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

Percentage Accurate: 99.9% → 99.9%

Time: 11.9s

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 99.8%

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

Alternative 2: 85.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ t_1 := t\_0 - z\\ \mathbf{if}\;x \leq -9 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-61}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))) (t_1 (- t_0 z)))
   (if (<= x -9e+29)
     t_1
     (if (<= x 3.9e-61) (- (- 0.0 z) y) (if (<= x 2.45e+83) t_1 (- t_0 y))))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double t_1 = t_0 - z;
	double tmp;
	if (x <= -9e+29) {
		tmp = t_1;
	} else if (x <= 3.9e-61) {
		tmp = (0.0 - z) - y;
	} else if (x <= 2.45e+83) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x * log(y)
    t_1 = t_0 - z
    if (x <= (-9d+29)) then
        tmp = t_1
    else if (x <= 3.9d-61) then
        tmp = (0.0d0 - z) - y
    else if (x <= 2.45d+83) then
        tmp = t_1
    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 t_1 = t_0 - z;
	double tmp;
	if (x <= -9e+29) {
		tmp = t_1;
	} else if (x <= 3.9e-61) {
		tmp = (0.0 - z) - y;
	} else if (x <= 2.45e+83) {
		tmp = t_1;
	} else {
		tmp = t_0 - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	t_1 = t_0 - z
	tmp = 0
	if x <= -9e+29:
		tmp = t_1
	elif x <= 3.9e-61:
		tmp = (0.0 - z) - y
	elif x <= 2.45e+83:
		tmp = t_1
	else:
		tmp = t_0 - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	t_1 = Float64(t_0 - z)
	tmp = 0.0
	if (x <= -9e+29)
		tmp = t_1;
	elseif (x <= 3.9e-61)
		tmp = Float64(Float64(0.0 - z) - y);
	elseif (x <= 2.45e+83)
		tmp = t_1;
	else
		tmp = Float64(t_0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	t_1 = t_0 - z;
	tmp = 0.0;
	if (x <= -9e+29)
		tmp = t_1;
	elseif (x <= 3.9e-61)
		tmp = (0.0 - z) - y;
	elseif (x <= 2.45e+83)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(t$95$0 - z), $MachinePrecision]}, If[LessEqual[x, -9e+29], t$95$1, If[LessEqual[x, 3.9e-61], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 2.45e+83], t$95$1, N[(t$95$0 - y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.0000000000000005e29 or 3.90000000000000033e-61 < x < 2.44999999999999989e83

   1. Initial program 99.7%

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

      1. sub-neg N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

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

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

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

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{\left(0 - z\right)} - y\right) \]

      8. --lowering--.f64 99.7

         \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{\left(0 - z\right)} - y\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(0 - z\right) - y\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot \log y - z} \]
   6. 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 88.8

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

   7. Simplified 88.8%

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

   if -9.0000000000000005e29 < x < 3.90000000000000033e-61

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 96.0

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

   5. Simplified 96.0%

      \[\leadsto \color{blue}{\left(0 - z\right)} - y \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 96.0

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

   7. Applied egg-rr 96.0%

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

   if 2.44999999999999989e83 < 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. +-rgt-identity N/A

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

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, 0\right)} - y \]

      4. log-lowering-log.f64 91.7

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\log y}, 0\right) - y \]

   5. Simplified 91.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, 0\right) - y} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

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

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

      4. log-lowering-log.f64 91.7

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

   7. Applied egg-rr 91.7%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-61}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y - z\\ \mathbf{if}\;x \leq -1.42 \cdot 10^{+29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-63}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log y)) z)))
   (if (<= x -1.42e+29) t_0 (if (<= x 5.1e-63) (- (- 0.0 z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(y)) - z;
	double tmp;
	if (x <= -1.42e+29) {
		tmp = t_0;
	} else if (x <= 5.1e-63) {
		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)) - z
    if (x <= (-1.42d+29)) then
        tmp = t_0
    else if (x <= 5.1d-63) 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)) - z;
	double tmp;
	if (x <= -1.42e+29) {
		tmp = t_0;
	} else if (x <= 5.1e-63) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log(y)) - z
	tmp = 0
	if x <= -1.42e+29:
		tmp = t_0
	elif x <= 5.1e-63:
		tmp = (0.0 - z) - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(y)) - z)
	tmp = 0.0
	if (x <= -1.42e+29)
		tmp = t_0;
	elseif (x <= 5.1e-63)
		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)) - z;
	tmp = 0.0;
	if (x <= -1.42e+29)
		tmp = t_0;
	elseif (x <= 5.1e-63)
		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] - z), $MachinePrecision]}, If[LessEqual[x, -1.42e+29], t$95$0, If[LessEqual[x, 5.1e-63], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.42e29 or 5.10000000000000024e-63 < x

   1. Initial program 99.7%

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

      1. sub-neg N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

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

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

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

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{\left(0 - z\right)} - y\right) \]

      8. --lowering--.f64 99.7

         \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{\left(0 - z\right)} - y\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(0 - z\right) - y\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot \log y - z} \]
   6. 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 85.6

