *-commutative 69.4%

         \[\leadsto e^{\color{blue}{\log y \cdot y}} \cdot e^{x - z} \]

      5. exp-to-pow 69.4%

         \[\leadsto \color{blue}{{y}^{y}} \cdot e^{x - z} \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{{y}^{y} \cdot e^{x - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 80.3%

      \[\leadsto {y}^{y} \cdot \color{blue}{e^{x}} \]

   6. Taylor expanded in x around 0 85.8%

      \[\leadsto \color{blue}{{y}^{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 54.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+102}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-24}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5e+102)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (<= z 5.3e-24)
     (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))
     0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+102) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 5.3e-24) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= (-9.5d+102)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if (z <= 5.3d-24) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+102) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 5.3e-24) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.5e+102:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif z <= 5.3e-24:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5e+102)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif (z <= 5.3e-24)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.5e+102)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif (z <= 5.3e-24)
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.5e+102], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e-24], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999992e102

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 86.5%

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

      1. neg-mul-1 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in z around 0 86.5%

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(0.5 + -0.16666666666666666 \cdot z\right) - 1\right)} \]

   7. Taylor expanded in z around inf 86.5%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(-0.16666666666666666 \cdot z\right)} - 1\right) \]
   8. Step-by-step derivation

      1. *-commutative 86.5%

         \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   9. Simplified 86.5%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   if -9.4999999999999992e102 < z < 5.29999999999999969e-24

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 64.2%

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

   4. Taylor expanded in x around 0 45.2%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto 1 + x \cdot \left(1 + x \cdot \left(0.5 + \color{blue}{x \cdot 0.16666666666666666}\right)\right) \]

   6. Simplified 45.2%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)} \]

   if 5.29999999999999969e-24 < z

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.4%

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

      1. neg-mul-1 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in z around 0 3.1%

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

      1. mul-1-neg 3.1%

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

      2. unsub-neg 3.1%

         \[\leadsto \color{blue}{1 - z} \]

   8. Simplified 3.1%

      \[\leadsto \color{blue}{1 - z} \]

   9. Taylor expanded in z around inf 1.6%

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

       1. neg-mul-1 1.6%

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

   11. Simplified 1.6%

       \[\leadsto \color{blue}{-z} \]
   12. Step-by-step derivation

       1. add-log-exp 3.4%

          \[\leadsto \color{blue}{\log \left(e^{-z}\right)} \]

       2. exp-neg 4.5%

          \[\leadsto \log \color{blue}{\left(\frac{1}{e^{z}}\right)} \]

       3. add-sqr-sqrt 4.5%

          \[\leadsto \log \left(\frac{1}{\color{blue}{\sqrt{e^{z}} \cdot \sqrt{e^{z}}}}\right) \]

       4. associate-/r* 4.5%

          \[\leadsto \log \color{blue}{\left(\frac{\frac{1}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right)} \]

       5. metadata-eval 4.5%

          \[\leadsto \log \left(\frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       6. sqrt-div 4.5%

          \[\leadsto \log \left(\frac{\color{blue}{\sqrt{\frac{1}{e^{z}}}}}{\sqrt{e^{z}}}\right) \]

       7. exp-neg 3.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       8. pow1 3.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{-z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       9. pow1 3.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       10. add-sqr-sqrt 0.0%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}}}{\sqrt{e^{z}}}\right) \]

       11. sqrt-unprod 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}}}{\sqrt{e^{z}}}\right) \]

       12. sqr-neg 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\sqrt{\color{blue}{z \cdot z}}}}}{\sqrt{e^{z}}}\right) \]

       13. sqrt-unprod 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}}{\sqrt{e^{z}}}\right) \]

       14. add-sqr-sqrt 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{z}}}}{\sqrt{e^{z}}}\right) \]

