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

Percentage Accurate: 99.9% → 99.9%

Time: 8.4s

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 99.9%

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

Alternative 2: 84.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(0 - z\right) - y\\ t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-30}:\\ \;\;\;\;t\_1 - y\\ \mathbf{elif}\;z \leq 620000000000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- 0.0 z) y)) (t_1 (* x (log y))))
   (if (<= z -6.6e+81)
     t_0
     (if (<= z 8.6e-30) (- t_1 y) (if (<= z 620000000000.0) t_0 (- t_1 z))))))

C

double code(double x, double y, double z) {
	double t_0 = (0.0 - z) - y;
	double t_1 = x * log(y);
	double tmp;
	if (z <= -6.6e+81) {
		tmp = t_0;
	} else if (z <= 8.6e-30) {
		tmp = t_1 - y;
	} else if (z <= 620000000000.0) {
		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 = (0.0d0 - z) - y
    t_1 = x * log(y)
    if (z <= (-6.6d+81)) then
        tmp = t_0
    else if (z <= 8.6d-30) then
        tmp = t_1 - y
    else if (z <= 620000000000.0d0) 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 = (0.0 - z) - y;
	double t_1 = x * Math.log(y);
	double tmp;
	if (z <= -6.6e+81) {
		tmp = t_0;
	} else if (z <= 8.6e-30) {
		tmp = t_1 - y;
	} else if (z <= 620000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.0 - z) - y
	t_1 = x * math.log(y)
	tmp = 0
	if z <= -6.6e+81:
		tmp = t_0
	elif z <= 8.6e-30:
		tmp = t_1 - y
	elif z <= 620000000000.0:
		tmp = t_0
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.0 - z) - y)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -6.6e+81)
		tmp = t_0;
	elseif (z <= 8.6e-30)
		tmp = Float64(t_1 - y);
	elseif (z <= 620000000000.0)
		tmp = t_0;
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.0 - z) - y;
	t_1 = x * log(y);
	tmp = 0.0;
	if (z <= -6.6e+81)
		tmp = t_0;
	elseif (z <= 8.6e-30)
		tmp = t_1 - y;
	elseif (z <= 620000000000.0)
		tmp = t_0;
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+81], t$95$0, If[LessEqual[z, 8.6e-30], N[(t$95$1 - y), $MachinePrecision], If[LessEqual[z, 620000000000.0], t$95$0, N[(t$95$1 - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.6e81 or 8.59999999999999932e-30 < z < 6.2e11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y + z\right)\right) \]

      2. distribute-neg-in N/A

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

      3. +-commutative N/A

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

      4. sub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \color{blue}{y}\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

      7. --lowering--.f64 86.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

   5. Simplified 86.5%

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

      1. sub0-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

      2. neg-lowering-neg.f64 86.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(z\right), y\right) \]

   7. Applied egg-rr 86.5%

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

   if -6.6e81 < z < 8.59999999999999932e-30

   1. Initial program 99.8%

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

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log y\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log y\right), y\right) \]

      3. log-lowering-log.f64 91.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), y\right) \]

   5. Simplified 91.2%

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

   if 6.2e11 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log y\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log y\right), z\right) \]

      3. log-lowering-log.f64 86.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right) \]

   5. Simplified 86.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+81}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;z \leq 620000000000:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y - y\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{-33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+129}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log y)) y)))
   (if (<= x -2.2e-33) t_0 (if (<= x 4.3e+129) (- (- 0.0 z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(y)) - y;
	double tmp;
	if (x <= -2.2e-33) {
		tmp = t_0;
	} else if (x <= 4.3e+129) {
		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)) - y
    if (x <= (-2.2d-33)) then
        tmp = t_0
    else if (x <= 4.3d+129) 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)) - y;
	double tmp;
	if (x <= -2.2e-33) {
		tmp = t_0;
	} else if (x <= 4.3e+129) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log(y)) - y
	tmp = 0
	if x <= -2.2e-33:
		tmp = t_0
	elif x <= 4.3e+129:
		tmp = (0.0 - z) - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (x <= -2.2e-33)
		tmp = t_0;
	elseif (x <= 4.3e+129)
		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)) - y;
	tmp = 0.0;
	if (x <= -2.2e-33)
		tmp = t_0;
	elseif (x <= 4.3e+129)
		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] - y), $MachinePrecision]}, If[LessEqual[x, -2.2e-33], t$95$0, If[LessEqual[x, 4.3e+129], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000005e-33 or 4.30000000000000021e129 < x

   1. Initial program 99.8%

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

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log y\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log y\right), y\right) \]

      3. log-lowering-log.f64 86.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), y\right) \]

   5. Simplified 86.1%

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

   if -2.20000000000000005e-33 < x < 4.30000000000000021e129

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y + z\right)\right) \]

      2. distribute-neg-in N/A

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

      3. +-commutative N/A

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

      4. sub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \color{blue}{y}\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

      7. --lowering--.f64 87.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

   5. Simplified 87.9%

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

      1. sub0-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

      2. neg-lowering-neg.f64 87.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(z\right), y\right) \]

