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

Percentage Accurate: 99.9% → 99.9%

Time: 13.3s

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 99.8%

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

Alternative 2: 82.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y - y\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+200}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{+26}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+47} \lor \neg \left(x \leq 7.6 \cdot 10^{+57}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{-1}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log y)) y)))
   (if (<= x -1.35e+200)
     t_0
     (if (<= x 6.1e+26)
       (- (- z) y)
       (if (or (<= x 1.3e+47) (not (<= x 7.6e+57))) t_0 (/ 1.0 (/ -1.0 z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(y)) - y;
	double tmp;
	if (x <= -1.35e+200) {
		tmp = t_0;
	} else if (x <= 6.1e+26) {
		tmp = -z - y;
	} else if ((x <= 1.3e+47) || !(x <= 7.6e+57)) {
		tmp = t_0;
	} else {
		tmp = 1.0 / (-1.0 / 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) :: t_0
    real(8) :: tmp
    t_0 = (x * log(y)) - y
    if (x <= (-1.35d+200)) then
        tmp = t_0
    else if (x <= 6.1d+26) then
        tmp = -z - y
    else if ((x <= 1.3d+47) .or. (.not. (x <= 7.6d+57))) then
        tmp = t_0
    else
        tmp = 1.0d0 / ((-1.0d0) / z)
    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 <= -1.35e+200) {
		tmp = t_0;
	} else if (x <= 6.1e+26) {
		tmp = -z - y;
	} else if ((x <= 1.3e+47) || !(x <= 7.6e+57)) {
		tmp = t_0;
	} else {
		tmp = 1.0 / (-1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log(y)) - y
	tmp = 0
	if x <= -1.35e+200:
		tmp = t_0
	elif x <= 6.1e+26:
		tmp = -z - y
	elif (x <= 1.3e+47) or not (x <= 7.6e+57):
		tmp = t_0
	else:
		tmp = 1.0 / (-1.0 / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (x <= -1.35e+200)
		tmp = t_0;
	elseif (x <= 6.1e+26)
		tmp = Float64(Float64(-z) - y);
	elseif ((x <= 1.3e+47) || !(x <= 7.6e+57))
		tmp = t_0;
	else
		tmp = Float64(1.0 / Float64(-1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * log(y)) - y;
	tmp = 0.0;
	if (x <= -1.35e+200)
		tmp = t_0;
	elseif (x <= 6.1e+26)
		tmp = -z - y;
	elseif ((x <= 1.3e+47) || ~((x <= 7.6e+57)))
		tmp = t_0;
	else
		tmp = 1.0 / (-1.0 / z);
	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, -1.35e+200], t$95$0, If[LessEqual[x, 6.1e+26], N[((-z) - y), $MachinePrecision], If[Or[LessEqual[x, 1.3e+47], N[Not[LessEqual[x, 7.6e+57]], $MachinePrecision]], t$95$0, N[(1.0 / N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35000000000000008e200 or 6.1000000000000003e26 < x < 1.30000000000000002e47 or 7.5999999999999997e57 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 90.5%

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

   if -1.35000000000000008e200 < x < 6.1000000000000003e26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.2%

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

      1. neg-mul-1 85.2%

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

      2. +-commutative 85.2%

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

      3. distribute-neg-in 85.2%

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

      4. sub-neg 85.2%

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

   5. Simplified 85.2%

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

   if 1.30000000000000002e47 < x < 7.5999999999999997e57

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 66.1%

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

      1. associate-*r/ 66.1%

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

      2. log-rec 66.1%

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

      3. mul-1-neg 66.1%

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

      4. associate-*r* 66.1%

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

      5. associate-*r* 66.1%

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

      6. neg-mul-1 66.1%

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

      7. mul-1-neg 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in z around inf 51.6%

