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

Percentage Accurate: 99.8% → 99.8%

Time: 9.7s

Alternatives: 7

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: 99.8% 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

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

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. Final simplification 99.8%

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

Alternative 2: 84.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+60} \lor \neg \left(x \leq -0.00021 \lor \neg \left(x \leq -7.1 \cdot 10^{-69}\right) \land x \leq 1.1 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e+60)
         (not (or (<= x -0.00021) (and (not (<= x -7.1e-69)) (<= x 1.1e+30)))))
   (- (* x (log y)) y)
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+60) || !((x <= -0.00021) || (!(x <= -7.1e-69) && (x <= 1.1e+30)))) {
		tmp = (x * log(y)) - 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 <= (-4d+60)) .or. (.not. (x <= (-0.00021d0)) .or. (.not. (x <= (-7.1d-69))) .and. (x <= 1.1d+30))) then
        tmp = (x * log(y)) - 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 <= -4e+60) || !((x <= -0.00021) || (!(x <= -7.1e-69) && (x <= 1.1e+30)))) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e+60) or not ((x <= -0.00021) or (not (x <= -7.1e-69) and (x <= 1.1e+30))):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e+60) || !((x <= -0.00021) || (!(x <= -7.1e-69) && (x <= 1.1e+30))))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4e+60) || ~(((x <= -0.00021) || (~((x <= -7.1e-69)) && (x <= 1.1e+30)))))
		tmp = (x * log(y)) - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e+60], N[Not[Or[LessEqual[x, -0.00021], And[N[Not[LessEqual[x, -7.1e-69]], $MachinePrecision], LessEqual[x, 1.1e+30]]]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9999999999999998e60 or -2.1000000000000001e-4 < x < -7.0999999999999998e-69 or 1.1e30 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 90.6%

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

   if -3.9999999999999998e60 < x < -2.1000000000000001e-4 or -7.0999999999999998e-69 < x < 1.1e30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.5%

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

      1. neg-mul-1 93.5%

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

      2. +-commutative 93.5%

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

      3. distribute-neg-in 93.5%

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

      4. sub-neg 93.5%

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

   5. Simplified 93.5%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+60} \lor \neg \left(x \leq -0.00021 \lor \neg \left(x \leq -7.1 \cdot 10^{-69}\right) \land x \leq 1.1 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ t_1 := t\_0 - y\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -0.00024:\\ \;\;\;\;t\_0 - z\\ \mathbf{elif}\;x \leq -7.7 \cdot 10^{-69} \lor \neg \left(x \leq 7 \cdot 10^{+30}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))) (t_1 (- t_0 y)))
   (if (<= x -6.2e+59)
     t_1
     (if (<= x -0.00024)
       (- t_0 z)
       (if (or (<= x -7.7e-69) (not (<= x 7e+30))) t_1 (- (- z) y))))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double t_1 = t_0 - y;
	double tmp;
	if (x <= -6.2e+59) {
		tmp = t_1;
	} else if (x <= -0.00024) {
		tmp = t_0 - z;
	} else if ((x <= -7.7e-69) || !(x <= 7e+30)) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * log(y)
    t_1 = t_0 - y
    if (x <= (-6.2d+59)) then
        tmp = t_1
    else if (x <= (-0.00024d0)) then
        tmp = t_0 - z
    else if ((x <= (-7.7d-69)) .or. (.not. (x <= 7d+30))) then
        tmp = t_1
    else
        tmp = -z - 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 - y;
	double tmp;
	if (x <= -6.2e+59) {
		tmp = t_1;
	} else if (x <= -0.00024) {
		tmp = t_0 - z;
	} else if ((x <= -7.7e-69) || !(x <= 7e+30)) {
		tmp = t_1;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	t_1 = t_0 - y
	tmp = 0
	if x <= -6.2e+59:
		tmp = t_1
	elif x <= -0.00024:
		tmp = t_0 - z
	elif (x <= -7.7e-69) or not (x <= 7e+30):
		tmp = t_1
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	t_1 = Float64(t_0 - y)
	tmp = 0.0
	if (x <= -6.2e+59)
		tmp = t_1;
	elseif (x <= -0.00024)
		tmp = Float64(t_0 - z);
	elseif ((x <= -7.7e-69) || !(x <= 7e+30))
		tmp = t_1;
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	t_1 = t_0 - y;
	tmp = 0.0;
	if (x <= -6.2e+59)
		tmp = t_1;
	elseif (x <= -0.00024)
		tmp = t_0 - z;
	elseif ((x <= -7.7e-69) || ~((x <= 7e+30)))
		tmp = t_1;
	else
		tmp = -z - 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 - y), $MachinePrecision]}, If[LessEqual[x, -6.2e+59], t$95$1, If[LessEqual[x, -0.00024], N[(t$95$0 - z), $MachinePrecision], If[Or[LessEqual[x, -7.7e-69], N[Not[LessEqual[x, 7e+30]], $MachinePrecision]], t$95$1, N[((-z) - y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.20000000000000029e59 or -2.40000000000000006e-4 < x < -7.70000000000000008e-69 or 7.00000000000000042e30 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 90.6%

