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

Percentage Accurate: 100.0% → 100.0%

Time: 8.4s

Alternatives: 16

Speedup: 1.0×

• Could not converge on a ground truth

  1. reg0 = (bf "-3.140690300548206871629959512531883831502e-60")
  2. reg1 = (bf 1026125826911236341628928)
  3. reg2 = (bf "-9.117546091748454125094377187260745419447e239")

• 58.2% 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: 93.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+52} \lor \neg \left(x \leq 0.0115\right):\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.8e+52) (not (<= x 0.0115)))
   (exp (- x z))
   (exp (- (* y (log y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e+52) || !(x <= 0.0115)) {
		tmp = exp((x - z));
	} else {
		tmp = exp(((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) :: tmp
    if ((x <= (-6.8d+52)) .or. (.not. (x <= 0.0115d0))) then
        tmp = exp((x - z))
    else
        tmp = exp(((y * log(y)) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e+52) || !(x <= 0.0115)) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.exp(((y * Math.log(y)) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.8e+52) or not (x <= 0.0115):
		tmp = math.exp((x - z))
	else:
		tmp = math.exp(((y * math.log(y)) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.8e+52) || !(x <= 0.0115))
		tmp = exp(Float64(x - z));
	else
		tmp = exp(Float64(Float64(y * log(y)) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.8e+52) || ~((x <= 0.0115)))
		tmp = exp((x - z));
	else
		tmp = exp(((y * log(y)) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.8e+52], N[Not[LessEqual[x, 0.0115]], $MachinePrecision]], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Exp[N[(N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.8e52 or 0.0115 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.8%

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

   if -6.8e52 < x < 0.0115

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.4%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+52} \lor \neg \left(x \leq 0.0115\right):\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot \log y \leq 10^{+31}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y (log y)) 1e+31) (exp (- x z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * log(y)) <= 1e+31) {
		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 * log(y)) <= 1d+31) 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 * Math.log(y)) <= 1e+31) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * math.log(y)) <= 1e+31:
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * log(y)) <= 1e+31)
		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 * log(y)) <= 1e+31)
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision], 1e+31], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (log.f64 y)) < 9.9999999999999996e30

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.7%

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

   if 9.9999999999999996e30 < (*.f64 y (log.f64 y))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.5%

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

   4. Taylor expanded in z around 0 78.7%

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

Alternative 4: 72.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.9 \cdot 10^{-204}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-15}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 5.9e-204)
   (exp x)
   (if (<= y 1.8e-33) (exp (- z)) (if (<= y 1.36e-15) (exp x) (pow y y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.9e-204) {
		tmp = exp(x);
	} else if (y <= 1.8e-33) {
		tmp = exp(-z);
	} else if (y <= 1.36e-15) {
		tmp = exp(x);
	} 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 <= 5.9d-204) then
        tmp = exp(x)
    else if (y <= 1.8d-33) then
        tmp = exp(-z)
    else if (y <= 1.36d-15) then
        tmp = exp(x)
    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 <= 5.9e-204) {
		tmp = Math.exp(x);
	} else if (y <= 1.8e-33) {
		tmp = Math.exp(-z);
	} else if (y <= 1.36e-15) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.9e-204:
		tmp = math.exp(x)
	elif y <= 1.8e-33:
		tmp = math.exp(-z)
	elif y <= 1.36e-15:
		tmp = math.exp(x)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.9e-204)
		tmp = exp(x);
	elseif (y <= 1.8e-33)
		tmp = exp(Float64(-z));
	elseif (y <= 1.36e-15)
		tmp = exp(x);
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.9e-204)
		tmp = exp(x);
	elseif (y <= 1.8e-33)
		tmp = exp(-z);
	elseif (y <= 1.36e-15)
		tmp = exp(x);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.9e-204], N[Exp[x], $MachinePrecision], If[LessEqual[y, 1.8e-33], N[Exp[(-z)], $MachinePrecision], If[LessEqual[y, 1.36e-15], N[Exp[x], $MachinePrecision], N[Power[y, y], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 5.9000000000000003e-204 or 1.80000000000000017e-33 < y < 1.36e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.0%

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

   if 5.9000000000000003e-204 < y < 1.80000000000000017e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 82.6%

