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

Percentage Accurate: 99.9% → 99.9%

Time: 9.8s

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

\[\begin{array}{l} \\ \left(\log \left(\frac{1}{y}\right) \cdot \left(-x\right) - z\right) - y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- (* (log (/ 1.0 y)) (- x)) z) y))

C

double code(double x, double y, double z) {
	return ((log((1.0 / y)) * -x) - z) - y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((log((1.0d0 / y)) * -x) - z) - y
end function

Java

public static double code(double x, double y, double z) {
	return ((Math.log((1.0 / y)) * -x) - z) - y;
}

Python

def code(x, y, z):
	return ((math.log((1.0 / y)) * -x) - z) - y

Julia

function code(x, y, z)
	return Float64(Float64(Float64(log(Float64(1.0 / y)) * Float64(-x)) - z) - y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((log((1.0 / y)) * -x) - z) - y;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around inf 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \left(\log \left(\frac{1}{y}\right) \cdot \left(-x\right) - z\right) - y \]
5. Add Preprocessing

Alternative 2: 83.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+137} \lor \neg \left(x \leq 3.3 \cdot 10^{-71}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e+137) (not (<= x 3.3e-71)))
   (- (* x (log y)) y)
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+137) || !(x <= 3.3e-71)) {
		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 <= (-1.05d+137)) .or. (.not. (x <= 3.3d-71))) 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 <= -1.05e+137) || !(x <= 3.3e-71)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.05e+137) or not (x <= 3.3e-71):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e+137) || !(x <= 3.3e-71))
		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 <= -1.05e+137) || ~((x <= 3.3e-71)))
		tmp = (x * log(y)) - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.05e+137], N[Not[LessEqual[x, 3.3e-71]], $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 < -1.05e137 or 3.3000000000000002e-71 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 88.9%

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

   if -1.05e137 < x < 3.3000000000000002e-71

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.0%

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

      1. neg-mul-1 89.0%

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

   5. Simplified 89.0%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+137} \lor \neg \left(x \leq 3.3 \cdot 10^{-71}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+153} \lor \neg \left(x \leq 5.2 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e+153) (not (<= x 5.2e+96))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+153) || !(x <= 5.2e+96)) {
		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 <= (-5.5d+153)) .or. (.not. (x <= 5.2d+96))) 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 <= -5.5e+153) || !(x <= 5.2e+96)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e+153) or not (x <= 5.2e+96):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e+153) || !(x <= 5.2e+96))
		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 <= -5.5e+153) || ~((x <= 5.2e+96)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e+153], N[Not[LessEqual[x, 5.2e+96]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000003e153 or 5.2e96 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 99.6%

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

   4. Taylor expanded in x around inf 91.6%

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

      1. add-sqr-sqrt 37.0%

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

      2. sqrt-unprod 8.8%

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

      3. mul-1-neg 8.8%

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

      4. mul-1-neg 8.8%

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

      5. sqr-neg 8.8%

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

      6. sqrt-unprod 8.0%

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

      7. add-sqr-sqrt 14.6%

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

      8. *-commutative 14.6%

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

      9. add-sqr-sqrt 0.4%

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

      10. sqrt-unprod 45.2%

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

      11. log-rec 45.2%

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

      12. log-rec 45.2%

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

      13. sqr-neg 45.2%

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

      14. sqrt-unprod 44.8%

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

      15. add-sqr-sqrt 91.5%

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

   6. Applied egg-rr 30.6%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} \]

   7. Taylor expanded in y around 0 76.0%

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

   if -5.5000000000000003e153 < x < 5.2e96

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.9%

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

      1. neg-mul-1 83.9%

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

   5. Simplified 83.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+153} \lor \neg \left(x \leq 5.2 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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 5: 52.7% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+113} \lor \neg \left(z \leq 4.5 \cdot 10^{+58}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e+113) (not (<= z 4.5e+58))) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e+113) || !(z <= 4.5e+58)) {
		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 ((z <= (-1.3d+113)) .or. (.not. (z <= 4.5d+58))) 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 ((z <= -1.3e+113) || !(z <= 4.5e+58)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e+113) or not (z <= 4.5e+58):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.3e+113) || !(z <= 4.5e+58))
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.3e+113) || ~((z <= 4.5e+58)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e+113], N[Not[LessEqual[z, 4.5e+58]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e113 or 4.4999999999999998e58 < z

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 46.9%

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

      2. pow2 46.9%

         \[\leadsto \left(\color{blue}{{\left(\sqrt{x \cdot \log y}\right)}^{2}} - z\right) - y \]

