Average Error: 0.3 → 0.3
Time: 29.0s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\begin{array}{l} t_0 := \sqrt{e^{w}}\\ {\left({\ell}^{t_0}\right)}^{t_0} \cdot e^{-w} \end{array} \]
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (let* ((t_0 (sqrt (exp w)))) (* (pow (pow l t_0) t_0) (exp (- w)))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	double t_0 = sqrt(exp(w));
	return pow(pow(l, t_0), t_0) * 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
    real(8) :: t_0
    t_0 = sqrt(exp(w))
    code = ((l ** t_0) ** t_0) * 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) {
	double t_0 = Math.sqrt(Math.exp(w));
	return Math.pow(Math.pow(l, t_0), t_0) * Math.exp(-w);
}

def code(w, l):
	return math.exp(-w) * math.pow(l, math.exp(w))
↓
def code(w, l):
	t_0 = math.sqrt(math.exp(w))
	return math.pow(math.pow(l, t_0), t_0) * math.exp(-w)

function code(w, l)
	return Float64(exp(Float64(-w)) * (l ^ exp(w)))
end
↓
function code(w, l)
	t_0 = sqrt(exp(w))
	return Float64(((l ^ t_0) ^ t_0) * exp(Float64(-w)))
end

function tmp = code(w, l)
	tmp = exp(-w) * (l ^ exp(w));
end
↓
function tmp = code(w, l)
	t_0 = sqrt(exp(w));
	tmp = ((l ^ t_0) ^ t_0) * exp(-w);
end

code[w_, l_] := N[(N[Exp[(-w)], $MachinePrecision] * N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[w_, l_] := Block[{t$95$0 = N[Sqrt[N[Exp[w], $MachinePrecision]], $MachinePrecision]}, N[(N[Power[N[Power[l, t$95$0], $MachinePrecision], t$95$0], $MachinePrecision] * N[Exp[(-w)], $MachinePrecision]), $MachinePrecision]]

e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\begin{array}{l}
t_0 := \sqrt{e^{w}}\\
{\left({\ell}^{t_0}\right)}^{t_0} \cdot e^{-w}
\end{array}

Error

Bits error versus w

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

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

  2. Applied add-sqr-sqrt_binary640.3

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

  3. Applied pow-unpow_binary640.3

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

  4. Applied *-commutative_binary640.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2022137 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))