exp-w (used to crash)

Average Error: 0.42% → 0.42%

Time: 15.7s

Precision: binary64

Cost: 19520

Math

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

↓

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

FPCore

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))

↓

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))

C

double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}

↓

double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}

Fortran

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 = exp(-w) * (l ** exp(w))
end function

Java

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.exp(-w) * Math.pow(l, Math.exp(w));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.42

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

2. Final simplification 0.42

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

Alternatives

Alternative 1
Error	0.43%
Cost	19456

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

Alternative 2
Error	2.84%
Cost	7360

\[\frac{\ell}{\left(1 + w \cdot \left(0.6666666666666666 + w \cdot 0.2222222222222222\right)\right) \cdot e^{w \cdot 0.3333333333333333}} \]

Alternative 3
Error	2.82%
Cost	6656

\[e^{-w} \cdot \ell \]

Alternative 4
Error	2.82%
Cost	6592

\[\frac{\ell}{e^{w}} \]

Alternative 5
Error	10.5%
Cost	1348

\[\begin{array}{l} \mathbf{if}\;w \leq 1.66 \cdot 10^{-21}:\\ \;\;\;\;\ell \cdot \left(1 - w\right) + \left(w \cdot w\right) \cdot \left(\ell \cdot 0.5 + w \cdot \left(\ell \cdot -0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell}{\ell + w \cdot \ell}\\ \end{array} \]

Alternative 6
Error	10.5%
Cost	1092

\[\begin{array}{l} \mathbf{if}\;w \leq 1.66 \cdot 10^{-21}:\\ \;\;\;\;\ell + \ell \cdot \left(\left(w \cdot w\right) \cdot \left(0.5 + w \cdot -0.16666666666666666\right) - w\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell}{\ell + w \cdot \ell}\\ \end{array} \]

Alternative 7
Error	10.5%
Cost	836

\[\begin{array}{l} \mathbf{if}\;w \leq 1.66 \cdot 10^{-21}:\\ \;\;\;\;\ell + \ell \cdot \left(w \cdot \left(w \cdot 0.5\right) - w\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell}{\ell + w \cdot \ell}\\ \end{array} \]

Alternative 8
Error	9.8%
Cost	708

\[\begin{array}{l} \mathbf{if}\;w \leq 0.062:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell}{\ell + w \cdot \ell}\\ \end{array} \]

Alternative 9
Error	21.45%
Cost	64

\[\ell \]

Reproduce

herbie shell --seed 2023089 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))