Average Error: 0.2 → 0.2
Time: 11.0s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \]
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l) :precision binary64 (/ (pow l (exp w)) (exp w)))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return pow(l, exp(w)) / exp(w);
}

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = exp(-w) * (l ** exp(w))
end function
↓
real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = (l ** exp(w)) / exp(w)
end function

public static double code(double w, double l) {
	return Math.exp(-w) * Math.pow(l, Math.exp(w));
}
↓
public static double code(double w, double l) {
	return Math.pow(l, Math.exp(w)) / Math.exp(w);
}

def code(w, l):
	return math.exp(-w) * math.pow(l, math.exp(w))
↓
def code(w, l):
	return math.pow(l, math.exp(w)) / math.exp(w)

function code(w, l)
	return Float64(exp(Float64(-w)) * (l ^ exp(w)))
end
↓
function code(w, l)
	return Float64((l ^ exp(w)) / exp(w))
end

function tmp = code(w, l)
	tmp = exp(-w) * (l ^ exp(w));
end
↓
function tmp = code(w, l)
	tmp = (l ^ exp(w)) / exp(w);
end

code[w_, l_] := N[(N[Exp[(-w)], $MachinePrecision] * N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[w_, l_] := N[(N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision] / N[Exp[w], $MachinePrecision]), $MachinePrecision]

e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]

  3. Applied egg-rr1.3

    \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}\right)}^{3}} \]

  4. Taylor expanded in l around 0 4.6

    \[\leadsto \color{blue}{\frac{e^{\log \ell \cdot e^{w}}}{e^{w}}} \]

  5. Simplified0.2

    \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]

  6. Final simplification0.2

    \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \]

Reproduce

herbie shell --seed 2022211 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))