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

Percentage Accurate: 99.9% → 99.9%

Time: 9.7s

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, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. *-commutative 99.8%

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

   3. fma-neg 99.8%

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

   4. distribute-neg-in 99.8%

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

   5. add-cube-cbrt 99.2%

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

   6. distribute-lft-neg-in 99.2%

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

   7. cancel-sign-sub-inv 99.2%

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

   8. add-cube-cbrt 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) - y\\ t_1 := \log y \cdot x\\ \mathbf{if}\;z \leq -1.92 \cdot 10^{+25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+92}:\\ \;\;\;\;t_1 - y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+133}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- z) y)) (t_1 (* (log y) x)))
   (if (<= z -1.92e+25)
     t_0
     (if (<= z 1.16e+92) (- t_1 y) (if (<= z 2.3e+133) t_0 (- t_1 z))))))

C

double code(double x, double y, double z) {
	double t_0 = -z - y;
	double t_1 = log(y) * x;
	double tmp;
	if (z <= -1.92e+25) {
		tmp = t_0;
	} else if (z <= 1.16e+92) {
		tmp = t_1 - y;
	} else if (z <= 2.3e+133) {
		tmp = t_0;
	} else {
		tmp = t_1 - 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) :: t_1
    real(8) :: tmp
    t_0 = -z - y
    t_1 = log(y) * x
    if (z <= (-1.92d+25)) then
        tmp = t_0
    else if (z <= 1.16d+92) then
        tmp = t_1 - y
    else if (z <= 2.3d+133) then
        tmp = t_0
    else
        tmp = t_1 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z - y;
	double t_1 = Math.log(y) * x;
	double tmp;
	if (z <= -1.92e+25) {
		tmp = t_0;
	} else if (z <= 1.16e+92) {
		tmp = t_1 - y;
	} else if (z <= 2.3e+133) {
		tmp = t_0;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z - y
	t_1 = math.log(y) * x
	tmp = 0
	if z <= -1.92e+25:
		tmp = t_0
	elif z <= 1.16e+92:
		tmp = t_1 - y
	elif z <= 2.3e+133:
		tmp = t_0
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) - y)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (z <= -1.92e+25)
		tmp = t_0;
	elseif (z <= 1.16e+92)
		tmp = Float64(t_1 - y);
	elseif (z <= 2.3e+133)
		tmp = t_0;
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z - y;
	t_1 = log(y) * x;
	tmp = 0.0;
	if (z <= -1.92e+25)
		tmp = t_0;
	elseif (z <= 1.16e+92)
		tmp = t_1 - y;
	elseif (z <= 2.3e+133)
		tmp = t_0;
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) - y), $MachinePrecision]}, Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1.92e+25], t$95$0, If[LessEqual[z, 1.16e+92], N[(t$95$1 - y), $MachinePrecision], If[LessEqual[z, 2.3e+133], t$95$0, N[(t$95$1 - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9200000000000001e25 or 1.16000000000000006e92 < z < 2.2999999999999999e133

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 86.0%

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

      1. mul-1-neg 86.0%

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

   4. Simplified 86.0%

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

   if -1.9200000000000001e25 < z < 1.16000000000000006e92

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 90.6%

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

   if 2.2999999999999999e133 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 97.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{+25}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+92}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+133}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - z\\ \end{array} \]

Alternative 3: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{+25} \lor \neg \left(z \leq 4.8 \cdot 10^{+86}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.92e+25) (not (<= z 4.8e+86)))
   (- (- z) y)
   (- (* (log y) x) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.92e+25) || !(z <= 4.8e+86)) {
		tmp = -z - y;
	} else {
		tmp = (log(y) * x) - 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 <= (-1.92d+25)) .or. (.not. (z <= 4.8d+86))) then
        tmp = -z - y
    else
        tmp = (log(y) * x) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.92e+25) || !(z <= 4.8e+86)) {
		tmp = -z - y;
	} else {
		tmp = (Math.log(y) * x) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.92e+25) or not (z <= 4.8e+86):
		tmp = -z - y
	else:
		tmp = (math.log(y) * x) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.92e+25) || !(z <= 4.8e+86))
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(Float64(log(y) * x) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.92e+25) || ~((z <= 4.8e+86)))
		tmp = -z - y;
	else
		tmp = (log(y) * x) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.92e+25], N[Not[LessEqual[z, 4.8e+86]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9200000000000001e25 or 4.8000000000000001e86 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 82.2%

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

      1. mul-1-neg 82.2%

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

   4. Simplified 82.2%

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

   if -1.9200000000000001e25 < z < 4.8000000000000001e86

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 90.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{+25} \lor \neg \left(z \leq 4.8 \cdot 10^{+86}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - y\\ \end{array} \]

Alternative 4: 79.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+102} \lor \neg \left(x \leq 8.2 \cdot 10^{+160}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.9e+102) (not (<= x 8.2e+160))) (* (log y) x) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.9e+102) || !(x <= 8.2e+160)) {
		tmp = log(y) * x;
	} 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 <= (-3.9d+102)) .or. (.not. (x <= 8.2d+160))) then
        tmp = log(y) * x
    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 <= -3.9e+102) || !(x <= 8.2e+160)) {
		tmp = Math.log(y) * x;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.9e+102) or not (x <= 8.2e+160):
		tmp = math.log(y) * x
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.9e+102) || !(x <= 8.2e+160))
		tmp = Float64(log(y) * x);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.9e+102) || ~((x <= 8.2e+160)))
		tmp = log(y) * x;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.9e+102], N[Not[LessEqual[x, 8.2e+160]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8999999999999998e102 or 8.19999999999999996e160 < x

   1. Initial program 99.6%

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

      1. associate--l- 99.6%

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

      2. *-commutative 99.6%

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

      3. fma-neg 99.6%

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

      4. distribute-neg-in 99.6%

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

      5. add-cube-cbrt 99.4%

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

      6. distribute-lft-neg-in 99.4%

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

      7. cancel-sign-sub-inv 99.4%

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

      8. add-cube-cbrt 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in x around inf 73.8%

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

   if -3.8999999999999998e102 < x < 8.19999999999999996e160

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 82.4%

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

      1. mul-1-neg 82.4%

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

   4. Simplified 82.4%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+102} \lor \neg \left(x \leq 8.2 \cdot 10^{+160}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 6: 52.3% accurate, 26.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{+42}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 3.2e+42) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.2e+42) {
		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 <= 3.2d+42) 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 <= 3.2e+42) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.2e+42:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.2e+42)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.2e+42)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.2e+42], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 3.20000000000000002e42

   1. Initial program 99.8%

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

      1. associate--l- 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-neg 99.8%

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

      4. distribute-neg-in 99.8%

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

      5. add-cube-cbrt 99.7%

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

      6. distribute-lft-neg-in 99.7%

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

      7. cancel-sign-sub-inv 99.7%

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

      8. add-cube-cbrt 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 46.6%

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

      1. mul-1-neg 46.6%

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

   6. Simplified 46.6%

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

   if 3.20000000000000002e42 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 61.0%

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

      1. mul-1-neg 61.0%

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

   4. Simplified 61.0%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{+42}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 7: 66.6% 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. Taylor expanded in x around 0 63.8%

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

   1. mul-1-neg 63.8%

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

4. Simplified 63.8%

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

5. Final simplification 63.8%

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

Alternative 8: 34.0% 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. Taylor expanded in y around inf 31.8%

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

   1. mul-1-neg 31.8%

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

4. Simplified 31.8%

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

5. Final simplification 31.8%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))