exp-w (used to crash)

Average Error: 0.41% → 0.41%

Time: 16.1s

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 0.41

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

2. Final simplification 0.41

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

Alternatives

Alternative 1
Error	0.41%
Cost	19456

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

Alternative 2
Error	1.36%
Cost	13184

\[{\ell}^{\left(e^{w}\right)} \cdot \left(1 - w\right) \]

Alternative 3
Error	2.07%
Cost	12928

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

Alternative 4
Error	2.74%
Cost	6660

\[\begin{array}{l} \mathbf{if}\;w \leq 420:\\ \;\;\;\;\frac{\ell \cdot \left(1 - w \cdot w\right)}{w + 1}\\ \mathbf{else}:\\ \;\;\;\;e^{-w}\\ \end{array} \]

Alternative 5
Error	2.73%
Cost	6592

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

Alternative 6
Error	13.11%
Cost	836

\[\begin{array}{l} \mathbf{if}\;w \leq 0.102:\\ \;\;\;\;\frac{\ell \cdot \left(1 - w \cdot w\right)}{w + 1}\\ \mathbf{else}:\\ \;\;\;\;-1 + \left(1 - \ell \cdot \left(w + -1\right)\right)\\ \end{array} \]

Alternative 7
Error	13.11%
Cost	708

\[\begin{array}{l} \mathbf{if}\;w \leq 0.098:\\ \;\;\;\;\ell \cdot \left(1 - w\right)\\ \mathbf{else}:\\ \;\;\;\;-1 + \left(1 - \ell \cdot \left(w + -1\right)\right)\\ \end{array} \]

Alternative 8
Error	21.68%
Cost	64

\[\ell \]

Reproduce

herbie shell --seed 2023115 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))