   7. Applied egg-rr 87.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+129}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+124}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+130}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= x -3.5e+124) t_0 (if (<= x 1.4e+130) (- (- 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 <= -3.5e+124) {
		tmp = t_0;
	} else if (x <= 1.4e+130) {
		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 <= (-3.5d+124)) then
        tmp = t_0
    else if (x <= 1.4d+130) 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 <= -3.5e+124) {
		tmp = t_0;
	} else if (x <= 1.4e+130) {
		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 <= -3.5e+124:
		tmp = t_0
	elif x <= 1.4e+130:
		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 <= -3.5e+124)
		tmp = t_0;
	elseif (x <= 1.4e+130)
		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 <= -3.5e+124)
		tmp = t_0;
	elseif (x <= 1.4e+130)
		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, -3.5e+124], t$95$0, If[LessEqual[x, 1.4e+130], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000001e124 or 1.3999999999999999e130 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\log y}\right) \]

      2. log-lowering-log.f64 84.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right) \]

   5. Simplified 84.8%

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

   if -3.5000000000000001e124 < x < 1.3999999999999999e130

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y + z\right)\right) \]

      2. distribute-neg-in N/A

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

      3. +-commutative N/A

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

      4. sub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \color{blue}{y}\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

      7. --lowering--.f64 82.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

   5. Simplified 82.8%

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

      1. sub0-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

      2. neg-lowering-neg.f64 82.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(z\right), y\right) \]

   7. Applied egg-rr 82.8%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+130}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.8% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+155}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;z \leq 1800000000:\\ \;\;\;\;0 - y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.65e+155) (- 0.0 z) (if (<= z 1800000000.0) (- 0.0 y) (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.65e+155) {
		tmp = 0.0 - z;
	} else if (z <= 1800000000.0) {
		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 <= (-1.65d+155)) then
        tmp = 0.0d0 - z
    else if (z <= 1800000000.0d0) 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 <= -1.65e+155) {
		tmp = 0.0 - z;
	} else if (z <= 1800000000.0) {
		tmp = 0.0 - y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.65e+155:
		tmp = 0.0 - z
	elif z <= 1800000000.0:
		tmp = 0.0 - y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.65e+155)
		tmp = Float64(0.0 - z);
	elseif (z <= 1800000000.0)
		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 <= -1.65e+155)
		tmp = 0.0 - z;
	elseif (z <= 1800000000.0)
		tmp = 0.0 - y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.65e+155], N[(0.0 - z), $MachinePrecision], If[LessEqual[z, 1800000000.0], N[(0.0 - y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999e155 or 1.8e9 < 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

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

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

      3. --lowering--.f64 68.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 68.1%

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

   if -1.6499999999999999e155 < z < 1.8e9

   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

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 42.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

   5. Simplified 42.4%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 42.4%

         \[\leadsto \mathsf{neg.f64}\left(y\right) \]

   7. Applied egg-rr 42.4%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+155}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;z \leq 1800000000:\\ \;\;\;\;0 - y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.5% accurate, 21.4× 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 99.9%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(\left(y + z\right)\right) \]

   2. distribute-neg-in N/A

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

   3. +-commutative N/A

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

   4. sub-neg N/A

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

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

      \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \color{blue}{y}\right) \]

   6. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

   7. --lowering--.f64 63.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

5. Simplified 63.2%

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

   1. sub0-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

   2. neg-lowering-neg.f64 63.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(z\right), y\right) \]

7. Applied egg-rr 63.2%

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

8. Final simplification 63.2%

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

Alternative 7: 33.2% accurate, 35.7× 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 99.9%

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

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

   2. neg-sub0 N/A

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

   3. --lowering--.f64 33.1%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

5. Simplified 33.1%

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

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 33.1%

      \[\leadsto \mathsf{neg.f64}\left(y\right) \]

7. Applied egg-rr 33.1%

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

8. Final simplification 33.1%

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

Alternative 8: 2.3% accurate, 107.0× 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 99.9%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(\left(y + z\right)\right) \]

   2. distribute-neg-in N/A

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

   3. +-commutative N/A

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

   4. sub-neg N/A

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

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

      \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \color{blue}{y}\right) \]

   6. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

   7. --lowering--.f64 63.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

5. Simplified 63.2%

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

   1. flip-- N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{0 \cdot 0 - z \cdot z}{0 + z}\right), y\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{1}{\frac{0 + z}{0 \cdot 0 - z \cdot z}}\right), y\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{0 + z}{0 \cdot 0 - z \cdot z}\right)\right), y\right) \]

   4. +-lft-identity N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{z}{0 \cdot 0 - z \cdot z}\right)\right), y\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{z}{0 - z \cdot z}\right)\right), y\right) \]

   6. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{z}{\mathsf{neg}\left(z \cdot z\right)}\right)\right), y\right) \]

   7. distribute-lft-neg-in N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{z}{\left(\mathsf{neg}\left(z\right)\right) \cdot z}\right)\right), y\right) \]

   8. sub0-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{z}{\left(0 - z\right) \cdot z}\right)\right), y\right) \]

7. Applied egg-rr 29.8%

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

8. Taylor expanded in z around inf

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

10. Simplified 2.4%

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

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))