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

Percentage Accurate: 100.0% → 100.0%

Time: 1.4s

Alternatives: 6

Speedup: 1.0×

• 58.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

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. Add Preprocessing

Alternative 2: 5.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

5. Applied rewrites 5.4%

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

6. Taylor expanded in x around 0

   \[\leadsto \left(x + y \cdot \log y\right) - z \]

8. Applied rewrites 5.4%

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

Alternative 3: 4.9% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

5. Applied rewrites 5.4%

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

Alternative 4: 4.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \log y \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[Log[y], $MachinePrecision]), $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 0

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

5. Applied rewrites 5.1%

   \[\leadsto \color{blue}{x + y \cdot \log y} \]
6. Add Preprocessing

Alternative 5: 4.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ y \cdot \log y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y (log y)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y * N[Log[y], $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 0

   \[\leadsto \color{blue}{e^{y \cdot \log y - z} + x \cdot \left(e^{y \cdot \log y - z} + x \cdot \left(\frac{1}{6} \cdot \left(x \cdot e^{y \cdot \log y - z}\right) + \frac{1}{2} \cdot e^{y \cdot \log y - z}\right)\right)} \]

5. Applied rewrites 4.8%

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

Alternative 6: 2.5% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Log[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

   \[\leadsto \color{blue}{e^{y \cdot \log y - z} + x \cdot \left(e^{y \cdot \log y - z} + x \cdot \left(\frac{1}{6} \cdot \left(x \cdot e^{y \cdot \log y - z}\right) + \frac{1}{2} \cdot e^{y \cdot \log y - z}\right)\right)} \]

5. Applied rewrites 4.8%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 2.5%

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

Developer Target 1: 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 2024321 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (exp (+ (- x z) (* (log y) y))))

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