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

Percentage Accurate: 99.8% → 99.8%

Time: 1.4s

Alternatives: 7

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

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: 99.8% 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: 99.8% accurate, 1.0× speedup

Math

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

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(Float64(x * log(y)) - y) - z)
end

MATLAB

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

Wolfram

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

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

5. Applied rewrites 70.0%

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

6. Taylor expanded in x around 0

   \[\leadsto x \cdot \log y - z \]

8. Applied rewrites 56.1%

   \[\leadsto \left(\log y - y\right) - z \]

9. Taylor expanded in x around 0

   \[\leadsto \left(\left(x \cdot \log y - z\right) - y\right) - z \]

11. Applied rewrites 99.9%

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

Alternative 2: 85.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;\left(\log y - y\right) - z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+64}:\\ \;\;\;\;t\_0 - y\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= z -6.5e+20)
     (- (- (log y) y) z)
     (if (<= z 3.4e+64) (- t_0 y) (- t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (z <= -6.5e+20) {
		tmp = (log(y) - y) - z;
	} else if (z <= 3.4e+64) {
		tmp = t_0 - y;
	} else {
		tmp = t_0 - 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) :: t_0
    real(8) :: tmp
    t_0 = x * log(y)
    if (z <= (-6.5d+20)) then
        tmp = (log(y) - y) - z
    else if (z <= 3.4d+64) then
        tmp = t_0 - y
    else
        tmp = t_0 - z
    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 (z <= -6.5e+20) {
		tmp = (Math.log(y) - y) - z;
	} else if (z <= 3.4e+64) {
		tmp = t_0 - y;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if z <= -6.5e+20:
		tmp = (math.log(y) - y) - z
	elif z <= 3.4e+64:
		tmp = t_0 - y
	else:
		tmp = t_0 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -6.5e+20)
		tmp = Float64(Float64(log(y) - y) - z);
	elseif (z <= 3.4e+64)
		tmp = Float64(t_0 - y);
	else
		tmp = Float64(t_0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	tmp = 0.0;
	if (z <= -6.5e+20)
		tmp = (log(y) - y) - z;
	elseif (z <= 3.4e+64)
		tmp = t_0 - y;
	else
		tmp = t_0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+20], N[(N[(N[Log[y], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[z, 3.4e+64], N[(t$95$0 - y), $MachinePrecision], N[(t$95$0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e20

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto x \cdot \log y - z \]

   8. Applied rewrites 88.2%

      \[\leadsto \left(\log y - y\right) - z \]

   if -6.5e20 < z < 3.4000000000000002e64

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.9%

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

   if 3.4000000000000002e64 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 86.9%

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

Alternative 3: 70.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+160}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+176}:\\ \;\;\;\;\left(\log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= x -2.1e+160) t_0 (if (<= x 6.5e+176) (- (- (log y) y) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (x <= -2.1e+160) {
		tmp = t_0;
	} else if (x <= 6.5e+176) {
		tmp = (log(y) - y) - z;
	} 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 <= (-2.1d+160)) then
        tmp = t_0
    else if (x <= 6.5d+176) then
        tmp = (log(y) - y) - z
    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 <= -2.1e+160) {
		tmp = t_0;
	} else if (x <= 6.5e+176) {
		tmp = (Math.log(y) - y) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if x <= -2.1e+160:
		tmp = t_0
	elif x <= 6.5e+176:
		tmp = (math.log(y) - y) - z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2.1e+160)
		tmp = t_0;
	elseif (x <= 6.5e+176)
		tmp = Float64(Float64(log(y) - y) - z);
	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 <= -2.1e+160)
		tmp = t_0;
	elseif (x <= 6.5e+176)
		tmp = (log(y) - y) - z;
	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, -2.1e+160], t$95$0, If[LessEqual[x, 6.5e+176], N[(N[(N[Log[y], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999997e160 or 6.49999999999999949e176 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 91.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 84.5%

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

   if -2.09999999999999997e160 < x < 6.49999999999999949e176

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto x \cdot \log y - z \]

   8. Applied rewrites 72.3%

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

Alternative 4: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log y - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.9e+190) (- (* x (log y)) z) (- (- (log y) y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.9e+190) {
		tmp = (x * log(y)) - z;
	} else {
		tmp = (log(y) - 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 (y <= 2.9d+190) then
        tmp = (x * log(y)) - z
    else
        tmp = (log(y) - y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.9e+190) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = (Math.log(y) - y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.9e+190:
		tmp = (x * math.log(y)) - z
	else:
		tmp = (math.log(y) - y) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.9e+190)
		tmp = Float64(Float64(x * log(y)) - z);
	else
		tmp = Float64(Float64(log(y) - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.9e+190)
		tmp = (x * log(y)) - z;
	else
		tmp = (log(y) - y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.9e+190], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.89999999999999989e190

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 83.4%

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

   if 2.89999999999999989e190 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 18.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto x \cdot \log y - z \]

   8. Applied rewrites 90.4%

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

Alternative 5: 48.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.9e+190) (* x (log y)) (- (log y) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.9e+190) {
		tmp = x * log(y);
	} else {
		tmp = 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 (y <= 2.9d+190) then
        tmp = x * log(y)
    else
        tmp = log(y) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.9e+190) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(y) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.9e+190:
		tmp = x * math.log(y)
	else:
		tmp = math.log(y) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.9e+190)
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(y) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.9e+190)
		tmp = x * log(y);
	else
		tmp = log(y) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.9e+190], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.89999999999999989e190

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 83.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 46.5%

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

   if 2.89999999999999989e190 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 79.6%

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

Alternative 6: 30.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[Log[y], $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

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

5. Applied rewrites 28.1%

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

Alternative 7: 2.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Log[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

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

5. Applied rewrites 70.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 2.5%

   \[\leadsto \log y \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  :pre (TRUE)
  (- (- (* x (log y)) z) y))