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

      1. neg-mul-1 82.6%

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

   5. Simplified 82.6%

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

   if 1.36e-15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.2%

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

   4. Taylor expanded in z around 0 77.3%

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

Alternative 5: 73.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.3 \lor \neg \left(x \leq 9.5 \cdot 10^{+18}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.3) (not (<= x 9.5e+18))) (exp x) (exp (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.3) || !(x <= 9.5e+18)) {
		tmp = exp(x);
	} else {
		tmp = exp(-z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.3d0)) .or. (.not. (x <= 9.5d+18))) then
        tmp = exp(x)
    else
        tmp = exp(-z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.3) || !(x <= 9.5e+18)) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.exp(-z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.3) or not (x <= 9.5e+18):
		tmp = math.exp(x)
	else:
		tmp = math.exp(-z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.3) || !(x <= 9.5e+18))
		tmp = exp(x);
	else
		tmp = exp(Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.3) || ~((x <= 9.5e+18)))
		tmp = exp(x);
	else
		tmp = exp(-z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.3], N[Not[LessEqual[x, 9.5e+18]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[Exp[(-z)], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.29999999999999982 or 9.5e18 < 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 83.1%

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

   if -5.29999999999999982 < x < 9.5e18

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 61.1%

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

      1. neg-mul-1 61.1%

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

   5. Simplified 61.1%

      \[\leadsto e^{\color{blue}{-z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \lor \neg \left(x \leq 9.5 \cdot 10^{+18}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+20}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e+103)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (<= z 9.8e+20) (exp x) (exp z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+103) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 9.8e+20) {
		tmp = exp(x);
	} else {
		tmp = exp(z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.05d+103)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if (z <= 9.8d+20) then
        tmp = exp(x)
    else
        tmp = exp(z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+103) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 9.8e+20) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.exp(z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05e+103:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif z <= 9.8e+20:
		tmp = math.exp(x)
	else:
		tmp = math.exp(z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e+103)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif (z <= 9.8e+20)
		tmp = exp(x);
	else
		tmp = exp(z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05e+103)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif (z <= 9.8e+20)
		tmp = exp(x);
	else
		tmp = exp(z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e+103], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+20], N[Exp[x], $MachinePrecision], N[Exp[z], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0500000000000001e103

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 93.1%

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

      1. neg-mul-1 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in z around 0 93.1%

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

   7. Taylor expanded in z around inf 93.1%

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

      1. *-commutative 93.1%

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

   9. Simplified 93.1%

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

   if -1.0500000000000001e103 < z < 9.8e20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 57.7%

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

   if 9.8e20 < 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 65.3%

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

      1. neg-mul-1 65.3%

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

   5. Simplified 65.3%

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

      1. expm1-log1p-u 65.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{-z}\right)\right)} \]

      2. expm1-undefine 65.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(e^{-z}\right)} - 1} \]

      3. add-sqr-sqrt 0.0%

         \[\leadsto e^{\mathsf{log1p}\left(e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}\right)} - 1 \]

      4. sqrt-unprod 36.3%

         \[\leadsto e^{\mathsf{log1p}\left(e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}\right)} - 1 \]

      5. sqr-neg 36.3%

         \[\leadsto e^{\mathsf{log1p}\left(e^{\sqrt{\color{blue}{z \cdot z}}}\right)} - 1 \]

      6. sqrt-unprod 36.3%

         \[\leadsto e^{\mathsf{log1p}\left(e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}\right)} - 1 \]

      7. add-sqr-sqrt 36.3%

         \[\leadsto e^{\mathsf{log1p}\left(e^{\color{blue}{z}}\right)} - 1 \]

   7. Applied egg-rr 36.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(e^{z}\right)} - 1} \]
   8. Step-by-step derivation

      1. log1p-undefine 36.3%

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

      2. rem-exp-log 36.3%

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

      3. associate-+r- 36.3%

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

      4. expm1-undefine 36.3%

         \[\leadsto 1 + \color{blue}{\mathsf{expm1}\left(z\right)} \]

      5. rem-exp-log 36.3%

         \[\leadsto \color{blue}{e^{\log \left(1 + \mathsf{expm1}\left(z\right)\right)}} \]

      6. log1p-define 36.3%

         \[\leadsto e^{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(z\right)\right)}} \]

      7. log1p-expm1 36.3%

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

   9. Simplified 36.3%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+20}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e+103)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (exp x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+103) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} 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 (z <= (-1.05d+103)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else
        tmp = exp(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+103) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05e+103:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e+103)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	else
		tmp = exp(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05e+103)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e+103], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Exp[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e103

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 93.1%

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

      1. neg-mul-1 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in z around 0 93.1%

