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

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

Alternatives: 5

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. Final simplification 99.9%

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

Alternative 2: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+162} \lor \neg \left(x \leq -5.675 \cdot 10^{+131}\right) \land \left(x \leq -6.6 \cdot 10^{+99} \lor \neg \left(x \leq -1080000000\right) \land \left(x \leq -5.5 \cdot 10^{-12} \lor \neg \left(x \leq 2.4 \cdot 10^{+60}\right) \land \left(x \leq 8.5 \cdot 10^{+90} \lor \neg \left(x \leq 8 \cdot 10^{+141}\right)\right)\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.2e+162)
         (and (not (<= x -5.675e+131))
              (or (<= x -6.6e+99)
                  (and (not (<= x -1080000000.0))
                       (or (<= x -5.5e-12)
                           (and (not (<= x 2.4e+60))
                                (or (<= x 8.5e+90) (not (<= x 8e+141)))))))))
   (* x (log y))
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e+162) || (!(x <= -5.675e+131) && ((x <= -6.6e+99) || (!(x <= -1080000000.0) && ((x <= -5.5e-12) || (!(x <= 2.4e+60) && ((x <= 8.5e+90) || !(x <= 8e+141)))))))) {
		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 <= (-8.2d+162)) .or. (.not. (x <= (-5.675d+131))) .and. (x <= (-6.6d+99)) .or. (.not. (x <= (-1080000000.0d0))) .and. (x <= (-5.5d-12)) .or. (.not. (x <= 2.4d+60)) .and. (x <= 8.5d+90) .or. (.not. (x <= 8d+141))) 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 <= -8.2e+162) || (!(x <= -5.675e+131) && ((x <= -6.6e+99) || (!(x <= -1080000000.0) && ((x <= -5.5e-12) || (!(x <= 2.4e+60) && ((x <= 8.5e+90) || !(x <= 8e+141)))))))) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.2e+162) or (not (x <= -5.675e+131) and ((x <= -6.6e+99) or (not (x <= -1080000000.0) and ((x <= -5.5e-12) or (not (x <= 2.4e+60) and ((x <= 8.5e+90) or not (x <= 8e+141))))))):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.2e+162) || (!(x <= -5.675e+131) && ((x <= -6.6e+99) || (!(x <= -1080000000.0) && ((x <= -5.5e-12) || (!(x <= 2.4e+60) && ((x <= 8.5e+90) || !(x <= 8e+141))))))))
		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 <= -8.2e+162) || (~((x <= -5.675e+131)) && ((x <= -6.6e+99) || (~((x <= -1080000000.0)) && ((x <= -5.5e-12) || (~((x <= 2.4e+60)) && ((x <= 8.5e+90) || ~((x <= 8e+141)))))))))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.2e+162], And[N[Not[LessEqual[x, -5.675e+131]], $MachinePrecision], Or[LessEqual[x, -6.6e+99], And[N[Not[LessEqual[x, -1080000000.0]], $MachinePrecision], Or[LessEqual[x, -5.5e-12], And[N[Not[LessEqual[x, 2.4e+60]], $MachinePrecision], Or[LessEqual[x, 8.5e+90], N[Not[LessEqual[x, 8e+141]], $MachinePrecision]]]]]]]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999998e162 or -5.67500000000000026e131 < x < -6.5999999999999998e99 or -1.08e9 < x < -5.5000000000000004e-12 or 2.4e60 < x < 8.5000000000000002e90 or 8.00000000000000014e141 < x

   1. Initial program 99.7%

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

      1. associate--l- 99.7%

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

      2. fma-neg 99.7%

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

      3. distribute-neg-in 99.7%

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

      4. +-commutative 99.7%

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

      5. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 95.3%

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

      1. fma-neg 95.3%

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

   7. Simplified 95.3%

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

   8. Taylor expanded in x around inf 89.9%

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

   if -8.1999999999999998e162 < x < -5.67500000000000026e131 or -6.5999999999999998e99 < x < -1.08e9 or -5.5000000000000004e-12 < x < 2.4e60 or 8.5000000000000002e90 < x < 8.00000000000000014e141

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.1%

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

      1. neg-mul-1 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+162} \lor \neg \left(x \leq -5.675 \cdot 10^{+131}\right) \land \left(x \leq -6.6 \cdot 10^{+99} \lor \neg \left(x \leq -1080000000\right) \land \left(x \leq -5.5 \cdot 10^{-12} \lor \neg \left(x \leq 2.4 \cdot 10^{+60}\right) \land \left(x \leq 8.5 \cdot 10^{+90} \lor \neg \left(x \leq 8 \cdot 10^{+141}\right)\right)\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-28} \lor \neg \left(x \leq 2.5 \cdot 10^{+58}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e-28) (not (<= x 2.5e+58)))
   (- (* x (log y)) y)
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-28) || !(x <= 2.5e+58)) {
		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 <= (-5.8d-28)) .or. (.not. (x <= 2.5d+58))) 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 <= -5.8e-28) || !(x <= 2.5e+58)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e-28) or not (x <= 2.5e+58):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e-28) || !(x <= 2.5e+58))
		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 <= -5.8e-28) || ~((x <= 2.5e+58)))
		tmp = (x * log(y)) - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e-28], N[Not[LessEqual[x, 2.5e+58]], $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 < -5.80000000000000026e-28 or 2.49999999999999993e58 < x

   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. fma-neg 99.8%

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

      3. distribute-neg-in 99.8%

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

      4. +-commutative 99.8%

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

      5. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 88.8%

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

   if -5.80000000000000026e-28 < x < 2.49999999999999993e58

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 92.7%

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

      1. neg-mul-1 92.7%

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

   5. Simplified 92.7%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-28} \lor \neg \left(x \leq 2.5 \cdot 10^{+58}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.9% 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 99.9%

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

3. Taylor expanded in x around 0 64.7%

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

   1. neg-mul-1 64.7%

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

5. Simplified 64.7%

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

6. Final simplification 64.7%

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

Alternative 5: 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 99.9%

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

   1. associate--l- 99.9%

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

   2. fma-neg 99.9%

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

   3. distribute-neg-in 99.9%

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

   4. +-commutative 99.9%

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

   5. sub-neg 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 38.1%

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

   1. mul-1-neg 38.1%

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

7. Simplified 38.1%

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

8. Final simplification 38.1%

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

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))