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

Percentage Accurate: 99.9% → 99.9%

Time: 9.0s

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: 99.9% 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. Final simplification 99.8%

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

Alternative 2: 82.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+202}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+165} \lor \neg \left(z \leq -3.3 \cdot 10^{+41}\right) \land z \leq 1.08 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;-\left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.1e+202)
   (- z)
   (if (or (<= z -1.5e+165) (and (not (<= z -3.3e+41)) (<= z 1.08e+58)))
     (- (* x (log y)) y)
     (- (+ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e+202) {
		tmp = -z;
	} else if ((z <= -1.5e+165) || (!(z <= -3.3e+41) && (z <= 1.08e+58))) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = -(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 (z <= (-3.1d+202)) then
        tmp = -z
    else if ((z <= (-1.5d+165)) .or. (.not. (z <= (-3.3d+41))) .and. (z <= 1.08d+58)) then
        tmp = (x * log(y)) - y
    else
        tmp = -(y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e+202) {
		tmp = -z;
	} else if ((z <= -1.5e+165) || (!(z <= -3.3e+41) && (z <= 1.08e+58))) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -(y + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.1e+202:
		tmp = -z
	elif (z <= -1.5e+165) or (not (z <= -3.3e+41) and (z <= 1.08e+58)):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -(y + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.1e+202)
		tmp = Float64(-z);
	elseif ((z <= -1.5e+165) || (!(z <= -3.3e+41) && (z <= 1.08e+58)))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(-Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.1e+202)
		tmp = -z;
	elseif ((z <= -1.5e+165) || (~((z <= -3.3e+41)) && (z <= 1.08e+58)))
		tmp = (x * log(y)) - y;
	else
		tmp = -(y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.1e+202], (-z), If[Or[LessEqual[z, -1.5e+165], And[N[Not[LessEqual[z, -3.3e+41]], $MachinePrecision], LessEqual[z, 1.08e+58]]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], (-N[(y + z), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if z < -3.09999999999999991e202

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

   4. Taylor expanded in x around 0 89.2%

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

      1. neg-mul-1 89.2%

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

   6. Simplified 89.2%

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

   if -3.09999999999999991e202 < z < -1.49999999999999995e165 or -3.3e41 < z < 1.0799999999999999e58

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 89.4%

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

   if -1.49999999999999995e165 < z < -3.3e41 or 1.0799999999999999e58 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 89.5%

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

      1. neg-mul-1 67.3%

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

   5. Simplified 89.5%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+202}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+165} \lor \neg \left(z \leq -3.3 \cdot 10^{+41}\right) \land z \leq 1.08 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;-\left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+82} \lor \neg \left(x \leq 1.04 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-\left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.9e+82) (not (<= x 1.04e+61))) (* x (log y)) (- (+ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.9e+82) || !(x <= 1.04e+61)) {
		tmp = x * log(y);
	} else {
		tmp = -(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 ((x <= (-5.9d+82)) .or. (.not. (x <= 1.04d+61))) then
        tmp = x * log(y)
    else
        tmp = -(y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.9e+82) || !(x <= 1.04e+61)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -(y + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.9e+82) or not (x <= 1.04e+61):
		tmp = x * math.log(y)
	else:
		tmp = -(y + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.9e+82) || !(x <= 1.04e+61))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(-Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.9e+82) || ~((x <= 1.04e+61)))
		tmp = x * log(y);
	else
		tmp = -(y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.9e+82], N[Not[LessEqual[x, 1.04e+61]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], (-N[(y + z), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if x < -5.8999999999999997e82 or 1.04000000000000003e61 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 72.4%

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

      1. associate-*r/ 72.4%

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

      2. mul-1-neg 72.4%

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

      3. log-rec 72.4%

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

   5. Simplified 72.4%

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

      1. add-sqr-sqrt 40.7%

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

      2. sqrt-unprod 19.1%

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

      3. sqr-neg 19.1%

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

      4. sqrt-unprod 5.3%

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

      5. add-sqr-sqrt 16.5%

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

      6. *-commutative 16.5%

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

      7. associate-/l* 16.5%

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

      8. add-sqr-sqrt 0.5%

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

      9. sqrt-unprod 53.9%

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

      10. sqr-neg 53.9%

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

      11. sqrt-unprod 53.2%

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

      12. add-sqr-sqrt 72.4%

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

   7. Applied egg-rr 72.4%

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

   8. Taylor expanded in x around inf 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-*r/ 54.2%

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

   10. Simplified 54.2%

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

   11. Taylor expanded in y around 0 74.6%

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

   if -5.8999999999999997e82 < x < 1.04000000000000003e61

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.5%

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

      1. neg-mul-1 49.5%

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

   5. Simplified 85.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+82} \lor \neg \left(x \leq 1.04 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-\left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;y \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y)))) (if (<= y 1.15e+116) (- 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 <= 1.15e+116) {
		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 <= 1.15d+116) 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 <= 1.15e+116) {
		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 <= 1.15e+116:
		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 <= 1.15e+116)
		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 <= 1.15e+116)
		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, 1.15e+116], N[(t$95$0 - z), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 1.14999999999999997e116

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 90.9%

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

   if 1.14999999999999997e116 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 83.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.6% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+119}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 2.9e+119) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.9e+119) {
		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 <= 2.9d+119) 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 <= 2.9e+119) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.9e+119:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.9e+119)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.9e+119)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.9e+119], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.90000000000000007e119

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 90.9%

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

   4. Taylor expanded in x around 0 45.8%

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

      1. neg-mul-1 45.8%

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

   6. Simplified 45.8%

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

   if 2.90000000000000007e119 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 64.2%

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

      1. neg-mul-1 64.2%

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

   5. Simplified 64.2%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+119}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.2% accurate, 26.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-N[(y + z), $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 62.5%

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

   1. neg-mul-1 37.0%

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

5. Simplified 62.5%

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

6. Final simplification 62.5%

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

3. Taylor expanded in y around inf 27.5%

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

   1. neg-mul-1 27.5%

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

5. Simplified 27.5%

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

6. Final simplification 27.5%

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

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))