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

Percentage Accurate: 99.9% → 99.9%

Time: 11.6s

Alternatives: 8

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, 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 2: 83.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y - y\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+142}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+117}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log y)) y)))
   (if (<= x -1.4e+142) t_0 (if (<= x 7e+117) (- (- z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(y)) - y;
	double tmp;
	if (x <= -1.4e+142) {
		tmp = t_0;
	} else if (x <= 7e+117) {
		tmp = -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 <= (-1.4d+142)) then
        tmp = t_0
    else if (x <= 7d+117) then
        tmp = -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 <= -1.4e+142) {
		tmp = t_0;
	} else if (x <= 7e+117) {
		tmp = -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 <= -1.4e+142:
		tmp = t_0
	elif x <= 7e+117:
		tmp = -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 <= -1.4e+142)
		tmp = t_0;
	elseif (x <= 7e+117)
		tmp = Float64(Float64(-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 <= -1.4e+142)
		tmp = t_0;
	elseif (x <= 7e+117)
		tmp = -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, -1.4e+142], t$95$0, If[LessEqual[x, 7e+117], N[((-z) - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e142 or 6.99999999999999965e117 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. --lowering--.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. log-lowering-log.f64 88.6

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

   5. Simplified 88.6%

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

   if -1.4e142 < x < 6.99999999999999965e117

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\left(y + z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(z + y\right)}\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) + \left(\mathsf{neg}\left(y\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y} \]

      5. --lowering--.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y} \]

      6. neg-lowering-neg.f64 86.0

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

   5. Simplified 86.0%

      \[\leadsto \color{blue}{\left(-z\right) - y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 79.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;x \leq -4 \cdot 10^{+145}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+166}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= x -4e+145) t_0 (if (<= x 4.5e+166) (- (- z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (x <= -4e+145) {
		tmp = t_0;
	} else if (x <= 4.5e+166) {
		tmp = -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 <= (-4d+145)) then
        tmp = t_0
    else if (x <= 4.5d+166) then
        tmp = -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 <= -4e+145) {
		tmp = t_0;
	} else if (x <= 4.5e+166) {
		tmp = -z - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if x <= -4e+145:
		tmp = t_0
	elif x <= 4.5e+166:
		tmp = -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 <= -4e+145)
		tmp = t_0;
	elseif (x <= 4.5e+166)
		tmp = Float64(Float64(-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 <= -4e+145)
		tmp = t_0;
	elseif (x <= 4.5e+166)
		tmp = -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, -4e+145], t$95$0, If[LessEqual[x, 4.5e+166], N[((-z) - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4e145 or 4.5000000000000003e166 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. log-lowering-log.f64 79.8

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

   5. Simplified 79.8%

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

   if -4e145 < x < 4.5000000000000003e166

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\left(y + z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(z + y\right)}\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) + \left(\mathsf{neg}\left(y\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y} \]

      5. --lowering--.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y} \]

      6. neg-lowering-neg.f64 85.4

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

   5. Simplified 85.4%

      \[\leadsto \color{blue}{\left(-z\right) - y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 3.1e+63) (- (* x (log y)) z) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.1e+63) {
		tmp = (x * log(y)) - z;
	} else {
		tmp = -z - 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 <= 3.1d+63) then
        tmp = (x * log(y)) - z
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.1e+63) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.1e+63:
		tmp = (x * math.log(y)) - z
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.1e+63)
		tmp = Float64(Float64(x * log(y)) - z);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.1e+63)
		tmp = (x * log(y)) - z;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.1e+63], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.1000000000000001e63

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. log-lowering-log.f64 93.1

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

   5. Simplified 93.1%

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

   if 3.1000000000000001e63 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\left(y + z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(z + y\right)}\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) + \left(\mathsf{neg}\left(y\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y} \]

      5. --lowering--.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y} \]

      6. neg-lowering-neg.f64 85.3

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

   5. Simplified 85.3%

      \[\leadsto \color{blue}{\left(-z\right) - y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 52.9% accurate, 12.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 26000000000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 26000000000000.0) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 26000000000000.0) {
		tmp = -z;
	} else {
		tmp = -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 <= 26000000000000.0d0) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 26000000000000.0) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 26000000000000.0:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 26000000000000.0)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 26000000000000.0)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 26000000000000.0], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.6e13

