Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 5

Speedup: 1.0×

• 57.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ e^{\left(x + y \cdot \log y\right) - z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (exp (- (+ x (* y (log y))) z)))

C

double code(double x, double y, double z) {
	return exp(((x + (y * log(y))) - 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 = exp(((x + (y * log(y))) - z))
end function

Java

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

Python

def code(x, y, z):
	return math.exp(((x + (y * math.log(y))) - z))

Julia

function code(x, y, z)
	return exp(Float64(Float64(x + Float64(y * log(y))) - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = exp(((x + (y * log(y))) - z));
end

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{\left(x + y \cdot \log y\right) - z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (exp (- (+ x (* y (log y))) z)))

C

double code(double x, double y, double z) {
	return exp(((x + (y * log(y))) - 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 = exp(((x + (y * log(y))) - z))
end function

Java

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

Python

def code(x, y, z):
	return math.exp(((x + (y * math.log(y))) - z))

Julia

function code(x, y, z)
	return exp(Float64(Float64(x + Float64(y * log(y))) - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = exp(((x + (y * log(y))) - z));
end

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{\left(x + y \cdot \log y\right) - z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (exp (- (+ x (* y (log y))) z)))

C

double code(double x, double y, double z) {
	return exp(((x + (y * log(y))) - 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 = exp(((x + (y * log(y))) - z))
end function

Java

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

Python

def code(x, y, z):
	return math.exp(((x + (y * math.log(y))) - z))

Julia

function code(x, y, z)
	return exp(Float64(Float64(x + Float64(y * log(y))) - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = exp(((x + (y * log(y))) - z));
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[e^{\left(x + y \cdot \log y\right) - z} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto e^{\left(x + y \cdot \log y\right) - z} \]
4. Add Preprocessing

Alternative 2: 78.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ e^{x - z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (exp (- x z)))

C

double code(double x, double y, double z) {
	return exp((x - 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 = exp((x - z))
end function

Java

public static double code(double x, double y, double z) {
	return Math.exp((x - z));
}

Python

def code(x, y, z):
	return math.exp((x - z))

Julia

function code(x, y, z)
	return exp(Float64(x - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = exp((x - z));
end

Wolfram

code[x_, y_, z_] := N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{\left(x + y \cdot \log y\right) - z} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 81.4%

   \[\leadsto e^{\color{blue}{x} - z} \]

4. Final simplification 81.4%

   \[\leadsto e^{x - z} \]
5. Add Preprocessing

Alternative 3: 52.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ e^{-z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (exp (- z)))

C

double code(double x, double y, double z) {
	return exp(-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 = exp(-z)
end function

Java

public static double code(double x, double y, double z) {
	return Math.exp(-z);
}

Python

def code(x, y, z):
	return math.exp(-z)

Julia

function code(x, y, z)
	return exp(Float64(-z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = exp(-z);
end

Wolfram

code[x_, y_, z_] := N[Exp[(-z)], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{\left(x + y \cdot \log y\right) - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 52.7%

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

   1. neg-mul-1 52.7%

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

5. Simplified 52.7%

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

6. Final simplification 52.7%

   \[\leadsto e^{-z} \]
7. Add Preprocessing

Alternative 4: 52.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ {y}^{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (pow y y))

C

double code(double x, double y, double z) {
	return pow(y, 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 ** y
end function

Java

public static double code(double x, double y, double z) {
	return Math.pow(y, y);
}

Python

def code(x, y, z):
	return math.pow(y, y)

Julia

function code(x, y, z)
	return y ^ y
end

MATLAB

function tmp = code(x, y, z)
	tmp = y ^ y;
end

Wolfram

code[x_, y_, z_] := N[Power[y, y], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{\left(x + y \cdot \log y\right) - z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 78.8%

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

4. Taylor expanded in y around inf 53.0%

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

   1. mul-1-neg 53.0%

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

   2. distribute-rgt-neg-in 53.0%

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

   3. log-rec 53.0%

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

   4. remove-double-neg 53.0%

      \[\leadsto e^{y \cdot \color{blue}{\log y}} \]

6. Simplified 53.0%

   \[\leadsto e^{\color{blue}{y \cdot \log y}} \]

7. Taylor expanded in y around inf 53.0%

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

8. Final simplification 53.0%

   \[\leadsto {y}^{y} \]
9. Add Preprocessing

Alternative 5: 14.3% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

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

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

   \[e^{\left(x + y \cdot \log y\right) - z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 78.8%

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

4. Taylor expanded in y around inf 53.0%

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

   1. mul-1-neg 53.0%

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

   2. distribute-rgt-neg-in 53.0%

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

   3. log-rec 53.0%

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

   4. remove-double-neg 53.0%

      \[\leadsto e^{y \cdot \color{blue}{\log y}} \]

6. Simplified 53.0%

   \[\leadsto e^{\color{blue}{y \cdot \log y}} \]

7. Taylor expanded in y around 0 14.3%

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

8. Final simplification 14.3%

   \[\leadsto 1 \]
9. Add Preprocessing

Developer target: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{\left(x - z\right) + \log y \cdot y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (exp (+ (- x z) (* (log y) y))))

C

double code(double x, double y, double z) {
	return exp(((x - z) + (log(y) * 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 = exp(((x - z) + (log(y) * y)))
end function

Java

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

Python

def code(x, y, z):
	return math.exp(((x - z) + (math.log(y) * y)))

Julia

function code(x, y, z)
	return exp(Float64(Float64(x - z) + Float64(log(y) * y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = exp(((x - z) + (log(y) * y)));
end

Wolfram

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

Reproduce

herbie shell --seed 2024033 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

  (exp (- (+ x (* y (log y))) z)))