exp-w (used to crash)

Average Error: 0.3 → 0.3

Time: 35.2s

Precision: binary64

Cost: 19712

Math

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

↓

\[\frac{{\ell}^{\left(e^{w}\right)} \cdot \frac{2}{e^{w}}}{2} \]

FPCore

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

↓

(FPCore (w l) :precision binary64 (/ (* (pow l (exp w)) (/ 2.0 (exp w))) 2.0))

C

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

↓

double code(double w, double l) {
	return (pow(l, exp(w)) * (2.0 / exp(w))) / 2.0;
}

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 = ((l ** exp(w)) * (2.0d0 / exp(w))) / 2.0d0
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.pow(l, Math.exp(w)) * (2.0 / Math.exp(w))) / 2.0;
}

Python

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)) * (2.0 / math.exp(w))) / 2.0

Julia

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

↓

function code(w, l)
	return Float64(Float64((l ^ exp(w)) * Float64(2.0 / exp(w))) / 2.0)
end

MATLAB

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

↓

function tmp = code(w, l)
	tmp = ((l ^ exp(w)) * (2.0 / exp(w))) / 2.0;
end

Wolfram

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

↓

code[w_, l_] := N[(N[(N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision] * N[(2.0 / N[Exp[w], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]

Derivation

1. Initial program 0.3

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

2. Applied egg-rr 0.3

   \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)} \cdot \frac{2}{e^{w}}}{2}} \]

3. Final simplification 0.3

   \[\leadsto \frac{{\ell}^{\left(e^{w}\right)} \cdot \frac{2}{e^{w}}}{2} \]

Alternatives

Alternative 1
Error	0.3
Cost	19456

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

Alternative 2
Error	0.9
Cost	13440

\[\frac{{\ell}^{\left(e^{w}\right)} \cdot \left(2 + -2 \cdot w\right)}{2} \]

Alternative 3
Error	1.4
Cost	13184

\[\frac{{\ell}^{\left(e^{w}\right)} \cdot 2}{2} \]

Alternative 4
Error	1.8
Cost	6660

\[\begin{array}{l} \mathbf{if}\;w \leq 550:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;e^{-w}\\ \end{array} \]

Alternative 5
Error	1.8
Cost	6656

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

Alternative 6
Error	1.8
Cost	6592

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

Alternative 7
Error	8.6
Cost	708

\[\begin{array}{l} \mathbf{if}\;w \leq 0.105:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;-1 + \left(1 - \ell \cdot \left(w + -1\right)\right)\\ \end{array} \]

Alternative 8
Error	13.7
Cost	64

\[\ell \]

Reproduce

herbie shell --seed 2023069 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))