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

      1. associate-*r/ 51.6%

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

      2. mul-1-neg 51.6%

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

   8. Simplified 51.6%

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

      1. associate-*r/ 51.8%

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

      2. clear-num 51.8%

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

      3. add-sqr-sqrt 0.4%

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

      4. sqrt-unprod 1.1%

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

      5. sqr-neg 1.1%

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

      6. sqrt-unprod 0.7%

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

      7. add-sqr-sqrt 4.7%

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

   10. Applied egg-rr 4.7%

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

       1. div-inv 4.7%

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

       2. associate-*r/ 4.7%

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

       3. *-commutative 4.7%

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

       4. *-un-lft-identity 4.7%

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

       5. add-sqr-sqrt 4.7%

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

       6. sqrt-unprod 1.9%

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

       7. *-un-lft-identity 1.9%

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

       8. metadata-eval 1.9%

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

       9. swap-sqr 1.9%

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

       10. metadata-eval 1.9%

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

       11. associate-/r/ 1.9%

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

       12. metadata-eval 1.9%

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

       13. associate-/r/ 1.9%

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

       14. sqrt-unprod 0.0%

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

       15. add-sqr-sqrt 51.8%

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

       16. associate-/r/ 51.8%

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

       17. metadata-eval 51.8%

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

       18. neg-mul-1 51.8%

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

       19. distribute-neg-frac 51.8%

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

       20. neg-sub0 51.8%

           \[\leadsto \frac{1}{\color{blue}{0 - \frac{y}{y \cdot z}}} \]

       21. associate-/r* 51.8%

           \[\leadsto \frac{1}{0 - \color{blue}{\frac{\frac{y}{y}}{z}}} \]

       22. *-inverses 51.8%

           \[\leadsto \frac{1}{0 - \frac{\color{blue}{1}}{z}} \]

   12. Applied egg-rr 51.8%

       \[\leadsto \frac{1}{\color{blue}{0 - \frac{1}{z}}} \]
   13. Step-by-step derivation

       1. neg-sub0 51.8%

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

       2. distribute-neg-frac 51.8%

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

       3. metadata-eval 51.8%

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

   14. Simplified 51.8%

       \[\leadsto \frac{1}{\color{blue}{\frac{-1}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+200}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{+26}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+47} \lor \neg \left(x \leq 7.6 \cdot 10^{+57}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{-1}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.24 \cdot 10^{+281} \lor \neg \left(x \leq 1.16 \cdot 10^{+27} \lor \neg \left(x \leq 5.8 \cdot 10^{+45}\right) \land x \leq 1.45 \cdot 10^{+87}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.24e+281)
         (not (or (<= x 1.16e+27) (and (not (<= x 5.8e+45)) (<= x 1.45e+87)))))
   (* x (log y))
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.24e+281) || !((x <= 1.16e+27) || (!(x <= 5.8e+45) && (x <= 1.45e+87)))) {
		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 <= (-1.24d+281)) .or. (.not. (x <= 1.16d+27) .or. (.not. (x <= 5.8d+45)) .and. (x <= 1.45d+87))) 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 <= -1.24e+281) || !((x <= 1.16e+27) || (!(x <= 5.8e+45) && (x <= 1.45e+87)))) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.24e+281) or not ((x <= 1.16e+27) or (not (x <= 5.8e+45) and (x <= 1.45e+87))):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.24e+281) || !((x <= 1.16e+27) || (!(x <= 5.8e+45) && (x <= 1.45e+87))))
		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 <= -1.24e+281) || ~(((x <= 1.16e+27) || (~((x <= 5.8e+45)) && (x <= 1.45e+87)))))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.24e+281], N[Not[Or[LessEqual[x, 1.16e+27], And[N[Not[LessEqual[x, 5.8e+45]], $MachinePrecision], LessEqual[x, 1.45e+87]]]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.24e281 or 1.16e27 < x < 5.7999999999999994e45 or 1.4499999999999999e87 < x