       15. pow1 3.7%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       16. pow1 3.7%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       17. log-div 3.7%

           \[\leadsto \color{blue}{\log \left(\sqrt{e^{z}}\right) - \log \left(\sqrt{e^{z}}\right)} \]

   13. Applied egg-rr 64.3%

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

       1. +-inverses 64.3%

          \[\leadsto \color{blue}{0} \]

   15. Simplified 64.3%

       \[\leadsto \color{blue}{0} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+102}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-24}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.4% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+102}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-24}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.5e+102)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (<= z 5.3e-24) (+ 1.0 (* x (+ 1.0 (* x 0.5)))) 0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+102) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 5.3e-24) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= (-4.5d+102)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if (z <= 5.3d-24) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+102) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 5.3e-24) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.5e+102:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif z <= 5.3e-24:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.5e+102)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif (z <= 5.3e-24)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.5e+102)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif (z <= 5.3e-24)
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.5e+102], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e-24], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]

Derivation

1. Split input into 3 regimes

2. if z < -4.50000000000000021e102

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 86.5%

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

      1. neg-mul-1 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in z around 0 86.5%

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(0.5 + -0.16666666666666666 \cdot z\right) - 1\right)} \]

   7. Taylor expanded in z around inf 86.5%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(-0.16666666666666666 \cdot z\right)} - 1\right) \]
   8. Step-by-step derivation

      1. *-commutative 86.5%

         \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   9. Simplified 86.5%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   if -4.50000000000000021e102 < z < 5.29999999999999969e-24

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 64.2%

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

   4. Taylor expanded in x around 0 39.8%

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

      1. *-commutative 39.8%

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

   6. Simplified 39.8%

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

   if 5.29999999999999969e-24 < z

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.4%

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

      1. neg-mul-1 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in z around 0 3.1%

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

      1. mul-1-neg 3.1%

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

      2. unsub-neg 3.1%

         \[\leadsto \color{blue}{1 - z} \]

   8. Simplified 3.1%

      \[\leadsto \color{blue}{1 - z} \]

   9. Taylor expanded in z around inf 1.6%

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

       1. neg-mul-1 1.6%

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

   11. Simplified 1.6%

       \[\leadsto \color{blue}{-z} \]
   12. Step-by-step derivation

       1. add-log-exp 3.4%

          \[\leadsto \color{blue}{\log \left(e^{-z}\right)} \]

       2. exp-neg 4.5%

          \[\leadsto \log \color{blue}{\left(\frac{1}{e^{z}}\right)} \]

       3. add-sqr-sqrt 4.5%

          \[\leadsto \log \left(\frac{1}{\color{blue}{\sqrt{e^{z}} \cdot \sqrt{e^{z}}}}\right) \]

       4. associate-/r* 4.5%

          \[\leadsto \log \color{blue}{\left(\frac{\frac{1}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right)} \]

       5. metadata-eval 4.5%

          \[\leadsto \log \left(\frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       6. sqrt-div 4.5%

          \[\leadsto \log \left(\frac{\color{blue}{\sqrt{\frac{1}{e^{z}}}}}{\sqrt{e^{z}}}\right) \]

       7. exp-neg 3.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       8. pow1 3.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{-z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       9. pow1 3.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       10. add-sqr-sqrt 0.0%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}}}{\sqrt{e^{z}}}\right) \]

       11. sqrt-unprod 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}}}{\sqrt{e^{z}}}\right) \]

       12. sqr-neg 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\sqrt{\color{blue}{z \cdot z}}}}}{\sqrt{e^{z}}}\right) \]

       13. sqrt-unprod 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}}{\sqrt{e^{z}}}\right) \]

       14. add-sqr-sqrt 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{z}}}}{\sqrt{e^{z}}}\right) \]

       15. pow1 3.7%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       16. pow1 3.7%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       17. log-div 3.7%

           \[\leadsto \color{blue}{\log \left(\sqrt{e^{z}}\right) - \log \left(\sqrt{e^{z}}\right)} \]

