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

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

Alternatives: 6

Speedup: 1.0×

• 25.3% 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

\[\begin{array}{l} \\ {\left(\sqrt[3]{e^{6}}\right)}^{\left(x \cdot \frac{{y}^{2}}{2}\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (pow (cbrt (exp 6.0)) (* x (/ (pow y 2.0) 2.0))))

C

double code(double x, double y) {
	return pow(cbrt(exp(6.0)), (x * (pow(y, 2.0) / 2.0)));
}

Java

public static double code(double x, double y) {
	return Math.pow(Math.cbrt(Math.exp(6.0)), (x * (Math.pow(y, 2.0) / 2.0)));
}

Julia

function code(x, y)
	return cbrt(exp(6.0)) ^ Float64(x * Float64((y ^ 2.0) / 2.0))
end

Wolfram

code[x_, y_] := N[Power[N[Power[N[Exp[6.0], $MachinePrecision], 1/3], $MachinePrecision], N[(x * N[(N[Power[y, 2.0], $MachinePrecision] / 2.0), $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 100.0%

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

   3. add-cube-cbrt 99.9%

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

   4. exp-1-e 99.9%

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

   5. add-cube-cbrt 100.0%

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

   6. associate-*l* 100.0%

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

   7. 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. Step-by-step derivation

   1. add-cbrt-cube 99.6%

      \[\leadsto \color{blue}{\sqrt[3]{\left({e}^{\left(x \cdot {y}^{2}\right)} \cdot {e}^{\left(x \cdot {y}^{2}\right)}\right) \cdot {e}^{\left(x \cdot {y}^{2}\right)}}} \]

   2. pow1/3 99.6%

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

   3. pow-to-exp 99.6%

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

   4. pow3 99.6%

      \[\leadsto e^{\log \color{blue}{\left({\left({e}^{\left(x \cdot {y}^{2}\right)}\right)}^{3}\right)} \cdot 0.3333333333333333} \]

   5. log-pow 100.0%

      \[\leadsto e^{\color{blue}{\left(3 \cdot \log \left({e}^{\left(x \cdot {y}^{2}\right)}\right)\right)} \cdot 0.3333333333333333} \]

   6. e-exp-1 100.0%

      \[\leadsto e^{\left(3 \cdot \log \left({\color{blue}{\left(e^{1}\right)}}^{\left(x \cdot {y}^{2}\right)}\right)\right) \cdot 0.3333333333333333} \]

   7. pow-exp 100.0%

      \[\leadsto e^{\left(3 \cdot \log \color{blue}{\left(e^{1 \cdot \left(x \cdot {y}^{2}\right)}\right)}\right) \cdot 0.3333333333333333} \]

   8. *-un-lft-identity 100.0%

      \[\leadsto e^{\left(3 \cdot \log \left(e^{\color{blue}{x \cdot {y}^{2}}}\right)\right) \cdot 0.3333333333333333} \]

   9. add-log-exp 100.0%

      \[\leadsto e^{\left(3 \cdot \color{blue}{\left(x \cdot {y}^{2}\right)}\right) \cdot 0.3333333333333333} \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{e^{\left(3 \cdot \left(x \cdot {y}^{2}\right)\right) \cdot 0.3333333333333333}} \]
7. Step-by-step derivation

   1. *-commutative 100.0%

      \[\leadsto e^{\color{blue}{0.3333333333333333 \cdot \left(3 \cdot \left(x \cdot {y}^{2}\right)\right)}} \]

   2. pow-exp 100.0%

      \[\leadsto \color{blue}{{\left(e^{0.3333333333333333}\right)}^{\left(3 \cdot \left(x \cdot {y}^{2}\right)\right)}} \]

   3. sqr-pow 100.0%

      \[\leadsto \color{blue}{{\left(e^{0.3333333333333333}\right)}^{\left(\frac{3 \cdot \left(x \cdot {y}^{2}\right)}{2}\right)} \cdot {\left(e^{0.3333333333333333}\right)}^{\left(\frac{3 \cdot \left(x \cdot {y}^{2}\right)}{2}\right)}} \]

   4. pow-prod-down 100.0%

      \[\leadsto \color{blue}{{\left(e^{0.3333333333333333} \cdot e^{0.3333333333333333}\right)}^{\left(\frac{3 \cdot \left(x \cdot {y}^{2}\right)}{2}\right)}} \]

   5. pow2 100.0%

      \[\leadsto {\color{blue}{\left({\left(e^{0.3333333333333333}\right)}^{2}\right)}}^{\left(\frac{3 \cdot \left(x \cdot {y}^{2}\right)}{2}\right)} \]

