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

Percentage Accurate: 99.9% → 99.9%

Time: 9.1s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate--l- 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
4. Add Preprocessing

5. Final simplification 99.8%

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

Alternative 2: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+24} \lor \neg \left(z \leq 4.2 \cdot 10^{+66}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e+24) (not (<= z 4.2e+66)))
   (- (- z) y)
   (- (* x (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e+24) || !(z <= 4.2e+66)) {
		tmp = -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 ((z <= (-2.4d+24)) .or. (.not. (z <= 4.2d+66))) then
        tmp = -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 ((z <= -2.4e+24) || !(z <= 4.2e+66)) {
		tmp = -z - y;
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e+24) or not (z <= 4.2e+66):
		tmp = -z - y
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e+24) || !(z <= 4.2e+66))
		tmp = Float64(Float64(-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 ((z <= -2.4e+24) || ~((z <= 4.2e+66)))
		tmp = -z - y;
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e+24], N[Not[LessEqual[z, 4.2e+66]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e24 or 4.20000000000000011e66 < z

   1. Initial program 99.9%

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

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.1%

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

      1. neg-mul-1 82.1%

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

      2. distribute-neg-in 82.1%

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

      3. +-commutative 82.1%

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

      4. sub-neg 82.1%

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

   7. Simplified 82.1%

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

   if -2.4000000000000001e24 < z < 4.20000000000000011e66

   1. Initial program 99.8%

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

      1. associate--l- 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 89.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+24} \lor \neg \left(z \leq 4.2 \cdot 10^{+66}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+40} \lor \neg \left(x \leq 8 \cdot 10^{+128}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.2e+40) (not (<= x 8e+128))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e+40) || !(x <= 8e+128)) {
		tmp = x * log(y);
	} 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 ((x <= (-7.2d+40)) .or. (.not. (x <= 8d+128))) then
        tmp = x * log(y)
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e+40) || !(x <= 8e+128)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.2e+40) or not (x <= 8e+128):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.2e+40) || !(x <= 8e+128))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.2e+40) || ~((x <= 8e+128)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.2e+40], N[Not[LessEqual[x, 8e+128]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.19999999999999993e40 or 8.0000000000000006e128 < x

   1. Initial program 99.7%

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

      1. associate--l- 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 73.4%

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

   if -7.19999999999999993e40 < x < 8.0000000000000006e128

   1. Initial program 99.9%

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

      1. associate--l- 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 83.9%

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

      1. neg-mul-1 83.9%

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

      2. distribute-neg-in 83.9%

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

      3. +-commutative 83.9%

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

      4. sub-neg 83.9%

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

   7. Simplified 83.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+40} \lor \neg \left(x \leq 8 \cdot 10^{+128}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;y \leq 8.5 \cdot 10^{+55}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y)))) (if (<= y 8.5e+55) (- t_0 z) (- t_0 y))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (y <= 8.5e+55) {
		tmp = t_0 - z;
	} 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 (y <= 8.5d+55) then
        tmp = t_0 - z
    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 (y <= 8.5e+55) {
		tmp = t_0 - z;
	} else {
		tmp = t_0 - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if y <= 8.5e+55:
		tmp = t_0 - z
	else:
		tmp = t_0 - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 8.5e+55)
		tmp = Float64(t_0 - z);
	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 (y <= 8.5e+55)
		tmp = t_0 - z;
	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[y, 8.5e+55], N[(t$95$0 - z), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 8.50000000000000002e55

   1. Initial program 99.8%

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

      1. associate--l- 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 92.5%

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

   if 8.50000000000000002e55 < y

   1. Initial program 99.9%

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

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 90.6%

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

Alternative 5: 52.9% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{+56}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 5.6e+56) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.6e+56) {
		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 <= 5.6d+56) 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 <= 5.6e+56) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.6e+56:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.6e+56)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.6e+56)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.6e+56], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 5.60000000000000017e56

   1. Initial program 99.8%

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

      1. associate--l- 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 44.3%

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

      1. neg-mul-1 44.3%

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

   7. Simplified 44.3%

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

   if 5.60000000000000017e56 < y

   1. Initial program 99.9%

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

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 70.9%

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

      1. neg-mul-1 70.9%

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

   7. Simplified 70.9%

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

Alternative 6: 66.2% accurate, 26.8× 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 99.8%

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

   1. associate--l- 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 63.8%

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

   1. neg-mul-1 63.8%

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

   2. distribute-neg-in 63.8%

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

   3. +-commutative 63.8%

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

   4. sub-neg 63.8%

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

7. Simplified 63.8%

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

Alternative 7: 33.8% 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 99.8%

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

   1. associate--l- 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 36.2%

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

   1. neg-mul-1 36.2%

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

7. Simplified 36.2%

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

Alternative 8: 2.3% accurate, 107.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

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

   1. associate--l- 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 29.8%

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

   1. neg-mul-1 29.8%

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

7. Simplified 29.8%

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

   1. neg-sub0 29.8%

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

   2. sub-neg 29.8%

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

   3. add-sqr-sqrt 15.0%

      \[\leadsto 0 + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}} \]

   4. sqrt-unprod 9.1%

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

   5. sqr-neg 9.1%

      \[\leadsto 0 + \sqrt{\color{blue}{z \cdot z}} \]

   6. sqrt-unprod 0.9%

      \[\leadsto 0 + \color{blue}{\sqrt{z} \cdot \sqrt{z}} \]

   7. add-sqr-sqrt 2.4%

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

9. Applied egg-rr 2.4%

   \[\leadsto \color{blue}{0 + z} \]
10. Step-by-step derivation

    1. +-lft-identity 2.4%

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

11. Simplified 2.4%

    \[\leadsto \color{blue}{z} \]
12. Add Preprocessing

Alternative 9: 2.3% accurate, 107.0× 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 99.8%

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

   1. associate--l- 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \log y - \left(z + y\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 36.2%

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

   1. neg-mul-1 36.2%

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

7. Simplified 36.2%

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

   1. neg-sub0 36.2%

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

   2. sub-neg 36.2%

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

   3. add-sqr-sqrt 0.0%

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

   4. sqrt-unprod 2.1%

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

   5. sqr-neg 2.1%

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

   6. sqrt-unprod 2.2%

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

   7. add-sqr-sqrt 2.2%

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

9. Applied egg-rr 2.2%

   \[\leadsto \color{blue}{0 + y} \]
10. Step-by-step derivation

    1. +-lft-identity 2.2%

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

11. Simplified 2.2%

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

Reproduce

herbie shell --seed 2024146 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))