   13. Applied egg-rr 64.3%

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

       1. +-inverses 64.3%

          \[\leadsto \color{blue}{0} \]

   15. Simplified 64.3%

       \[\leadsto \color{blue}{0} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+102}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-24}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.9% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-25}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+108}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.1e-25)
   0.0
   (if (<= x 3.5e+108)
     (+ 1.0 (* z (+ (* z 0.5) -1.0)))
     (+ 1.0 (* x (+ 1.0 (* x 0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.1e-25) {
		tmp = 0.0;
	} else if (x <= 3.5e+108) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 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 (x <= (-4.1d-25)) then
        tmp = 0.0d0
    else if (x <= 3.5d+108) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.1e-25) {
		tmp = 0.0;
	} else if (x <= 3.5e+108) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.1e-25:
		tmp = 0.0
	elif x <= 3.5e+108:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.1e-25)
		tmp = 0.0;
	elseif (x <= 3.5e+108)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.1e-25)
		tmp = 0.0;
	elseif (x <= 3.5e+108)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.1e-25], 0.0, If[LessEqual[x, 3.5e+108], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.09999999999999987e-25

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 59.0%

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

      1. neg-mul-1 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in z around 0 5.1%

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

      1. mul-1-neg 5.1%

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

      2. unsub-neg 5.1%

         \[\leadsto \color{blue}{1 - z} \]

   8. Simplified 5.1%

      \[\leadsto \color{blue}{1 - z} \]

   9. Taylor expanded in z around inf 3.3%

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

       1. neg-mul-1 3.3%

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

   11. Simplified 3.3%

       \[\leadsto \color{blue}{-z} \]
   12. Step-by-step derivation

       1. add-log-exp 32.5%

          \[\leadsto \color{blue}{\log \left(e^{-z}\right)} \]

       2. exp-neg 33.9%

          \[\leadsto \log \color{blue}{\left(\frac{1}{e^{z}}\right)} \]

       3. add-sqr-sqrt 33.9%

          \[\leadsto \log \left(\frac{1}{\color{blue}{\sqrt{e^{z}} \cdot \sqrt{e^{z}}}}\right) \]

       4. associate-/r* 33.9%

          \[\leadsto \log \color{blue}{\left(\frac{\frac{1}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right)} \]

       5. metadata-eval 33.9%

          \[\leadsto \log \left(\frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       6. sqrt-div 33.9%

          \[\leadsto \log \left(\frac{\color{blue}{\sqrt{\frac{1}{e^{z}}}}}{\sqrt{e^{z}}}\right) \]

       7. exp-neg 32.5%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       8. pow1 32.5%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{-z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       9. pow1 32.5%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       10. add-sqr-sqrt 23.2%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}}}{\sqrt{e^{z}}}\right) \]

       11. sqrt-unprod 33.3%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}}}{\sqrt{e^{z}}}\right) \]

       12. sqr-neg 33.3%

           \[\leadsto \log \left(\frac{\sqrt{e^{\sqrt{\color{blue}{z \cdot z}}}}}{\sqrt{e^{z}}}\right) \]

       13. sqrt-unprod 10.1%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}}{\sqrt{e^{z}}}\right) \]

       14. add-sqr-sqrt 18.8%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{z}}}}{\sqrt{e^{z}}}\right) \]

       15. pow1 18.8%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       16. pow1 18.8%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       17. log-div 18.8%

           \[\leadsto \color{blue}{\log \left(\sqrt{e^{z}}\right) - \log \left(\sqrt{e^{z}}\right)} \]

   13. Applied egg-rr 74.7%

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

       1. +-inverses 74.7%

          \[\leadsto \color{blue}{0} \]

   15. Simplified 74.7%

       \[\leadsto \color{blue}{0} \]

   if -4.09999999999999987e-25 < x < 3.5000000000000002e108

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 59.2%

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

      1. neg-mul-1 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in z around 0 35.6%