   4. Applied egg-rr 46.9%

      \[\leadsto \left(\color{blue}{{\left(\sqrt{x \cdot \log y}\right)}^{2}} - z\right) - y \]
   5. Step-by-step derivation

      1. add-cbrt-cube 42.6%

         \[\leadsto \left({\color{blue}{\left(\sqrt[3]{\left(\sqrt{x \cdot \log y} \cdot \sqrt{x \cdot \log y}\right) \cdot \sqrt{x \cdot \log y}}\right)}}^{2} - z\right) - y \]

      2. pow1/3 42.3%

         \[\leadsto \left({\color{blue}{\left({\left(\left(\sqrt{x \cdot \log y} \cdot \sqrt{x \cdot \log y}\right) \cdot \sqrt{x \cdot \log y}\right)}^{0.3333333333333333}\right)}}^{2} - z\right) - y \]

      3. add-sqr-sqrt 42.3%

         \[\leadsto \left({\left({\left(\color{blue}{\left(x \cdot \log y\right)} \cdot \sqrt{x \cdot \log y}\right)}^{0.3333333333333333}\right)}^{2} - z\right) - y \]

      4. pow1 42.3%

         \[\leadsto \left({\left({\left(\color{blue}{{\left(x \cdot \log y\right)}^{1}} \cdot \sqrt{x \cdot \log y}\right)}^{0.3333333333333333}\right)}^{2} - z\right) - y \]

      5. pow1/2 42.3%

         \[\leadsto \left({\left({\left({\left(x \cdot \log y\right)}^{1} \cdot \color{blue}{{\left(x \cdot \log y\right)}^{0.5}}\right)}^{0.3333333333333333}\right)}^{2} - z\right) - y \]

      6. pow-prod-up 42.3%

         \[\leadsto \left({\left({\color{blue}{\left({\left(x \cdot \log y\right)}^{\left(1 + 0.5\right)}\right)}}^{0.3333333333333333}\right)}^{2} - z\right) - y \]

      7. metadata-eval 42.3%

         \[\leadsto \left({\left({\left({\left(x \cdot \log y\right)}^{\color{blue}{1.5}}\right)}^{0.3333333333333333}\right)}^{2} - z\right) - y \]

   6. Applied egg-rr 42.3%

      \[\leadsto \left({\color{blue}{\left({\left({\left(x \cdot \log y\right)}^{1.5}\right)}^{0.3333333333333333}\right)}}^{2} - z\right) - y \]
   7. Step-by-step derivation

      1. unpow1/3 42.6%

         \[\leadsto \left({\color{blue}{\left(\sqrt[3]{{\left(x \cdot \log y\right)}^{1.5}}\right)}}^{2} - z\right) - y \]

   8. Simplified 42.6%

      \[\leadsto \left({\color{blue}{\left(\sqrt[3]{{\left(x \cdot \log y\right)}^{1.5}}\right)}}^{2} - z\right) - y \]

   9. Taylor expanded in z around inf 61.3%

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

       1. neg-mul-1 61.3%

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

   11. Simplified 61.3%

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

   if -1.3e113 < z < 4.4999999999999998e58

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 47.6%

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

      1. mul-1-neg 47.6%

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

   5. Simplified 47.6%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+113} \lor \neg \left(z \leq 4.5 \cdot 10^{+58}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 99.8%

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

3. Taylor expanded in x around 0 65.8%

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

   1. neg-mul-1 65.8%

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

5. Simplified 65.8%

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

6. Final simplification 65.8%

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

Alternative 7: 34.1% 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 37.6%

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

   1. mul-1-neg 37.6%

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

5. Simplified 37.6%

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

6. Final simplification 37.6%

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

Alternative 8: 2.3% 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. Step-by-step derivation

   1. associate--l- 99.8%

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

   2. *-commutative 99.8%

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

   3. fma-neg 99.8%

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

   4. +-commutative 99.8%

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

   5. distribute-neg-out 99.8%

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

   6. sub-neg 99.8%

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

   7. add-sqr-sqrt 0.0%

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

   8. sqrt-unprod 56.7%

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

   9. sqr-neg 56.7%

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

   10. sqrt-unprod 61.9%

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

   11. add-sqr-sqrt 61.9%

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

4. Applied egg-rr 61.9%

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

5. Taylor expanded in y around inf 2.4%

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

6. Final simplification 2.4%

   \[\leadsto y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))