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

   7. Taylor expanded in z around inf 93.1%

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

      1. *-commutative 93.1%

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

   9. Simplified 93.1%

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

   if -1.0500000000000001e103 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 48.6%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 42.6% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+69}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-307}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+95}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.5e+69)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (<= z -3.5e-307)
     (+ 1.0 (* x (+ 1.0 (* x 0.5))))
     (if (<= z 1.32e+95)
       (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))
       (+ 1.0 (* z (+ 1.0 (* z (+ 0.5 (* z 0.16666666666666666))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+69) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= -3.5e-307) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else if (z <= 1.32e+95) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = 1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666)))));
	}
	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+69)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if (z <= (-3.5d-307)) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    else if (z <= 1.32d+95) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    else
        tmp = 1.0d0 + (z * (1.0d0 + (z * (0.5d0 + (z * 0.16666666666666666d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+69) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= -3.5e-307) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else if (z <= 1.32e+95) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = 1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.5e+69:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif z <= -3.5e-307:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	elif z <= 1.32e+95:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	else:
		tmp = 1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.5e+69)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif (z <= -3.5e-307)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	elseif (z <= 1.32e+95)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	else
		tmp = Float64(1.0 + Float64(z * Float64(1.0 + Float64(z * Float64(0.5 + Float64(z * 0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.5e+69)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif (z <= -3.5e-307)
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	elseif (z <= 1.32e+95)
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	else
		tmp = 1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.5e+69], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-307], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e+95], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(z * N[(1.0 + N[(z * N[(0.5 + N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.4999999999999999e69

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.7%

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

      1. neg-mul-1 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in z around 0 83.9%

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

   7. Taylor expanded in z around inf 83.9%

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

      1. *-commutative 83.9%

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

   9. Simplified 83.9%

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

   if -4.4999999999999999e69 < z < -3.5000000000000002e-307

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.9%

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

   4. Taylor expanded in x around 0 33.6%

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

   if -3.5000000000000002e-307 < z < 1.32e95

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 54.9%

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

   4. Taylor expanded in x around 0 34.6%

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

   if 1.32e95 < 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 76.1%

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

      1. neg-mul-1 76.1%

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

   5. Simplified 76.1%

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

      1. expm1-log1p-u 76.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{-z}\right)\right)} \]

      2. expm1-undefine 76.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(e^{-z}\right)} - 1} \]

      3. add-sqr-sqrt 0.0%

         \[\leadsto e^{\mathsf{log1p}\left(e^{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}\right)} - 1 \]

      4. sqrt-unprod 25.5%

         \[\leadsto e^{\mathsf{log1p}\left(e^{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}\right)} - 1 \]

      5. sqr-neg 25.5%

         \[\leadsto e^{\mathsf{log1p}\left(e^{\sqrt{\color{blue}{z \cdot z}}}\right)} - 1 \]

      6. sqrt-unprod 25.5%

         \[\leadsto e^{\mathsf{log1p}\left(e^{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}\right)} - 1 \]

      7. add-sqr-sqrt 25.5%

         \[\leadsto e^{\mathsf{log1p}\left(e^{\color{blue}{z}}\right)} - 1 \]

   7. Applied egg-rr 25.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(e^{z}\right)} - 1} \]
   8. Step-by-step derivation

      1. log1p-undefine 25.5%

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

      2. rem-exp-log 25.5%

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

      3. associate-+r- 25.5%

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

      4. expm1-undefine 25.5%

         \[\leadsto 1 + \color{blue}{\mathsf{expm1}\left(z\right)} \]

      5. rem-exp-log 25.5%

         \[\leadsto \color{blue}{e^{\log \left(1 + \mathsf{expm1}\left(z\right)\right)}} \]

      6. log1p-define 25.5%

         \[\leadsto e^{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(z\right)\right)}} \]

      7. log1p-expm1 25.5%

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

   9. Simplified 25.5%

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

   10. Taylor expanded in z around 0 20.7%

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

       1. *-commutative 20.7%

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

   12. Simplified 20.7%

       \[\leadsto \color{blue}{1 + z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+69}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-307}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+95}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+153}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+90}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9e+153)
   (+ 1.0 (* x (+ 1.0 (* x 0.5))))
   (if (<= x 1.95e+90)
     (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
     (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e+153) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else if (x <= 1.95e+90) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	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 <= (-9d+153)) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    else if (x <= 1.95d+90) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e+153) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else if (x <= 1.95e+90) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9e+153:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	elif x <= 1.95e+90:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9e+153)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	elseif (x <= 1.95e+90)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9e+153)
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	elseif (x <= 1.95e+90)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9e+153], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e+90], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.0000000000000002e153

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.6%

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

   4. Taylor expanded in x around 0 16.5%

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

   if -9.0000000000000002e153 < x < 1.9500000000000001e90

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 56.0%

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

      1. neg-mul-1 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in z around 0 35.1%