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

   if 3.5000000000000002e108 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.7%

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

   4. Taylor expanded in x around 0 70.5%

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

      1. *-commutative 70.5%

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

   6. Simplified 70.5%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot 0.5\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-25}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+108}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.6% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-27}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+108}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.5e-27)
   0.0
   (if (<= x 3.5e+108)
     (+ 1.0 (* z (* z 0.5)))
     (+ 1.0 (* x (+ 1.0 (* x 0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.5e-27) {
		tmp = 0.0;
	} else if (x <= 3.5e+108) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 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 (x <= (-4.5d-27)) then
        tmp = 0.0d0
    else if (x <= 3.5d+108) then
        tmp = 1.0d0 + (z * (z * 0.5d0))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.5e-27) {
		tmp = 0.0;
	} else if (x <= 3.5e+108) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.5e-27:
		tmp = 0.0
	elif x <= 3.5e+108:
		tmp = 1.0 + (z * (z * 0.5))
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.5e-27)
		tmp = 0.0;
	elseif (x <= 3.5e+108)
		tmp = Float64(1.0 + Float64(z * Float64(z * 0.5)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.5e-27)
		tmp = 0.0;
	elseif (x <= 3.5e+108)
		tmp = 1.0 + (z * (z * 0.5));
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.5e-27], 0.0, If[LessEqual[x, 3.5e+108], N[(1.0 + N[(z * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5000000000000002e-27

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 59.0%

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

      1. neg-mul-1 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in z around 0 5.1%

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

      1. mul-1-neg 5.1%

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

      2. unsub-neg 5.1%

         \[\leadsto \color{blue}{1 - z} \]

   8. Simplified 5.1%

      \[\leadsto \color{blue}{1 - z} \]

   9. Taylor expanded in z around inf 3.3%

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

       1. neg-mul-1 3.3%

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

   11. Simplified 3.3%

       \[\leadsto \color{blue}{-z} \]
   12. Step-by-step derivation

       1. add-log-exp 32.5%

          \[\leadsto \color{blue}{\log \left(e^{-z}\right)} \]

       2. exp-neg 33.9%

          \[\leadsto \log \color{blue}{\left(\frac{1}{e^{z}}\right)} \]

       3. add-sqr-sqrt 33.9%

          \[\leadsto \log \left(\frac{1}{\color{blue}{\sqrt{e^{z}} \cdot \sqrt{e^{z}}}}\right) \]

       4. associate-/r* 33.9%

          \[\leadsto \log \color{blue}{\left(\frac{\frac{1}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right)} \]

       5. metadata-eval 33.9%

          \[\leadsto \log \left(\frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       6. sqrt-div 33.9%

          \[\leadsto \log \left(\frac{\color{blue}{\sqrt{\frac{1}{e^{z}}}}}{\sqrt{e^{z}}}\right) \]

       7. exp-neg 32.5%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       8. pow1 32.5%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{-z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       9. pow1 32.5%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       10. add-sqr-sqrt 23.2%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}}}{\sqrt{e^{z}}}\right) \]

       11. sqrt-unprod 33.3%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}}}{\sqrt{e^{z}}}\right) \]

       12. sqr-neg 33.3%

           \[\leadsto \log \left(\frac{\sqrt{e^{\sqrt{\color{blue}{z \cdot z}}}}}{\sqrt{e^{z}}}\right) \]

       13. sqrt-unprod 10.1%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}}{\sqrt{e^{z}}}\right) \]

       14. add-sqr-sqrt 18.8%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{z}}}}{\sqrt{e^{z}}}\right) \]

       15. pow1 18.8%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       16. pow1 18.8%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       17. log-div 18.8%

           \[\leadsto \color{blue}{\log \left(\sqrt{e^{z}}\right) - \log \left(\sqrt{e^{z}}\right)} \]

   13. Applied egg-rr 74.7%

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

       1. +-inverses 74.7%

          \[\leadsto \color{blue}{0} \]

