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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 5

Speedup: 1.0×

• 24.7% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ e^{x \cdot \left(\left(y \cdot y\right) \cdot 0.6666666666666666\right)} \cdot {e}^{\left(x \cdot \left(\left(y \cdot y\right) \cdot 0.3333333333333333\right)\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (*
  (exp (* x (* (* y y) 0.6666666666666666)))
  (pow E (* x (* (* y y) 0.3333333333333333)))))

C

double code(double x, double y) {
	return exp((x * ((y * y) * 0.6666666666666666))) * pow(((double) M_E), (x * ((y * y) * 0.3333333333333333)));
}

Java

public static double code(double x, double y) {
	return Math.exp((x * ((y * y) * 0.6666666666666666))) * Math.pow(Math.E, (x * ((y * y) * 0.3333333333333333)));
}

Python

def code(x, y):
	return math.exp((x * ((y * y) * 0.6666666666666666))) * math.pow(math.e, (x * ((y * y) * 0.3333333333333333)))

Julia

function code(x, y)
	return Float64(exp(Float64(x * Float64(Float64(y * y) * 0.6666666666666666))) * (exp(1) ^ Float64(x * Float64(Float64(y * y) * 0.3333333333333333))))
end

MATLAB

function tmp = code(x, y)
	tmp = exp((x * ((y * y) * 0.6666666666666666))) * (2.71828182845904523536 ^ (x * ((y * y) * 0.3333333333333333)));
end

Wolfram

code[x_, y_] := N[(N[Exp[N[(x * N[(N[(y * y), $MachinePrecision] * 0.6666666666666666), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Power[E, N[(x * N[(N[(y * y), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. associate-*l* 100.0%

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

3. Simplified 100.0%

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

   1. *-un-lft-identity 100.0%

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

   2. exp-prod 100.0%

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

   3. add-log-exp 100.0%

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

   4. add-cube-cbrt 99.9%

      \[\leadsto {\left(e^{1}\right)}^{\log \color{blue}{\left(\left(\sqrt[3]{e^{x \cdot \left(y \cdot y\right)}} \cdot \sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right) \cdot \sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right)}} \]

   5. log-prod 99.9%

      \[\leadsto {\left(e^{1}\right)}^{\color{blue}{\left(\log \left(\sqrt[3]{e^{x \cdot \left(y \cdot y\right)}} \cdot \sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right) + \log \left(\sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right)\right)}} \]

   6. unpow-prod-up 99.9%

      \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\log \left(\sqrt[3]{e^{x \cdot \left(y \cdot y\right)}} \cdot \sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right)} \cdot {\left(e^{1}\right)}^{\log \left(\sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right)}} \]

6. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{{e}^{\left(2 \cdot \left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)\right)} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)}} \]
7. Step-by-step derivation

   1. associate-*r* 99.9%

      \[\leadsto {e}^{\color{blue}{\left(\left(2 \cdot 0.3333333333333333\right) \cdot \left(x \cdot {y}^{2}\right)\right)}} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   2. metadata-eval 99.9%

      \[\leadsto {e}^{\left(\color{blue}{0.6666666666666666} \cdot \left(x \cdot {y}^{2}\right)\right)} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   3. *-commutative 99.9%

      \[\leadsto {e}^{\left(0.6666666666666666 \cdot \color{blue}{\left({y}^{2} \cdot x\right)}\right)} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   4. associate-*r* 99.9%

      \[\leadsto {e}^{\color{blue}{\left(\left(0.6666666666666666 \cdot {y}^{2}\right) \cdot x\right)}} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   5. *-commutative 99.9%

      \[\leadsto {e}^{\color{blue}{\left(x \cdot \left(0.6666666666666666 \cdot {y}^{2}\right)\right)}} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   6. *-commutative 99.9%

      \[\leadsto {e}^{\left(x \cdot \color{blue}{\left({y}^{2} \cdot 0.6666666666666666\right)}\right)} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   7. *-commutative 99.9%

      \[\leadsto {e}^{\left(x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)\right)} \cdot {e}^{\color{blue}{\left(\left(x \cdot {y}^{2}\right) \cdot 0.3333333333333333\right)}} \]

