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

Percentage Accurate: 99.9% → 99.9%

Time: 9.8s

Alternatives: 4

Speedup: 1.0×

• could not determine a ground truth

  1. x = 6.152860504082485e-239
  2. y = 2.5840236024470984e+215
  3. z = 5.0200940547379354e+216

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: 85.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+91} \lor \neg \left(z \leq 8.2 \cdot 10^{+46}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.2e+91) (not (<= z 8.2e+46)))
   (- (- z) y)
   (- (* x (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e+91) || !(z <= 8.2e+46)) {
		tmp = -z - y;
	} else {
		tmp = (x * log(y)) - 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 <= (-5.2d+91)) .or. (.not. (z <= 8.2d+46))) then
        tmp = -z - y
    else
        tmp = (x * log(y)) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e+91) || !(z <= 8.2e+46)) {
		tmp = -z - y;
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.2e+91) or not (z <= 8.2e+46):
		tmp = -z - y
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.2e+91) || !(z <= 8.2e+46))
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(Float64(x * log(y)) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.2e+91) || ~((z <= 8.2e+46)))
		tmp = -z - y;
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.2e+91], N[Not[LessEqual[z, 8.2e+46]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000001e91 or 8.19999999999999999e46 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.0%

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

      1. neg-mul-1 84.0%

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

   5. Simplified 84.0%

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

   if -5.2000000000000001e91 < z < 8.19999999999999999e46

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. add-cube-cbrt 99.1%

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

      3. associate-*r* 99.1%

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

      4. fma-neg 99.1%

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

      5. pow2 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in x around inf 90.3%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+91} \lor \neg \left(z \leq 8.2 \cdot 10^{+46}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.0% 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 66.6%

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

   1. neg-mul-1 66.6%

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

5. Simplified 66.6%

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

6. Final simplification 66.6%

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

Alternative 4: 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 99.9%

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

   1. *-commutative 99.9%

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

   2. add-cube-cbrt 99.4%

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

   3. associate-*r* 99.4%

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

   4. fma-neg 99.4%

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

   5. pow2 99.4%

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

4. Applied egg-rr 99.4%

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

5. Taylor expanded in x around inf 65.9%

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

   1. add-cube-cbrt 65.3%

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

   2. pow3 65.3%

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

7. Applied egg-rr 65.3%

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

8. Taylor expanded in x around 0 34.2%

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

   1. neg-mul-1 34.2%

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

10. Simplified 34.2%

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

11. Final simplification 34.2%

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

Reproduce

herbie shell --seed 2024073 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))