   6. add-cbrt-cube 99.9%

      \[\leadsto {\left({\color{blue}{\left(\sqrt[3]{\left(e^{0.3333333333333333} \cdot e^{0.3333333333333333}\right) \cdot e^{0.3333333333333333}}\right)}}^{2}\right)}^{\left(\frac{3 \cdot \left(x \cdot {y}^{2}\right)}{2}\right)} \]

   7. pow3 99.9%

      \[\leadsto {\left({\left(\sqrt[3]{\color{blue}{{\left(e^{0.3333333333333333}\right)}^{3}}}\right)}^{2}\right)}^{\left(\frac{3 \cdot \left(x \cdot {y}^{2}\right)}{2}\right)} \]

   8. pow-exp 99.9%

      \[\leadsto {\left({\left(\sqrt[3]{\color{blue}{e^{0.3333333333333333 \cdot 3}}}\right)}^{2}\right)}^{\left(\frac{3 \cdot \left(x \cdot {y}^{2}\right)}{2}\right)} \]

   9. metadata-eval 99.9%

      \[\leadsto {\left({\left(\sqrt[3]{e^{\color{blue}{1}}}\right)}^{2}\right)}^{\left(\frac{3 \cdot \left(x \cdot {y}^{2}\right)}{2}\right)} \]

   10. e-exp-1 99.9%

       \[\leadsto {\left({\left(\sqrt[3]{\color{blue}{e}}\right)}^{2}\right)}^{\left(\frac{3 \cdot \left(x \cdot {y}^{2}\right)}{2}\right)} \]

   11. pow2 99.9%

       \[\leadsto {\color{blue}{\left(\sqrt[3]{e} \cdot \sqrt[3]{e}\right)}}^{\left(\frac{3 \cdot \left(x \cdot {y}^{2}\right)}{2}\right)} \]

   12. pow2 99.9%

       \[\leadsto {\left(\sqrt[3]{e} \cdot \sqrt[3]{e}\right)}^{\left(\frac{3 \cdot \left(x \cdot \color{blue}{\left(y \cdot y\right)}\right)}{2}\right)} \]

   13. associate-/l* 99.9%

       \[\leadsto {\left(\sqrt[3]{e} \cdot \sqrt[3]{e}\right)}^{\color{blue}{\left(3 \cdot \frac{x \cdot \left(y \cdot y\right)}{2}\right)}} \]

   14. pow-unpow 99.9%

       \[\leadsto \color{blue}{{\left({\left(\sqrt[3]{e} \cdot \sqrt[3]{e}\right)}^{3}\right)}^{\left(\frac{x \cdot \left(y \cdot y\right)}{2}\right)}} \]

8. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{{\left({\left(e^{0.6666666666666666}\right)}^{3}\right)}^{\left(x \cdot \frac{{y}^{2}}{2}\right)}} \]
9. Step-by-step derivation

   1. add-cbrt-cube 99.9%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{\left({\left(e^{0.6666666666666666}\right)}^{3} \cdot {\left(e^{0.6666666666666666}\right)}^{3}\right) \cdot {\left(e^{0.6666666666666666}\right)}^{3}}\right)}}^{\left(x \cdot \frac{{y}^{2}}{2}\right)} \]

   2. add-exp-log 100.0%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{e^{\log \left(\left({\left(e^{0.6666666666666666}\right)}^{3} \cdot {\left(e^{0.6666666666666666}\right)}^{3}\right) \cdot {\left(e^{0.6666666666666666}\right)}^{3}\right)}}}\right)}^{\left(x \cdot \frac{{y}^{2}}{2}\right)} \]

   3. pow3 100.0%

      \[\leadsto {\left(\sqrt[3]{e^{\log \color{blue}{\left({\left({\left(e^{0.6666666666666666}\right)}^{3}\right)}^{3}\right)}}}\right)}^{\left(x \cdot \frac{{y}^{2}}{2}\right)} \]

   4. log-pow 100.0%

      \[\leadsto {\left(\sqrt[3]{e^{\color{blue}{3 \cdot \log \left({\left(e^{0.6666666666666666}\right)}^{3}\right)}}}\right)}^{\left(x \cdot \frac{{y}^{2}}{2}\right)} \]

   5. pow-exp 100.0%

      \[\leadsto {\left(\sqrt[3]{e^{3 \cdot \log \color{blue}{\left(e^{0.6666666666666666 \cdot 3}\right)}}}\right)}^{\left(x \cdot \frac{{y}^{2}}{2}\right)} \]

