Average Error: 0.0 → 0.0
Time: 2.5s
Precision: binary64
\[x \cdot e^{y \cdot y} \]
↓
\[x \cdot {\left({\left(e^{y}\right)}^{2}\right)}^{\left(y \cdot 0.5\right)} \]
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y) :precision binary64 (* x (pow (pow (exp y) 2.0) (* y 0.5))))
double code(double x, double y) {
	return x * exp((y * y));
}
↓
double code(double x, double y) {
	return x * pow(pow(exp(y), 2.0), (y * 0.5));
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * exp((y * y))
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * ((exp(y) ** 2.0d0) ** (y * 0.5d0))
end function

public static double code(double x, double y) {
	return x * Math.exp((y * y));
}
↓
public static double code(double x, double y) {
	return x * Math.pow(Math.pow(Math.exp(y), 2.0), (y * 0.5));
}

def code(x, y):
	return x * math.exp((y * y))
↓
def code(x, y):
	return x * math.pow(math.pow(math.exp(y), 2.0), (y * 0.5))

function code(x, y)
	return Float64(x * exp(Float64(y * y)))
end
↓
function code(x, y)
	return Float64(x * ((exp(y) ^ 2.0) ^ Float64(y * 0.5)))
end

function tmp = code(x, y)
	tmp = x * exp((y * y));
end
↓
function tmp = code(x, y)
	tmp = x * ((exp(y) ^ 2.0) ^ (y * 0.5));
end

code[x_, y_] := N[(x * N[Exp[N[(y * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x * N[Power[N[Power[N[Exp[y], $MachinePrecision], 2.0], $MachinePrecision], N[(y * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

x \cdot e^{y \cdot y}
↓
x \cdot {\left({\left(e^{y}\right)}^{2}\right)}^{\left(y \cdot 0.5\right)}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[x \cdot {\left(e^{y}\right)}^{y} \]

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y} \]

  2. Simplified0.0

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

  3. Taylor expanded in y around inf 0.0

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

  4. Applied egg-rr0.1

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

  5. Applied egg-rr0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2022210 
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"
  :precision binary64

  :herbie-target
  (* x (pow (exp y) y))

  (* x (exp (* y y))))