   15. Simplified 74.7%

       \[\leadsto \color{blue}{0} \]

   if -4.5000000000000002e-27 < x < 3.5000000000000002e108

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 59.2%

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

      1. neg-mul-1 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in z around 0 35.6%

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

   7. Taylor expanded in z around inf 34.6%

      \[\leadsto 1 + z \cdot \color{blue}{\left(0.5 \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.6%

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

   9. Simplified 34.6%

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

   if 3.5000000000000002e108 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.7%

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

   4. Taylor expanded in x around 0 70.5%

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

      1. *-commutative 70.5%

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

   6. Simplified 70.5%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot 0.5\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 32.4% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3500:\\ \;\;\;\;0\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3500.0) 0.0 (if (<= z 3.5e-26) (+ x 1.0) 0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3500.0) {
		tmp = 0.0;
	} else if (z <= 3.5e-26) {
		tmp = x + 1.0;
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= (-3500.0d0)) then
        tmp = 0.0d0
    else if (z <= 3.5d-26) then
        tmp = x + 1.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3500.0) {
		tmp = 0.0;
	} else if (z <= 3.5e-26) {
		tmp = x + 1.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3500.0:
		tmp = 0.0
	elif z <= 3.5e-26:
		tmp = x + 1.0
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3500.0)
		tmp = 0.0;
	elseif (z <= 3.5e-26)
		tmp = Float64(x + 1.0);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3500.0)
		tmp = 0.0;
	elseif (z <= 3.5e-26)
		tmp = x + 1.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3500.0], 0.0, If[LessEqual[z, 3.5e-26], N[(x + 1.0), $MachinePrecision], 0.0]]

Derivation

1. Split input into 2 regimes

2. if z < -3500 or 3.49999999999999985e-26 < z

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 73.3%

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

      1. neg-mul-1 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in z around 0 3.9%

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

      1. mul-1-neg 3.9%

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

      2. unsub-neg 3.9%

         \[\leadsto \color{blue}{1 - z} \]

   8. Simplified 3.9%

      \[\leadsto \color{blue}{1 - z} \]

   9. Taylor expanded in z around inf 3.0%

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

       1. neg-mul-1 3.0%

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

   11. Simplified 3.0%

       \[\leadsto \color{blue}{-z} \]
   12. Step-by-step derivation

       1. add-log-exp 38.4%

          \[\leadsto \color{blue}{\log \left(e^{-z}\right)} \]

       2. exp-neg 39.0%

          \[\leadsto \log \color{blue}{\left(\frac{1}{e^{z}}\right)} \]

       3. add-sqr-sqrt 39.0%

          \[\leadsto \log \left(\frac{1}{\color{blue}{\sqrt{e^{z}} \cdot \sqrt{e^{z}}}}\right) \]

       4. associate-/r* 39.0%

          \[\leadsto \log \color{blue}{\left(\frac{\frac{1}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right)} \]

       5. metadata-eval 39.0%

          \[\leadsto \log \left(\frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       6. sqrt-div 39.0%

          \[\leadsto \log \left(\frac{\color{blue}{\sqrt{\frac{1}{e^{z}}}}}{\sqrt{e^{z}}}\right) \]

       7. exp-neg 38.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       8. pow1 38.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{-z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       9. pow1 38.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       10. add-sqr-sqrt 36.5%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}}}{\sqrt{e^{z}}}\right) \]

       11. sqrt-unprod 38.6%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}}}{\sqrt{e^{z}}}\right) \]

       12. sqr-neg 38.6%

           \[\leadsto \log \left(\frac{\sqrt{e^{\sqrt{\color{blue}{z \cdot z}}}}}{\sqrt{e^{z}}}\right) \]

       13. sqrt-unprod 2.1%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}}{\sqrt{e^{z}}}\right) \]