   8. associate-*l* 99.9%

      \[\leadsto {e}^{\left(x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)\right)} \cdot {e}^{\color{blue}{\left(x \cdot \left({y}^{2} \cdot 0.3333333333333333\right)\right)}} \]

8. Simplified 99.9%

   \[\leadsto \color{blue}{{e}^{\left(x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)\right)} \cdot {e}^{\left(x \cdot \left({y}^{2} \cdot 0.3333333333333333\right)\right)}} \]
9. Step-by-step derivation

   1. e-exp-1 99.9%

      \[\leadsto {\color{blue}{\left(e^{1}\right)}}^{\left(x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)\right)} \cdot {e}^{\left(x \cdot \left({y}^{2} \cdot 0.3333333333333333\right)\right)} \]

   2. pow-exp 100.0%

      \[\leadsto \color{blue}{e^{1 \cdot \left(x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)\right)}} \cdot {e}^{\left(x \cdot \left({y}^{2} \cdot 0.3333333333333333\right)\right)} \]

   3. *-un-lft-identity 100.0%

      \[\leadsto e^{\color{blue}{x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)}} \cdot {e}^{\left(x \cdot \left({y}^{2} \cdot 0.3333333333333333\right)\right)} \]

10. Applied egg-rr 100.0%

    \[\leadsto \color{blue}{e^{x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)}} \cdot {e}^{\left(x \cdot \left({y}^{2} \cdot 0.3333333333333333\right)\right)} \]
11. Step-by-step derivation

    1. unpow2 100.0%

       \[\leadsto e^{x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)} \cdot {e}^{\left(x \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot 0.3333333333333333\right)\right)} \]

12. Applied egg-rr 100.0%

    \[\leadsto e^{x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)} \cdot {e}^{\left(x \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot 0.3333333333333333\right)\right)} \]
13. Step-by-step derivation

    1. unpow2 100.0%

       \[\leadsto e^{x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)} \cdot {e}^{\left(x \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot 0.3333333333333333\right)\right)} \]

14. Applied egg-rr 100.0%

    \[\leadsto e^{x \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot 0.6666666666666666\right)} \cdot {e}^{\left(x \cdot \left(\left(y \cdot y\right) \cdot 0.3333333333333333\right)\right)} \]
15. Add Preprocessing

Alternative 2: 100.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate-*l* 100.0%

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

3. Simplified 100.0%

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

   1. *-un-lft-identity 100.0%

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

   2. exp-prod 100.0%

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

   3. add-log-exp 100.0%

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

   4. add-cube-cbrt 99.9%

      \[\leadsto {\left(e^{1}\right)}^{\log \color{blue}{\left(\left(\sqrt[3]{e^{x \cdot \left(y \cdot y\right)}} \cdot \sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right) \cdot \sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right)}} \]

   5. log-prod 99.9%

      \[\leadsto {\left(e^{1}\right)}^{\color{blue}{\left(\log \left(\sqrt[3]{e^{x \cdot \left(y \cdot y\right)}} \cdot \sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right) + \log \left(\sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right)\right)}} \]

   6. unpow-prod-up 99.9%

      \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\log \left(\sqrt[3]{e^{x \cdot \left(y \cdot y\right)}} \cdot \sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right)} \cdot {\left(e^{1}\right)}^{\log \left(\sqrt[3]{e^{x \cdot \left(y \cdot y\right)}}\right)}} \]

6. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{{e}^{\left(2 \cdot \left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)\right)} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)}} \]
7. Step-by-step derivation

   1. associate-*r* 99.9%

      \[\leadsto {e}^{\color{blue}{\left(\left(2 \cdot 0.3333333333333333\right) \cdot \left(x \cdot {y}^{2}\right)\right)}} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   2. metadata-eval 99.9%

      \[\leadsto {e}^{\left(\color{blue}{0.6666666666666666} \cdot \left(x \cdot {y}^{2}\right)\right)} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   3. *-commutative 99.9%

      \[\leadsto {e}^{\left(0.6666666666666666 \cdot \color{blue}{\left({y}^{2} \cdot x\right)}\right)} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   4. associate-*r* 99.9%

