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

Percentage Accurate: 100.0% → 100.0%

Time: 11.2s

Alternatives: 4

Speedup: 1.0×

• 24.1% 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, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{{e}^{\left(1 + x \cdot \left(y \cdot y\right)\right)}}{e} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (pow E (+ 1.0 (* x (* y y)))) E))

C

double code(double x, double y) {
	return pow(((double) M_E), (1.0 + (x * (y * y)))) / ((double) M_E);
}

Java

public static double code(double x, double y) {
	return Math.pow(Math.E, (1.0 + (x * (y * y)))) / Math.E;
}

Python

def code(x, y):
	return math.pow(math.e, (1.0 + (x * (y * y)))) / math.e

Julia

function code(x, y)
	return Float64((exp(1) ^ Float64(1.0 + Float64(x * Float64(y * y)))) / exp(1))
end

MATLAB

function tmp = code(x, y)
	tmp = (2.71828182845904523536 ^ (1.0 + (x * (y * y)))) / 2.71828182845904523536;
end

Wolfram

code[x_, y_] := N[(N[Power[E, N[(1.0 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / E), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. *-un-lft-identity 99.9%

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

   2. exp-prod 99.9%

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

   3. expm1-log1p-u 73.0%

      \[\leadsto {\left(e^{1}\right)}^{\color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\left(x \cdot y\right) \cdot y\right)\right)\right)}} \]

   4. expm1-undefine 73.0%

      \[\leadsto {\left(e^{1}\right)}^{\color{blue}{\left(e^{\mathsf{log1p}\left(\left(x \cdot y\right) \cdot y\right)} - 1\right)}} \]

   5. pow-sub 73.0%

      \[\leadsto \color{blue}{\frac{{\left(e^{1}\right)}^{\left(e^{\mathsf{log1p}\left(\left(x \cdot y\right) \cdot y\right)}\right)}}{{\left(e^{1}\right)}^{1}}} \]

   6. exp-1-e 73.0%

      \[\leadsto \frac{{\color{blue}{e}}^{\left(e^{\mathsf{log1p}\left(\left(x \cdot y\right) \cdot y\right)}\right)}}{{\left(e^{1}\right)}^{1}} \]

   7. log1p-undefine 73.0%

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

   8. rem-exp-log 100.0%

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

   9. associate-*l* 100.0%

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

   10. pow2 100.0%

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

   11. pow1 100.0%

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

   12. exp-1-e 100.0%

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

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{{e}^{\left(1 + x \cdot {y}^{2}\right)}}{e}} \]
5. Step-by-step derivation

   1. unpow2 100.0%

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

6. Applied egg-rr 100.0%

   \[\leadsto \frac{{e}^{\left(1 + x \cdot \color{blue}{\left(y \cdot y\right)}\right)}}{e} \]
7. Add Preprocessing

Alternative 2: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-un-lft-identity 99.9%

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

   2. exp-prod 99.9%

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

   3. exp-1-e 99.9%

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

   4. associate-*l* 99.9%

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

   5. pow2 99.9%

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

4. Applied egg-rr 99.9%

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

   1. unpow2 100.0%

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

6. Applied egg-rr 99.9%

   \[\leadsto {e}^{\left(x \cdot \color{blue}{\left(y \cdot y\right)}\right)} \]
7. 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 99.9%

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

3. Final simplification 99.9%

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

Alternative 4: 50.6% 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 99.9%

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

3. Taylor expanded in x around 0 54.0%

   \[\leadsto \color{blue}{1} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))