   6. metadata-eval 100.0%

      \[\leadsto {\left(\sqrt[3]{e^{3 \cdot \log \left(e^{\color{blue}{2}}\right)}}\right)}^{\left(x \cdot \frac{{y}^{2}}{2}\right)} \]

   7. rem-log-exp 100.0%

      \[\leadsto {\left(\sqrt[3]{e^{3 \cdot \color{blue}{2}}}\right)}^{\left(x \cdot \frac{{y}^{2}}{2}\right)} \]

   8. metadata-eval 100.0%

      \[\leadsto {\left(\sqrt[3]{e^{\color{blue}{6}}}\right)}^{\left(x \cdot \frac{{y}^{2}}{2}\right)} \]

10. Applied egg-rr 100.0%

    \[\leadsto {\color{blue}{\left(\sqrt[3]{e^{6}}\right)}}^{\left(x \cdot \frac{{y}^{2}}{2}\right)} \]
11. Add Preprocessing

Alternative 2: 100.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ {\left(e^{0.3333333333333333}\right)}^{\left(3 \cdot \left(x \cdot \left(y \cdot y\right)\right)\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (pow (exp 0.3333333333333333) (* 3.0 (* x (* y y)))))

C

double code(double x, double y) {
	return pow(exp(0.3333333333333333), (3.0 * (x * (y * y))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp(0.3333333333333333d0) ** (3.0d0 * (x * (y * y)))
end function

Java

public static double code(double x, double y) {
	return Math.pow(Math.exp(0.3333333333333333), (3.0 * (x * (y * y))));
}

Python

def code(x, y):
	return math.pow(math.exp(0.3333333333333333), (3.0 * (x * (y * y))))

Julia

function code(x, y)
	return exp(0.3333333333333333) ^ Float64(3.0 * Float64(x * Float64(y * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = exp(0.3333333333333333) ^ (3.0 * (x * (y * y)));
end

Wolfram

code[x_, y_] := N[Power[N[Exp[0.3333333333333333], $MachinePrecision], N[(3.0 * N[(x * N[(y * y), $MachinePrecision]), $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. add-cbrt-cube 99.6%

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

   2. pow3 99.6%

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

4. Applied egg-rr 99.6%

   \[\leadsto e^{\color{blue}{\sqrt[3]{{\left(x \cdot y\right)}^{3}}} \cdot y} \]
5. Step-by-step derivation

   1. rem-cbrt-cube 99.9%

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

   2. associate-*r* 99.9%

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

   3. unpow2 99.9%

      \[\leadsto e^{x \cdot \color{blue}{{y}^{2}}} \]

   4. *-un-lft-identity 99.9%

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

   5. pow-exp 100.0%

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

   6. e-exp-1 100.0%

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

   7. add-cube-cbrt 99.9%

      \[\leadsto {\color{blue}{\left(\left(\sqrt[3]{e} \cdot \sqrt[3]{e}\right) \cdot \sqrt[3]{e}\right)}}^{\left(x \cdot {y}^{2}\right)} \]

   8. pow3 99.9%

      \[\leadsto {\color{blue}{\left({\left(\sqrt[3]{e}\right)}^{3}\right)}}^{\left(x \cdot {y}^{2}\right)} \]

   9. pow-pow 99.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{e}\right)}^{\left(3 \cdot \left(x \cdot {y}^{2}\right)\right)}} \]

   10. pow1/3 100.0%

       \[\leadsto {\color{blue}{\left({e}^{0.3333333333333333}\right)}}^{\left(3 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   11. pow-to-exp 100.0%

       \[\leadsto {\color{blue}{\left(e^{\log e \cdot 0.3333333333333333}\right)}}^{\left(3 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   12. log-E 100.0%

       \[\leadsto {\left(e^{\color{blue}{1} \cdot 0.3333333333333333}\right)}^{\left(3 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

   13. metadata-eval 100.0%

       \[\leadsto {\left(e^{\color{blue}{0.3333333333333333}}\right)}^{\left(3 \cdot \left(x \cdot {y}^{2}\right)\right)} \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{{\left(e^{0.3333333333333333}\right)}^{\left(3 \cdot \left(x \cdot {y}^{2}\right)\right)}} \]
7. Step-by-step derivation

   1. unpow2 100.0%

      \[\leadsto {\left(e^{0.3333333333333333}\right)}^{\left(3 \cdot \left(x \cdot \color{blue}{\left(y \cdot y\right)}\right)\right)} \]

8. Applied egg-rr 100.0%

   \[\leadsto {\left(e^{0.3333333333333333}\right)}^{\left(3 \cdot \left(x \cdot \color{blue}{\left(y \cdot y\right)}\right)\right)} \]
9. Add Preprocessing