       14. add-sqr-sqrt 2.1%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{z}}}}{\sqrt{e^{z}}}\right) \]

       15. pow1 2.1%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       16. pow1 2.1%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       17. log-div 2.1%

           \[\leadsto \color{blue}{\log \left(\sqrt{e^{z}}\right) - \log \left(\sqrt{e^{z}}\right)} \]

   13. Applied egg-rr 43.8%

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

       1. +-inverses 43.8%

          \[\leadsto \color{blue}{0} \]

   15. Simplified 43.8%

       \[\leadsto \color{blue}{0} \]

   if -3500 < z < 3.49999999999999985e-26

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 64.6%

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

   4. Taylor expanded in x around 0 27.3%

      \[\leadsto \color{blue}{1 + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3500:\\ \;\;\;\;0\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.8% accurate, 17.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.3 \cdot 10^{-28}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 3.3e-28) (+ 1.0 (* z (* z 0.5))) 0.0))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.3e-28) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= 3.3d-28) then
        tmp = 1.0d0 + (z * (z * 0.5d0))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.3e-28) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 3.3e-28:
		tmp = 1.0 + (z * (z * 0.5))
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 3.3e-28)
		tmp = Float64(1.0 + Float64(z * Float64(z * 0.5)));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 3.3e-28)
		tmp = 1.0 + (z * (z * 0.5));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 3.3e-28], N[(1.0 + N[(z * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if z < 3.3000000000000002e-28

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 50.1%

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

      1. neg-mul-1 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in z around 0 33.4%

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

   7. Taylor expanded in z around inf 33.1%

      \[\leadsto 1 + z \cdot \color{blue}{\left(0.5 \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.1%

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

   9. Simplified 33.1%

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

   if 3.3000000000000002e-28 < z

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.4%

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

      1. neg-mul-1 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in z around 0 3.1%

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

      1. mul-1-neg 3.1%

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

      2. unsub-neg 3.1%

         \[\leadsto \color{blue}{1 - z} \]

   8. Simplified 3.1%

      \[\leadsto \color{blue}{1 - z} \]

   9. Taylor expanded in z around inf 1.6%

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

       1. neg-mul-1 1.6%

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

   11. Simplified 1.6%

       \[\leadsto \color{blue}{-z} \]
   12. Step-by-step derivation

       1. add-log-exp 3.4%

          \[\leadsto \color{blue}{\log \left(e^{-z}\right)} \]

       2. exp-neg 4.5%

          \[\leadsto \log \color{blue}{\left(\frac{1}{e^{z}}\right)} \]

       3. add-sqr-sqrt 4.5%

          \[\leadsto \log \left(\frac{1}{\color{blue}{\sqrt{e^{z}} \cdot \sqrt{e^{z}}}}\right) \]

       4. associate-/r* 4.5%

          \[\leadsto \log \color{blue}{\left(\frac{\frac{1}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right)} \]

       5. metadata-eval 4.5%

          \[\leadsto \log \left(\frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       6. sqrt-div 4.5%

          \[\leadsto \log \left(\frac{\color{blue}{\sqrt{\frac{1}{e^{z}}}}}{\sqrt{e^{z}}}\right) \]

       7. exp-neg 3.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       8. pow1 3.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{-z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       9. pow1 3.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       10. add-sqr-sqrt 0.0%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}}}{\sqrt{e^{z}}}\right) \]

       11. sqrt-unprod 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}}}{\sqrt{e^{z}}}\right) \]

       12. sqr-neg 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\sqrt{\color{blue}{z \cdot z}}}}}{\sqrt{e^{z}}}\right) \]

       13. sqrt-unprod 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}}{\sqrt{e^{z}}}\right) \]

       14. add-sqr-sqrt 3.7%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{z}}}}{\sqrt{e^{z}}}\right) \]

       15. pow1 3.7%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       16. pow1 3.7%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       17. log-div 3.7%

           \[\leadsto \color{blue}{\log \left(\sqrt{e^{z}}\right) - \log \left(\sqrt{e^{z}}\right)} \]