      \[\leadsto {e}^{\color{blue}{\left(\left(0.6666666666666666 \cdot {y}^{2}\right) \cdot x\right)}} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   5. *-commutative 99.9%

      \[\leadsto {e}^{\color{blue}{\left(x \cdot \left(0.6666666666666666 \cdot {y}^{2}\right)\right)}} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   6. *-commutative 99.9%

      \[\leadsto {e}^{\left(x \cdot \color{blue}{\left({y}^{2} \cdot 0.6666666666666666\right)}\right)} \cdot {e}^{\left(0.3333333333333333 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   7. *-commutative 99.9%

      \[\leadsto {e}^{\left(x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)\right)} \cdot {e}^{\color{blue}{\left(\left(x \cdot {y}^{2}\right) \cdot 0.3333333333333333\right)}} \]

   8. associate-*l* 99.9%

      \[\leadsto {e}^{\left(x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)\right)} \cdot {e}^{\color{blue}{\left(x \cdot \left({y}^{2} \cdot 0.3333333333333333\right)\right)}} \]

8. Simplified 99.9%

   \[\leadsto \color{blue}{{e}^{\left(x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)\right)} \cdot {e}^{\left(x \cdot \left({y}^{2} \cdot 0.3333333333333333\right)\right)}} \]

10. Applied egg-rr 99.9%

    \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt{e}\right)}^{\left(x \cdot {y}^{2}\right)}, {\left(\sqrt{e}\right)}^{\left(x \cdot {y}^{2}\right)}, 0\right)} \]
11. Step-by-step derivation

    1. fma-undefine 99.9%

       \[\leadsto \color{blue}{{\left(\sqrt{e}\right)}^{\left(x \cdot {y}^{2}\right)} \cdot {\left(\sqrt{e}\right)}^{\left(x \cdot {y}^{2}\right)} + 0} \]

    2. +-rgt-identity 99.9%

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

    3. pow-sqr 100.0%

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

    4. count-2 100.0%

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

    5. distribute-lft-out 100.0%

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

    6. count-2 100.0%

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

12. Simplified 100.0%

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

    1. unpow2 100.0%

       \[\leadsto e^{x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)} \cdot {e}^{\left(x \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot 0.3333333333333333\right)\right)} \]

14. Applied egg-rr 100.0%

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

15. Final simplification 100.0%

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

Alternative 3: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \mathsf{expm1}\left(x \cdot \left(y \cdot y\right)\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ 1.0 (expm1 (* x (* y y)))))

C

double code(double x, double y) {
	return 1.0 + expm1((x * (y * y)));
}

Java

public static double code(double x, double y) {
	return 1.0 + Math.expm1((x * (y * y)));
}

Python

def code(x, y):
	return 1.0 + math.expm1((x * (y * y)))

Julia

function code(x, y)
	return Float64(1.0 + expm1(Float64(x * Float64(y * y))))
end

Wolfram

code[x_, y_] := N[(1.0 + N[(Exp[N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. associate-*l* 100.0%

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

3. Simplified 100.0%

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

   1. log1p-expm1-u 100.0%

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

   2. log1p-undefine 100.0%

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

   3. add-exp-log 100.0%

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

   4. pow2 100.0%

      \[\leadsto 1 + \mathsf{expm1}\left(x \cdot \color{blue}{{y}^{2}}\right) \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{1 + \mathsf{expm1}\left(x \cdot {y}^{2}\right)} \]
7. Step-by-step derivation

   1. unpow2 100.0%

      \[\leadsto e^{x \cdot \left({y}^{2} \cdot 0.6666666666666666\right)} \cdot {e}^{\left(x \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot 0.3333333333333333\right)\right)} \]

8. Applied egg-rr 100.0%

   \[\leadsto 1 + \mathsf{expm1}\left(x \cdot \color{blue}{\left(y \cdot y\right)}\right) \]
9. Add Preprocessing

Alternative 4: 100.0% accurate, 1.0× speedup

Math

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

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(x * Float64(y * y)))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate-*l* 100.0%

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

3. Simplified 100.0%

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

Alternative 5: 52.0% 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. Step-by-step derivation

   1. associate-*l* 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around 0 55.3%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))