Average Error: 0.3 → 0.3
Time: 34.9s
Precision: binary64
Cost: 51776
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\begin{array}{l} t_0 := \sqrt[3]{e^{w}}\\ \frac{\frac{\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}}{t_0}}{t_0} \end{array} \]
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (let* ((t_0 (cbrt (exp w))))
   (/ (/ (* (cbrt (exp (- w))) (pow l (exp w))) t_0) t_0)))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	double t_0 = cbrt(exp(w));
	return ((cbrt(exp(-w)) * pow(l, exp(w))) / t_0) / t_0;
}

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.cbrt(Math.exp(w));
	return ((Math.cbrt(Math.exp(-w)) * Math.pow(l, Math.exp(w))) / t_0) / t_0;
}

function code(w, l)
	return Float64(exp(Float64(-w)) * (l ^ exp(w)))
end
↓
function code(w, l)
	t_0 = cbrt(exp(w))
	return Float64(Float64(Float64(cbrt(exp(Float64(-w))) * (l ^ exp(w))) / t_0) / t_0)
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[Power[N[Exp[w], $MachinePrecision], 1/3], $MachinePrecision]}, N[(N[(N[(N[Power[N[Exp[(-w)], $MachinePrecision], 1/3], $MachinePrecision] * N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] / t$95$0), $MachinePrecision]]

e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\begin{array}{l}
t_0 := \sqrt[3]{e^{w}}\\
\frac{\frac{\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}}{t_0}}{t_0}
\end{array}

Error

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. Simplified0.3

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

  3. Applied egg-rr0.3

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

Alternatives

Alternative 1
Error0.3
Cost32512
\[\frac{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w \cdot 0.6666666666666666}}}{\sqrt[3]{e^{w}}} \]
Alternative 2
Error0.3
Cost26112
\[{\ell}^{\left(e^{w}\right)} \cdot {\left(-e^{w \cdot -0.5}\right)}^{2} \]
Alternative 3
Error0.3
Cost26048
\[{\ell}^{\left(e^{w}\right)} \cdot {\left(e^{w \cdot -0.25}\right)}^{4} \]
Alternative 4
Error0.3
Cost19456
\[\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \]
Alternative 5
Error0.8
Cost13248
\[{\ell}^{\left(e^{w}\right)} \cdot \left(1 + \left(-w\right)\right) \]
Alternative 6
Error1.3
Cost13056
\[{\ell}^{\left(e^{w}\right)} \cdot 1 \]
Alternative 7
Error5.6
Cost7236
\[\begin{array}{l} \mathbf{if}\;w \leq 0.125:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{\frac{-1}{\frac{1}{\ell}}}{\frac{-1}{\ell \cdot \ell}}}\\ \end{array} \]
Alternative 8
Error5.3
Cost7236
\[\begin{array}{l} \mathbf{if}\;w \leq 0.095:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt[3]{\frac{-1}{\ell \cdot \ell} \cdot \frac{-1}{\ell}}}\\ \end{array} \]
Alternative 9
Error7.4
Cost1352
\[\begin{array}{l} t_0 := \frac{-1}{\frac{-1}{\ell}}\\ \mathbf{if}\;w \leq 0.135:\\ \;\;\;\;\ell\\ \mathbf{elif}\;\frac{-1}{\frac{1}{\ell}} \ne 0:\\ \;\;\;\;\frac{\frac{-1}{\frac{\frac{-1}{\ell}}{\ell}}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 10
Error13.5
Cost64
\[\ell \]

Error

Reproduce

herbie shell --seed 2023010 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))