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

   7. Simplified 85.6%

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

   if -1.42e29 < x < 5.10000000000000024e-63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 96.0

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

   5. Simplified 96.0%

      \[\leadsto \color{blue}{\left(0 - z\right)} - y \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 96.0

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

   7. Applied egg-rr 96.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-63}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+185}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{+142}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= x -1.8e+185) t_0 (if (<= x 1.82e+142) (- (- 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 <= -1.8e+185) {
		tmp = t_0;
	} else if (x <= 1.82e+142) {
		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 <= (-1.8d+185)) then
        tmp = t_0
    else if (x <= 1.82d+142) 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 <= -1.8e+185) {
		tmp = t_0;
	} else if (x <= 1.82e+142) {
		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 <= -1.8e+185:
		tmp = t_0
	elif x <= 1.82e+142:
		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 <= -1.8e+185)
		tmp = t_0;
	elseif (x <= 1.82e+142)
		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 <= -1.8e+185)
		tmp = t_0;
	elseif (x <= 1.82e+142)
		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, -1.8e+185], t$95$0, If[LessEqual[x, 1.82e+142], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000014e185 or 1.8200000000000001e142 < x

   1. Initial program 99.6%

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

      1. sub-neg N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

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

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

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

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{\left(0 - z\right)} - y\right) \]

      8. --lowering--.f64 99.6

         \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{\left(0 - z\right)} - y\right) \]

   4. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(0 - z\right) - y\right)} \]

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 84.9

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

   7. Simplified 84.9%

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

   if -1.80000000000000014e185 < x < 1.8200000000000001e142

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 81.2

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

   5. Simplified 81.2%

      \[\leadsto \color{blue}{\left(0 - z\right)} - y \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 81.2

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

   7. Applied egg-rr 81.2%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{+142}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.2% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+91}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+98}:\\ \;\;\;\;0 - y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.7e+91) (- 0.0 z) (if (<= z 3.5e+98) (- 0.0 y) (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.7e+91) {
		tmp = 0.0 - z;
	} else if (z <= 3.5e+98) {
		tmp = 0.0 - y;
	} else {
		tmp = 0.0 - 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) :: tmp
    if (z <= (-1.7d+91)) then
        tmp = 0.0d0 - z
    else if (z <= 3.5d+98) then
        tmp = 0.0d0 - y
    else
        tmp = 0.0d0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.7e+91) {
		tmp = 0.0 - z;
	} else if (z <= 3.5e+98) {
		tmp = 0.0 - y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.7e+91:
		tmp = 0.0 - z
	elif z <= 3.5e+98:
		tmp = 0.0 - y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.7e+91)
		tmp = Float64(0.0 - z);
	elseif (z <= 3.5e+98)
		tmp = Float64(0.0 - y);
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.7e+91)
		tmp = 0.0 - z;
	elseif (z <= 3.5e+98)
		tmp = 0.0 - y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.7e+91], N[(0.0 - z), $MachinePrecision], If[LessEqual[z, 3.5e+98], N[(0.0 - y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e91 or 3.5e98 < z

   1. Initial program 100.0%

      \[\left(x \cdot \log y - z\right) - y \]
   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-sub0 N/A

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

      3. --lowering--.f64 74.9

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

   5. Simplified 74.9%

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

   if -1.7e91 < z < 3.5e98

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   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-sub0 N/A

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

      3. --lowering--.f64 42.2

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

   5. Simplified 42.2%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 42.2

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

   7. Applied egg-rr 42.2%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+91}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+98}:\\ \;\;\;\;0 - y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.0% accurate, 16.0× 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 99.8%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

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

   3. --lowering--.f64 63.5

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

5. Simplified 63.5%

   \[\leadsto \color{blue}{\left(0 - z\right)} - y \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 63.5

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

7. Applied egg-rr 63.5%

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

8. Final simplification 63.5%

   \[\leadsto \left(0 - z\right) - y \]
9. Add Preprocessing

Alternative 7: 33.2% accurate, 28.0× speedup

Math

\[\begin{array}{l} \\ 0 - y \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(x \cdot \log y - z\right) - y \]
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-sub0 N/A

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

   3. --lowering--.f64 32.8

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

5. Simplified 32.8%

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

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 32.8

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

7. Applied egg-rr 32.8%

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

8. Final simplification 32.8%

   \[\leadsto 0 - y \]
9. Add Preprocessing

Alternative 8: 2.3% accurate, 112.0× 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. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

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

   3. --lowering--.f64 63.5

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

5. Simplified 63.5%

   \[\leadsto \color{blue}{\left(0 - z\right)} - y \]
6. Step-by-step derivation

   1. flip-- N/A

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

   2. clear-num N/A

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

   3. /-lowering-/.f64 N/A

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

   4. clear-num N/A

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

   5. flip-- N/A

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

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

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

   7. +-rgt-identity N/A

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

7. Applied egg-rr 32.1%

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

8. Taylor expanded in z around inf

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

10. Simplified 2.2%

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

Reproduce

herbie shell --seed 2024195 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))