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

   if -6.20000000000000029e59 < x < -2.40000000000000006e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 80.7%

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

   if -7.70000000000000008e-69 < x < 7.00000000000000042e30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.1%

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

      1. neg-mul-1 95.1%

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

      2. +-commutative 95.1%

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

      3. distribute-neg-in 95.1%

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

      4. sub-neg 95.1%

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

   5. Simplified 95.1%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \leq -0.00024:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;x \leq -7.7 \cdot 10^{-69} \lor \neg \left(x \leq 7 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+133} \lor \neg \left(x \leq 1.45 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+133) (not (<= x 1.45e+32))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+133) || !(x <= 1.45e+32)) {
		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 <= (-7d+133)) .or. (.not. (x <= 1.45d+32))) 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 <= -7e+133) || !(x <= 1.45e+32)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e+133) or not (x <= 1.45e+32):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e+133) || !(x <= 1.45e+32))
		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 <= -7e+133) || ~((x <= 1.45e+32)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e+133], N[Not[LessEqual[x, 1.45e+32]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.9999999999999997e133 or 1.45000000000000001e32 < 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 99.6%

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

      2. associate--l+ 99.6%

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

      3. *-commutative 99.6%

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

      4. add-cube-cbrt 98.5%

         \[\leadsto \log y \cdot \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} + \left(\left(-z\right) - y\right) \]

      5. associate-*r* 98.4%

         \[\leadsto \color{blue}{\left(\log y \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x}} + \left(\left(-z\right) - y\right) \]

      6. fma-define 98.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right), \sqrt[3]{x}, \left(-z\right) - y\right)} \]

      7. pow2 98.4%

         \[\leadsto \mathsf{fma}\left(\log y \cdot \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(-z\right) - y\right) \]

   4. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot {\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(-z\right) - y\right)} \]

   5. Taylor expanded in x around inf 76.6%

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

   if -6.9999999999999997e133 < x < 1.45000000000000001e32

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.6%

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

      1. neg-mul-1 87.6%

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

      2. +-commutative 87.6%

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

      3. distribute-neg-in 87.6%

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

      4. sub-neg 87.6%

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

   5. Simplified 87.6%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+133} \lor \neg \left(x \leq 1.45 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.0% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{-7} \lor \neg \left(y \leq 2.8 \cdot 10^{+15}\right) \land y \leq 9.6 \cdot 10^{+86}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 5.6e-7) (and (not (<= y 2.8e+15)) (<= y 9.6e+86))) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 5.6e-7) || (!(y <= 2.8e+15) && (y <= 9.6e+86))) {
		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-7) .or. (.not. (y <= 2.8d+15)) .and. (y <= 9.6d+86)) 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-7) || (!(y <= 2.8e+15) && (y <= 9.6e+86))) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 5.6e-7) or (not (y <= 2.8e+15) and (y <= 9.6e+86)):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 5.6e-7) || (!(y <= 2.8e+15) && (y <= 9.6e+86)))
		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-7) || (~((y <= 2.8e+15)) && (y <= 9.6e+86)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 5.6e-7], And[N[Not[LessEqual[y, 2.8e+15]], $MachinePrecision], LessEqual[y, 9.6e+86]]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 5.60000000000000038e-7 or 2.8e15 < y < 9.6000000000000001e86

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 42.1%

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

      1. neg-mul-1 42.1%

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

   5. Simplified 42.1%

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

   if 5.60000000000000038e-7 < y < 2.8e15 or 9.6000000000000001e86 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. neg-mul-1 72.8%

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

   5. Simplified 72.8%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{-7} \lor \neg \left(y \leq 2.8 \cdot 10^{+15}\right) \land y \leq 9.6 \cdot 10^{+86}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.4% 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. Add Preprocessing

3. Taylor expanded in x around 0 63.4%

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

   1. neg-mul-1 63.4%

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

   2. +-commutative 63.4%

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

   3. distribute-neg-in 63.4%

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

   4. sub-neg 63.4%

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

5. Simplified 63.4%

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

6. Final simplification 63.4%

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

Alternative 7: 33.6% 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. Add Preprocessing

3. Taylor expanded in y around inf 33.9%

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

   1. neg-mul-1 33.9%

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

5. Simplified 33.9%

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

6. Final simplification 33.9%

   \[\leadsto -y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))