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

   7. Taylor expanded in z around inf 35.0%

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

      1. *-commutative 35.0%

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

   9. Simplified 35.0%

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

   if 1.9500000000000001e90 < 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 91.6%

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

   4. Taylor expanded in x around 0 86.3%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+153}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+90}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.5% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+151} \lor \neg \left(x \leq 1.95 \cdot 10^{+90}\right):\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.06e+151) (not (<= x 1.95e+90)))
   (+ 1.0 (* x (+ 1.0 (* x 0.5))))
   (+ 1.0 (* z (+ (* z 0.5) -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.06e+151) || !(x <= 1.95e+90)) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	}
	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 ((x <= (-1.06d+151)) .or. (.not. (x <= 1.95d+90))) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    else
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.06e+151) || !(x <= 1.95e+90)) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.06e+151) or not (x <= 1.95e+90):
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	else:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.06e+151) || !(x <= 1.95e+90))
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	else
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.06e+151) || ~((x <= 1.95e+90)))
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	else
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.06e+151], N[Not[LessEqual[x, 1.95e+90]], $MachinePrecision]], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.06000000000000003e151 or 1.9500000000000001e90 < 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 87.2%

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

   4. Taylor expanded in x around 0 43.8%

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

   if -1.06000000000000003e151 < x < 1.9500000000000001e90

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 56.0%

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

      1. neg-mul-1 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in z around 0 33.4%

      \[\leadsto \color{blue}{1 + z \cdot \left(0.5 \cdot z - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+151} \lor \neg \left(x \leq 1.95 \cdot 10^{+90}\right):\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.9% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+69}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.5e+69)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+69) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -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 (z <= (-4.5d+69)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-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 (z <= -4.5e+69) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.5e+69:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.5e+69)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -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 (z <= -4.5e+69)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.5e+69], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $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 2 regimes

2. if z < -4.4999999999999999e69

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.7%

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

      1. neg-mul-1 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in z around 0 83.9%

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

   7. Taylor expanded in z around inf 83.9%

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

      1. *-commutative 83.9%

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

   9. Simplified 83.9%

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

   if -4.4999999999999999e69 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 48.8%

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

   4. Taylor expanded in x around 0 26.9%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + 0.5 \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+69}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.7% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+128}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.3e+128) (+ 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 (z <= -1.3e+128) {
		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 (z <= (-1.3d+128)) 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 (z <= -1.3e+128) {
		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 z <= -1.3e+128:
		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 (z <= -1.3e+128)
		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 (z <= -1.3e+128)
		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[z, -1.3e+128], 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 2 regimes

2. if z < -1.3e128

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.2%

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

      1. neg-mul-1 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in z around 0 86.7%

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

   7. Taylor expanded in z around inf 86.7%

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

      1. *-commutative 86.7%

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

   9. Simplified 86.7%

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

   if -1.3e128 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 48.7%

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

   4. Taylor expanded in x around 0 26.3%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + 0.5 \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+128}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.0% accurate, 29.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return 1.0 + (z * (z * 0.5))

Julia

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

MATLAB

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

Wolfram

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

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 47.7%

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

   1. neg-mul-1 47.7%

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

5. Simplified 47.7%

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

6. Taylor expanded in z around 0 26.8%

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

7. Taylor expanded in z around inf 26.6%

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

   1. *-commutative 26.6%

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

9. Simplified 26.6%

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

Alternative 14: 14.6% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ 1 - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- 1.0 z))

C

double code(double x, double y, double z) {
	return 1.0 - 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 = 1.0d0 - z
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 - z;
}

Python

def code(x, y, z):
	return 1.0 - z

Julia

function code(x, y, z)
	return Float64(1.0 - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 - z;
end

Wolfram

code[x_, y_, z_] := N[(1.0 - z), $MachinePrecision]

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 47.7%

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

   1. neg-mul-1 47.7%

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

5. Simplified 47.7%

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

6. Taylor expanded in z around 0 13.5%

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

   1. neg-mul-1 13.5%

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

   2. unsub-neg 13.5%

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

8. Simplified 13.5%

   \[\leadsto \color{blue}{1 - z} \]
9. Add Preprocessing

Alternative 15: 14.6% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

Fortran

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

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 45.1%

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

4. Taylor expanded in x around 0 13.4%

   \[\leadsto \color{blue}{1 + x} \]

5. Final simplification 13.4%

   \[\leadsto x + 1 \]
6. Add Preprocessing

Alternative 16: 14.4% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 45.1%

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

4. Taylor expanded in x around 0 13.2%

   \[\leadsto \color{blue}{1} \]
5. 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 2024144 
(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)))