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. neg-lowering-neg.f64 51.1

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

   5. Simplified 51.1%

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

   if 2.6e13 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

      2. neg-lowering-neg.f64 60.0

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

   5. Simplified 60.0%

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

Alternative 6: 66.6% accurate, 18.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(\left(y + z\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\left(z + y\right)}\right) \]

   3. distribute-neg-in N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) + \left(\mathsf{neg}\left(y\right)\right)} \]

   4. sub-neg N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y} \]

   5. --lowering--.f64 N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y} \]

   6. neg-lowering-neg.f64 66.9

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

5. Simplified 66.9%

   \[\leadsto \color{blue}{\left(-z\right) - y} \]
6. Add Preprocessing

Alternative 7: 34.5% accurate, 37.3× 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

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. neg-lowering-neg.f64 32.7

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

5. Simplified 32.7%

   \[\leadsto \color{blue}{-y} \]
6. Add Preprocessing

Alternative 8: 2.2% accurate, 112.0× 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 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

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. neg-lowering-neg.f64 32.7

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

5. Simplified 32.7%

   \[\leadsto \color{blue}{-y} \]
6. Step-by-step derivation

   1. neg-sub0 N/A

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

   2. flip-- N/A

      \[\leadsto \color{blue}{\frac{0 \cdot 0 - y \cdot y}{0 + y}} \]

   3. div-inv N/A

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

   4. *-lowering-*.f64 N/A

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

   5. metadata-eval N/A

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

   6. --lowering--.f64 N/A

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

   7. *-lowering-*.f64 N/A

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

   8. /-lowering-/.f64 N/A

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

   9. +-lowering-+.f64 12.3

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

7. Applied egg-rr 12.3%

   \[\leadsto \color{blue}{\left(0 - y \cdot y\right) \cdot \frac{1}{0 + y}} \]
8. Step-by-step derivation

   1. un-div-inv N/A

      \[\leadsto \color{blue}{\frac{0 - y \cdot y}{0 + y}} \]

   2. flip-- N/A

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

   3. +-lft-identity N/A

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

   4. +-lft-identity N/A

      \[\leadsto \frac{\frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{y \cdot y}}{\color{blue}{y}} \]

   5. associate-/l/ N/A

      \[\leadsto \color{blue}{\frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{y \cdot \left(y \cdot y\right)}} \]

   6. cube-mult N/A

      \[\leadsto \frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{\color{blue}{{y}^{3}}} \]

   7. sqr-pow N/A

      \[\leadsto \frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{\color{blue}{{y}^{\left(\frac{3}{2}\right)} \cdot {y}^{\left(\frac{3}{2}\right)}}} \]

   8. unpow-prod-down N/A

      \[\leadsto \frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{\color{blue}{{\left(y \cdot y\right)}^{\left(\frac{3}{2}\right)}}} \]

   9. sqr-neg N/A

      \[\leadsto \frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{{\color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}}^{\left(\frac{3}{2}\right)}} \]

   10. unpow-prod-down N/A

       \[\leadsto \frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)}}} \]

   11. sqr-pow N/A

       \[\leadsto \frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{3}}} \]

   12. cube-mult N/A

       \[\leadsto \frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{\color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}} \]

   13. sqr-neg N/A

       \[\leadsto \frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{\left(\mathsf{neg}\left(y\right)\right) \cdot \color{blue}{\left(y \cdot y\right)}} \]

   14. associate-/l/ N/A

       \[\leadsto \color{blue}{\frac{\frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{y \cdot y}}{\mathsf{neg}\left(y\right)}} \]

   15. +-lft-identity N/A

       \[\leadsto \frac{\frac{0 \cdot 0 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)}{\color{blue}{0 + y \cdot y}}}{\mathsf{neg}\left(y\right)} \]

   16. flip-- N/A

       \[\leadsto \frac{\color{blue}{0 - y \cdot y}}{\mathsf{neg}\left(y\right)} \]

   17. metadata-eval N/A

       \[\leadsto \frac{\color{blue}{0 \cdot 0} - y \cdot y}{\mathsf{neg}\left(y\right)} \]

   18. neg-sub0 N/A

       \[\leadsto \frac{0 \cdot 0 - y \cdot y}{\color{blue}{0 - y}} \]

   19. flip-+ N/A

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

   20. +-lft-identity 2.2

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

9. Applied egg-rr 2.2%

   \[\leadsto \color{blue}{y} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024205 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))