   13. Applied egg-rr 64.3%

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

       1. +-inverses 64.3%

          \[\leadsto \color{blue}{0} \]

   15. Simplified 64.3%

       \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 32.1% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3500:\\ \;\;\;\;0\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-29}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3500.0) 0.0 (if (<= z 3.8e-29) 1.0 0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3500.0) {
		tmp = 0.0;
	} else if (z <= 3.8e-29) {
		tmp = 1.0;
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= (-3500.0d0)) then
        tmp = 0.0d0
    else if (z <= 3.8d-29) then
        tmp = 1.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3500.0) {
		tmp = 0.0;
	} else if (z <= 3.8e-29) {
		tmp = 1.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3500.0:
		tmp = 0.0
	elif z <= 3.8e-29:
		tmp = 1.0
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3500.0)
		tmp = 0.0;
	elseif (z <= 3.8e-29)
		tmp = 1.0;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3500.0)
		tmp = 0.0;
	elseif (z <= 3.8e-29)
		tmp = 1.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3500.0], 0.0, If[LessEqual[z, 3.8e-29], 1.0, 0.0]]

Derivation

1. Split input into 2 regimes

2. if z < -3500 or 3.79999999999999976e-29 < z

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 73.3%

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

      1. neg-mul-1 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in z around 0 3.9%

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

      1. mul-1-neg 3.9%

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

      2. unsub-neg 3.9%

         \[\leadsto \color{blue}{1 - z} \]

   8. Simplified 3.9%

      \[\leadsto \color{blue}{1 - z} \]

   9. Taylor expanded in z around inf 3.0%

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

       1. neg-mul-1 3.0%

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

   11. Simplified 3.0%

       \[\leadsto \color{blue}{-z} \]
   12. Step-by-step derivation

       1. add-log-exp 38.4%

          \[\leadsto \color{blue}{\log \left(e^{-z}\right)} \]

       2. exp-neg 39.0%

          \[\leadsto \log \color{blue}{\left(\frac{1}{e^{z}}\right)} \]

       3. add-sqr-sqrt 39.0%

          \[\leadsto \log \left(\frac{1}{\color{blue}{\sqrt{e^{z}} \cdot \sqrt{e^{z}}}}\right) \]

       4. associate-/r* 39.0%

          \[\leadsto \log \color{blue}{\left(\frac{\frac{1}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right)} \]

       5. metadata-eval 39.0%

          \[\leadsto \log \left(\frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       6. sqrt-div 39.0%

          \[\leadsto \log \left(\frac{\color{blue}{\sqrt{\frac{1}{e^{z}}}}}{\sqrt{e^{z}}}\right) \]

       7. exp-neg 38.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       8. pow1 38.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{-z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       9. pow1 38.4%

          \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

       10. add-sqr-sqrt 36.5%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}}}{\sqrt{e^{z}}}\right) \]

       11. sqrt-unprod 38.6%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}}}{\sqrt{e^{z}}}\right) \]

       12. sqr-neg 38.6%

           \[\leadsto \log \left(\frac{\sqrt{e^{\sqrt{\color{blue}{z \cdot z}}}}}{\sqrt{e^{z}}}\right) \]

       13. sqrt-unprod 2.1%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}}{\sqrt{e^{z}}}\right) \]

       14. add-sqr-sqrt 2.1%

           \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{z}}}}{\sqrt{e^{z}}}\right) \]

       15. pow1 2.1%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

       16. pow1 2.1%

           \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{z}}}}{\sqrt{e^{z}}}\right) \]

       17. log-div 2.1%

           \[\leadsto \color{blue}{\log \left(\sqrt{e^{z}}\right) - \log \left(\sqrt{e^{z}}\right)} \]

   13. Applied egg-rr 43.8%

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

       1. +-inverses 43.8%

          \[\leadsto \color{blue}{0} \]

