Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

Alternatives: 4

Speedup: 1.0×

• 24.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (exp (* (* x y) y)))

C

double code(double x, double y) {
	return exp(((x * y) * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp(((x * y) * y))
end function

Java

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

Python

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

Julia

function code(x, y)
	return exp(Float64(Float64(x * y) * y))
end

MATLAB

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

Wolfram

code[x_, y_] := N[Exp[N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (exp (* (* x y) y)))

C

double code(double x, double y) {
	return exp(((x * y) * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp(((x * y) * y))
end function

Java

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

Python

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

Julia

function code(x, y)
	return exp(Float64(Float64(x * y) * y))
end

MATLAB

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

Wolfram

code[x_, y_] := N[Exp[N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]

Alternative 1: 100.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {e}^{\left(0.5 \cdot \left(x \cdot {y}^{2}\right)\right)}\\ t\_0 \cdot t\_0 \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (pow E (* 0.5 (* x (pow y 2.0)))))) (* t_0 t_0)))

C

double code(double x, double y) {
	double t_0 = pow(((double) M_E), (0.5 * (x * pow(y, 2.0))));
	return t_0 * t_0;
}

Java

public static double code(double x, double y) {
	double t_0 = Math.pow(Math.E, (0.5 * (x * Math.pow(y, 2.0))));
	return t_0 * t_0;
}

Python

def code(x, y):
	t_0 = math.pow(math.e, (0.5 * (x * math.pow(y, 2.0))))
	return t_0 * t_0

Julia

function code(x, y)
	t_0 = exp(1) ^ Float64(0.5 * Float64(x * (y ^ 2.0)))
	return Float64(t_0 * t_0)
end

MATLAB

function tmp = code(x, y)
	t_0 = 2.71828182845904523536 ^ (0.5 * (x * (y ^ 2.0)));
	tmp = t_0 * t_0;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[Power[E, N[(0.5 * N[(x * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, N[(t$95$0 * t$95$0), $MachinePrecision]]

Derivation

1. Initial program 100.0%

   \[e^{\left(x \cdot y\right) \cdot y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-un-lft-identity 100.0%

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

   2. exp-prod 100.0%

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

   3. add-log-exp 100.0%

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

   4. add-sqr-sqrt 100.0%

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

   5. log-prod 100.0%

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

   6. unpow-prod-up 100.0%

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

   7. exp-1-e 100.0%

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

   8. pow1/2 100.0%

      \[\leadsto {e}^{\log \color{blue}{\left({\left(e^{\left(x \cdot y\right) \cdot y}\right)}^{0.5}\right)}} \cdot {\left(e^{1}\right)}^{\log \left(\sqrt{e^{\left(x \cdot y\right) \cdot y}}\right)} \]

   9. log-pow 100.0%

      \[\leadsto {e}^{\color{blue}{\left(0.5 \cdot \log \left(e^{\left(x \cdot y\right) \cdot y}\right)\right)}} \cdot {\left(e^{1}\right)}^{\log \left(\sqrt{e^{\left(x \cdot y\right) \cdot y}}\right)} \]

   10. add-log-exp 100.0%

       \[\leadsto {e}^{\left(0.5 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot y\right)}\right)} \cdot {\left(e^{1}\right)}^{\log \left(\sqrt{e^{\left(x \cdot y\right) \cdot y}}\right)} \]

   11. associate-*l* 100.0%

       \[\leadsto {e}^{\left(0.5 \cdot \color{blue}{\left(x \cdot \left(y \cdot y\right)\right)}\right)} \cdot {\left(e^{1}\right)}^{\log \left(\sqrt{e^{\left(x \cdot y\right) \cdot y}}\right)} \]

   12. pow2 100.0%

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

   13. exp-1-e 100.0%

       \[\leadsto {e}^{\left(0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \cdot {\color{blue}{e}}^{\log \left(\sqrt{e^{\left(x \cdot y\right) \cdot y}}\right)} \]

   14. pow1/2 100.0%

       \[\leadsto {e}^{\left(0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \cdot {e}^{\log \color{blue}{\left({\left(e^{\left(x \cdot y\right) \cdot y}\right)}^{0.5}\right)}} \]

   15. log-pow 100.0%

       \[\leadsto {e}^{\left(0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \cdot {e}^{\color{blue}{\left(0.5 \cdot \log \left(e^{\left(x \cdot y\right) \cdot y}\right)\right)}} \]

   16. add-log-exp 100.0%

       \[\leadsto {e}^{\left(0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \cdot {e}^{\left(0.5 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot y\right)}\right)} \]

   17. associate-*l* 100.0%

       \[\leadsto {e}^{\left(0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \cdot {e}^{\left(0.5 \cdot \color{blue}{\left(x \cdot \left(y \cdot y\right)\right)}\right)} \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{{e}^{\left(0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \cdot {e}^{\left(0.5 \cdot \left(x \cdot {y}^{2}\right)\right)}} \]

5. Final simplification 100.0%

   \[\leadsto {e}^{\left(0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \cdot {e}^{\left(0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \]
6. Add Preprocessing

Alternative 2: 100.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ {e}^{\left(x \cdot {y}^{2}\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (pow E (* x (pow y 2.0))))

C

double code(double x, double y) {
	return pow(((double) M_E), (x * pow(y, 2.0)));
}

Java

public static double code(double x, double y) {
	return Math.pow(Math.E, (x * Math.pow(y, 2.0)));
}

Python

def code(x, y):
	return math.pow(math.e, (x * math.pow(y, 2.0)))

Julia

function code(x, y)
	return exp(1) ^ Float64(x * (y ^ 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = 2.71828182845904523536 ^ (x * (y ^ 2.0));
end

Wolfram

code[x_, y_] := N[Power[E, N[(x * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{\left(x \cdot y\right) \cdot y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-un-lft-identity 100.0%

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

   2. exp-prod 100.0%

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

   3. exp-1-e 100.0%

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

   4. associate-*l* 100.0%

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

   5. pow2 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto {e}^{\left(x \cdot {y}^{2}\right)} \]
6. Add Preprocessing

Alternative 3: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (exp (* y (* x y))))

C

double code(double x, double y) {
	return exp((y * (x * y)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp((y * (x * y)))
end function

Java

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

Python

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

Julia

function code(x, y)
	return exp(Float64(y * Float64(x * y)))
end

MATLAB

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

Wolfram

code[x_, y_] := N[Exp[N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 4: 51.3% accurate, 105.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 54.0%

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

4. Final simplification 54.0%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))