Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2

Percentage Accurate: 99.9% → 99.9%

Time: 14.0s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\log y, x, \left(0 - z\right) - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (log y) x (- (- 0.0 z) y)))

C

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

Julia

function code(x, y, z)
	return fma(log(y), x, Float64(Float64(0.0 - z) - y))
end

Wolfram

code[x_, y_, z_] := N[(N[Log[y], $MachinePrecision] * x + N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 2: 85.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(\log y - \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+25}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e+69)
   (* x (- (log y) (/ z x)))
   (if (<= x 2.6e+25) (- (- 0.0 z) y) (- (* x (log y)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e+69) {
		tmp = x * (log(y) - (z / x));
	} else if (x <= 2.6e+25) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = (x * log(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 (x <= (-1.9d+69)) then
        tmp = x * (log(y) - (z / x))
    else if (x <= 2.6d+25) then
        tmp = (0.0d0 - z) - y
    else
        tmp = (x * log(y)) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e+69) {
		tmp = x * (Math.log(y) - (z / x));
	} else if (x <= 2.6e+25) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.9e+69:
		tmp = x * (math.log(y) - (z / x))
	elif x <= 2.6e+25:
		tmp = (0.0 - z) - y
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e+69)
		tmp = Float64(x * Float64(log(y) - Float64(z / x)));
	elseif (x <= 2.6e+25)
		tmp = Float64(Float64(0.0 - z) - y);
	else
		tmp = Float64(Float64(x * log(y)) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.9e+69)
		tmp = x * (log(y) - (z / x));
	elseif (x <= 2.6e+25)
		tmp = (0.0 - z) - y;
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e+69], N[(x * N[(N[Log[y], $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+25], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.90000000000000014e69

   1. Initial program 99.6%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.90000000000000014e69 < x < 2.5999999999999998e25

   1. Initial program 100.0%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.5999999999999998e25 < x

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+69}:\\ \;\;\;\;t\_0 - z\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+23}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= x -1.45e+69)
     (- t_0 z)
     (if (<= x 1.7e+23) (- (- 0.0 z) y) (- t_0 y)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (x <= -1.45e+69) {
		tmp = t_0 - z;
	} else if (x <= 1.7e+23) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_0 - 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) :: t_0
    real(8) :: tmp
    t_0 = x * log(y)
    if (x <= (-1.45d+69)) then
        tmp = t_0 - z
    else if (x <= 1.7d+23) then
        tmp = (0.0d0 - z) - y
    else
        tmp = t_0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log(y);
	double tmp;
	if (x <= -1.45e+69) {
		tmp = t_0 - z;
	} else if (x <= 1.7e+23) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_0 - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if x <= -1.45e+69:
		tmp = t_0 - z
	elif x <= 1.7e+23:
		tmp = (0.0 - z) - y
	else:
		tmp = t_0 - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.45e+69)
		tmp = Float64(t_0 - z);
	elseif (x <= 1.7e+23)
		tmp = Float64(Float64(0.0 - z) - y);
	else
		tmp = Float64(t_0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	tmp = 0.0;
	if (x <= -1.45e+69)
		tmp = t_0 - z;
	elseif (x <= 1.7e+23)
		tmp = (0.0 - z) - y;
	else
		tmp = t_0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+69], N[(t$95$0 - z), $MachinePrecision], If[LessEqual[x, 1.7e+23], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4499999999999999e69

   1. Initial program 99.6%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.4499999999999999e69 < x < 1.69999999999999996e23

   1. Initial program 100.0%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.69999999999999996e23 < x

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y - y\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+25}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log y)) y)))
   (if (<= x -5.6e+73) t_0 (if (<= x 2.3e+25) (- (- 0.0 z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(y)) - y;
	double tmp;
	if (x <= -5.6e+73) {
		tmp = t_0;
	} else if (x <= 2.3e+25) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * log(y)) - y
    if (x <= (-5.6d+73)) then
        tmp = t_0
    else if (x <= 2.3d+25) then
        tmp = (0.0d0 - z) - y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * Math.log(y)) - y;
	double tmp;
	if (x <= -5.6e+73) {
		tmp = t_0;
	} else if (x <= 2.3e+25) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log(y)) - y
	tmp = 0
	if x <= -5.6e+73:
		tmp = t_0
	elif x <= 2.3e+25:
		tmp = (0.0 - z) - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (x <= -5.6e+73)
		tmp = t_0;
	elseif (x <= 2.3e+25)
		tmp = Float64(Float64(0.0 - z) - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * log(y)) - y;
	tmp = 0.0;
	if (x <= -5.6e+73)
		tmp = t_0;
	elseif (x <= 2.3e+25)
		tmp = (0.0 - z) - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -5.6e+73], t$95$0, If[LessEqual[x, 2.3e+25], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.60000000000000016e73 or 2.2999999999999998e25 < x

   1. Initial program 99.7%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.60000000000000016e73 < x < 2.2999999999999998e25

   1. Initial program 100.0%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 79.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+99}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= x -3.3e+75) t_0 (if (<= x 9e+99) (- (- 0.0 z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (x <= -3.3e+75) {
		tmp = t_0;
	} else if (x <= 9e+99) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * log(y)
    if (x <= (-3.3d+75)) then
        tmp = t_0
    else if (x <= 9d+99) then
        tmp = (0.0d0 - z) - y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log(y);
	double tmp;
	if (x <= -3.3e+75) {
		tmp = t_0;
	} else if (x <= 9e+99) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if x <= -3.3e+75:
		tmp = t_0
	elif x <= 9e+99:
		tmp = (0.0 - z) - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -3.3e+75)
		tmp = t_0;
	elseif (x <= 9e+99)
		tmp = Float64(Float64(0.0 - z) - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	tmp = 0.0;
	if (x <= -3.3e+75)
		tmp = t_0;
	elseif (x <= 9e+99)
		tmp = (0.0 - z) - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+75], t$95$0, If[LessEqual[x, 9e+99], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.29999999999999998e75 or 8.9999999999999999e99 < x

   1. Initial program 99.7%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.29999999999999998e75 < x < 8.9999999999999999e99

   1. Initial program 100.0%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 7: 52.5% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+77}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 10^{+92}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.5e+77) (- z) (if (<= z 1e+92) (- y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5e+77) {
		tmp = -z;
	} else if (z <= 1e+92) {
		tmp = -y;
	} else {
		tmp = -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 <= (-5.5d+77)) then
        tmp = -z
    else if (z <= 1d+92) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5e+77) {
		tmp = -z;
	} else if (z <= 1e+92) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.5e+77:
		tmp = -z
	elif z <= 1e+92:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.5e+77)
		tmp = Float64(-z);
	elseif (z <= 1e+92)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.5e+77)
		tmp = -z;
	elseif (z <= 1e+92)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.5e+77], (-z), If[LessEqual[z, 1e+92], (-y), (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000036e77 or 1e92 < z

   1. Initial program 99.9%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -5.50000000000000036e77 < z < 1e92

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 66.9% accurate, 21.4× speedup

Math

\[\begin{array}{l} \\ \left(0 - z\right) - y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (0.0 - z) - 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 = (0.0d0 - z) - y
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(Float64(0.0 - z) - y)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

3. Taylor expanded in x around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 9: 35.1% accurate, 53.5× speedup

Math

\[\begin{array}{l} \\ -y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-y)

Derivation

1. Initial program 99.9%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

3. Taylor expanded in y around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))