   15. Simplified 43.8%

       \[\leadsto \color{blue}{0} \]

   if -3500 < z < 3.79999999999999976e-29

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 64.6%

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

   4. Taylor expanded in x around 0 26.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 29.6% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 0.0)

C

double code(double x, double y, double z) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 0.0;
}

Python

def code(x, y, z):
	return 0.0

Julia

function code(x, y, z)
	return 0.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_] := 0.0

Derivation

1. Initial program 100.0%

   \[e^{\left(x + y \cdot \log y\right) - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 55.0%

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

   1. neg-mul-1 55.0%

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

5. Simplified 55.0%

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

6. Taylor expanded in z around 0 12.8%

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

   1. mul-1-neg 12.8%

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

   2. unsub-neg 12.8%

      \[\leadsto \color{blue}{1 - z} \]

8. Simplified 12.8%

   \[\leadsto \color{blue}{1 - z} \]

9. Taylor expanded in z around inf 2.9%

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

    1. neg-mul-1 2.9%

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

11. Simplified 2.9%

    \[\leadsto \color{blue}{-z} \]
12. Step-by-step derivation

    1. add-log-exp 28.2%

       \[\leadsto \color{blue}{\log \left(e^{-z}\right)} \]

    2. exp-neg 28.5%

       \[\leadsto \log \color{blue}{\left(\frac{1}{e^{z}}\right)} \]

    3. add-sqr-sqrt 28.5%

       \[\leadsto \log \left(\frac{1}{\color{blue}{\sqrt{e^{z}} \cdot \sqrt{e^{z}}}}\right) \]

    4. associate-/r* 28.5%

       \[\leadsto \log \color{blue}{\left(\frac{\frac{1}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right)} \]

    5. metadata-eval 28.5%

       \[\leadsto \log \left(\frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{e^{z}}}}{\sqrt{e^{z}}}\right) \]

    6. sqrt-div 28.5%

       \[\leadsto \log \left(\frac{\color{blue}{\sqrt{\frac{1}{e^{z}}}}}{\sqrt{e^{z}}}\right) \]

    7. exp-neg 28.2%

       \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

    8. pow1 28.2%

       \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{-z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

    9. pow1 28.2%

       \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{-z}}}}{\sqrt{e^{z}}}\right) \]

    10. add-sqr-sqrt 25.1%

        \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}}}{\sqrt{e^{z}}}\right) \]

    11. sqrt-unprod 28.3%

        \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}}}{\sqrt{e^{z}}}\right) \]

    12. sqr-neg 28.3%

        \[\leadsto \log \left(\frac{\sqrt{e^{\sqrt{\color{blue}{z \cdot z}}}}}{\sqrt{e^{z}}}\right) \]

    13. sqrt-unprod 3.2%

        \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}}{\sqrt{e^{z}}}\right) \]

    14. add-sqr-sqrt 5.9%

        \[\leadsto \log \left(\frac{\sqrt{e^{\color{blue}{z}}}}{\sqrt{e^{z}}}\right) \]

    15. pow1 5.9%

        \[\leadsto \log \left(\frac{\sqrt{\color{blue}{{\left(e^{z}\right)}^{1}}}}{\sqrt{e^{z}}}\right) \]

    16. pow1 5.9%

        \[\leadsto \log \left(\frac{\sqrt{\color{blue}{e^{z}}}}{\sqrt{e^{z}}}\right) \]

    17. log-div 5.9%

        \[\leadsto \color{blue}{\log \left(\sqrt{e^{z}}\right) - \log \left(\sqrt{e^{z}}\right)} \]

13. Applied egg-rr 31.0%

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

    1. +-inverses 31.0%

       \[\leadsto \color{blue}{0} \]

15. Simplified 31.0%

    \[\leadsto \color{blue}{0} \]
16. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (exp (+ (- x z) (* (log y) y))))

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