Alternative 3: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{0.3333333333333333 \cdot \left(3 \cdot \left(x \cdot \left(y \cdot y\right)\right)\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (exp (* 0.3333333333333333 (* 3.0 (* x (* y y))))))

C

double code(double x, double y) {
	return exp((0.3333333333333333 * (3.0 * (x * (y * y)))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp((0.3333333333333333d0 * (3.0d0 * (x * (y * y)))))
end function

Java

public static double code(double x, double y) {
	return Math.exp((0.3333333333333333 * (3.0 * (x * (y * y)))));
}

Python

def code(x, y):
	return math.exp((0.3333333333333333 * (3.0 * (x * (y * y)))))

Julia

function code(x, y)
	return exp(Float64(0.3333333333333333 * Float64(3.0 * Float64(x * Float64(y * y)))))
end

MATLAB

function tmp = code(x, y)
	tmp = exp((0.3333333333333333 * (3.0 * (x * (y * y)))));
end

Wolfram

code[x_, y_] := N[Exp[N[(0.3333333333333333 * N[(3.0 * N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $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 100.0%

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

   3. add-cube-cbrt 99.9%

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

   4. exp-1-e 99.9%

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

   5. add-cube-cbrt 100.0%

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

   6. associate-*l* 100.0%

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

   7. 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. Step-by-step derivation

   1. add-cbrt-cube 99.6%

      \[\leadsto \color{blue}{\sqrt[3]{\left({e}^{\left(x \cdot {y}^{2}\right)} \cdot {e}^{\left(x \cdot {y}^{2}\right)}\right) \cdot {e}^{\left(x \cdot {y}^{2}\right)}}} \]

   2. pow1/3 99.6%

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

   3. pow-to-exp 99.6%

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

   4. pow3 99.6%

      \[\leadsto e^{\log \color{blue}{\left({\left({e}^{\left(x \cdot {y}^{2}\right)}\right)}^{3}\right)} \cdot 0.3333333333333333} \]

   5. log-pow 100.0%

      \[\leadsto e^{\color{blue}{\left(3 \cdot \log \left({e}^{\left(x \cdot {y}^{2}\right)}\right)\right)} \cdot 0.3333333333333333} \]

   6. e-exp-1 100.0%

      \[\leadsto e^{\left(3 \cdot \log \left({\color{blue}{\left(e^{1}\right)}}^{\left(x \cdot {y}^{2}\right)}\right)\right) \cdot 0.3333333333333333} \]

   7. pow-exp 100.0%

      \[\leadsto e^{\left(3 \cdot \log \color{blue}{\left(e^{1 \cdot \left(x \cdot {y}^{2}\right)}\right)}\right) \cdot 0.3333333333333333} \]

   8. *-un-lft-identity 100.0%

      \[\leadsto e^{\left(3 \cdot \log \left(e^{\color{blue}{x \cdot {y}^{2}}}\right)\right) \cdot 0.3333333333333333} \]

   9. add-log-exp 100.0%

      \[\leadsto e^{\left(3 \cdot \color{blue}{\left(x \cdot {y}^{2}\right)}\right) \cdot 0.3333333333333333} \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{e^{\left(3 \cdot \left(x \cdot {y}^{2}\right)\right) \cdot 0.3333333333333333}} \]
7. Step-by-step derivation

   1. unpow2 100.0%

      \[\leadsto {\left(e^{0.3333333333333333}\right)}^{\left(3 \cdot \left(x \cdot \color{blue}{\left(y \cdot y\right)}\right)\right)} \]

8. Applied egg-rr 100.0%

   \[\leadsto e^{\left(3 \cdot \left(x \cdot \color{blue}{\left(y \cdot y\right)}\right)\right) \cdot 0.3333333333333333} \]

9. Final simplification 100.0%

   \[\leadsto e^{0.3333333333333333 \cdot \left(3 \cdot \left(x \cdot \left(y \cdot y\right)\right)\right)} \]
10. Add Preprocessing

Alternative 4: 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 100.0%

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

   3. add-cube-cbrt 99.9%

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

   4. exp-1-e 99.9%

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

   5. add-cube-cbrt 100.0%

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

   6. associate-*l* 100.0%

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

   7. 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. Step-by-step derivation

   1. unpow2 100.0%

      \[\leadsto {\left(e^{0.3333333333333333}\right)}^{\left(3 \cdot \left(x \cdot \color{blue}{\left(y \cdot y\right)}\right)\right)} \]

6. Applied egg-rr 100.0%

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

Alternative 5: 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 6: 51.1% 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 48.7%

   \[\leadsto \color{blue}{1} \]
4. 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)))