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in x around inf 87.7%

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

   if -1.24e281 < x < 1.16e27 or 5.7999999999999994e45 < x < 1.4499999999999999e87

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.2%

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

      1. neg-mul-1 82.2%

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

      2. +-commutative 82.2%

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

      3. distribute-neg-in 82.2%

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

      4. sub-neg 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.24 \cdot 10^{+281} \lor \neg \left(x \leq 1.16 \cdot 10^{+27} \lor \neg \left(x \leq 5.8 \cdot 10^{+45}\right) \land x \leq 1.45 \cdot 10^{+87}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;y \leq 1.65 \cdot 10^{+19}:\\ \;\;\;\;t\_0 - z\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+128}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= y 1.65e+19) (- t_0 z) (if (<= y 7.5e+128) (- (- z) y) (- t_0 y)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (y <= 1.65e+19) {
		tmp = t_0 - z;
	} else if (y <= 7.5e+128) {
		tmp = -z - y;
	} 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 <= 1.65d+19) then
        tmp = t_0 - z
    else if (y <= 7.5d+128) then
        tmp = -z - y
    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 <= 1.65e+19) {
		tmp = t_0 - z;
	} else if (y <= 7.5e+128) {
		tmp = -z - y;
	} else {
		tmp = t_0 - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if y <= 1.65e+19:
		tmp = t_0 - z
	elif y <= 7.5e+128:
		tmp = -z - y
	else:
		tmp = t_0 - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 1.65e+19)
		tmp = Float64(t_0 - z);
	elseif (y <= 7.5e+128)
		tmp = Float64(Float64(-z) - y);
	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 <= 1.65e+19)
		tmp = t_0 - z;
	elseif (y <= 7.5e+128)
		tmp = -z - y;
	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, 1.65e+19], N[(t$95$0 - z), $MachinePrecision], If[LessEqual[y, 7.5e+128], N[((-z) - y), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.65e19

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 90.5%

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

   if 1.65e19 < y < 7.50000000000000076e128

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.3%

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

      1. neg-mul-1 84.3%

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

      2. +-commutative 84.3%

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

      3. distribute-neg-in 84.3%

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

      4. sub-neg 84.3%

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

   5. Simplified 84.3%

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

   if 7.50000000000000076e128 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 93.0%

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

Alternative 5: 51.7% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-19} \lor \neg \left(y \leq 5.1 \cdot 10^{+73}\right) \land y \leq 7 \cdot 10^{+86}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 1.85e-19) (and (not (<= y 5.1e+73)) (<= y 7e+86))) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 1.85e-19) || (!(y <= 5.1e+73) && (y <= 7e+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 <= 1.85d-19) .or. (.not. (y <= 5.1d+73)) .and. (y <= 7d+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 <= 1.85e-19) || (!(y <= 5.1e+73) && (y <= 7e+86))) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 1.85e-19) or (not (y <= 5.1e+73) and (y <= 7e+86)):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 1.85e-19) || (!(y <= 5.1e+73) && (y <= 7e+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 <= 1.85e-19) || (~((y <= 5.1e+73)) && (y <= 7e+86)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 1.85e-19], And[N[Not[LessEqual[y, 5.1e+73]], $MachinePrecision], LessEqual[y, 7e+86]]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.85000000000000003e-19 or 5.10000000000000024e73 < y < 7.00000000000000038e86

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 51.0%

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

      1. neg-mul-1 51.0%

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

   5. Simplified 51.0%

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

   if 1.85000000000000003e-19 < y < 5.10000000000000024e73 or 7.00000000000000038e86 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 65.7%

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

      1. neg-mul-1 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-19} \lor \neg \left(y \leq 5.1 \cdot 10^{+73}\right) \land y \leq 7 \cdot 10^{+86}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.5% 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 68.4%

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

   1. neg-mul-1 68.4%

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

   2. +-commutative 68.4%

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

   3. distribute-neg-in 68.4%

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

   4. sub-neg 68.4%

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

5. Simplified 68.4%

   \[\leadsto \color{blue}{\left(-z\right) - y} \]
6. Add Preprocessing

Alternative 7: 34.3% 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 34.6%

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

   1. neg-mul-1 34.6%

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

5. Simplified 34.6%

   \[\leadsto \color{blue}{-y} \]
6. Add Preprocessing

Alternative 8: 2.2% accurate, 107.0× 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 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 x around inf 79.4%

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

   1. mul-1-neg 79.4%

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

   2. unsub-neg 79.4%

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

5. Simplified 79.4%

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

6. Taylor expanded in y around inf 24.9%

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

   1. mul-1-neg 24.9%

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

   2. distribute-neg-frac2 24.9%

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

8. Simplified 24.9%

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

   1. clear-num 24.8%

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

   2. un-div-inv 25.3%

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

   3. add-sqr-sqrt 12.3%

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

   4. sqrt-unprod 9.8%

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

   5. sqr-neg 9.8%

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

   6. sqrt-unprod 1.2%

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

   7. add-sqr-sqrt 2.2%

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

10. Applied egg-rr 2.2%

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

    1. associate-/r/ 2.3%

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

    2. *-inverses 2.3%

       \[\leadsto \color{blue}{1} \cdot y \]

    3. *-lft-identity 2.3%

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

12. Simplified 2.3%

    \[\leadsto \color{blue}{y} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))