exp-w (used to crash)

?

Percentage Accurate: 99.5% → 99.5%
Time: 16.8s
Precision: binary64
Cost: 19456

?

\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \]
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l) :precision binary64 (/ (pow l (exp w)) (exp w)))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return pow(l, exp(w)) / 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
    code = (l ** exp(w)) / 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) {
	return Math.pow(l, Math.exp(w)) / Math.exp(w);
}

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)) / math.exp(w)

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

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

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

e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}

Local Percentage Accuracy?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

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Your Program's Arguments

Results

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Derivation?

  1. Initial program 99.7%

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

  2. Simplified99.7%

    \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]
    Step-by-step derivation

    [Start]99.7

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

    exp-neg [=>]99.7

    \[ \color{blue}{\frac{1}{e^{w}}} \cdot {\ell}^{\left(e^{w}\right)} \]

    associate-*l/ [=>]99.7

    \[ \color{blue}{\frac{1 \cdot {\ell}^{\left(e^{w}\right)}}{e^{w}}} \]

    *-lft-identity [=>]99.7

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

  3. Final simplification99.7%

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

Alternatives

Alternative 1
Accuracy98.0%
Cost6592
\[\frac{\ell}{e^{w}} \]
Alternative 2
Accuracy78.2%
Cost1348
\[\begin{array}{l} \mathbf{if}\;w \leq 0.051:\\ \;\;\;\;\ell \cdot \left(1 - w\right) - \left(w \cdot w\right) \cdot \left(\ell \cdot -0.5 + w \cdot \left(\ell \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell - \left(\ell \cdot w\right) \cdot \left(\ell \cdot w\right)}{\ell + \ell \cdot w}\\ \end{array} \]
Alternative 3
Accuracy76.6%
Cost1216
\[\ell \cdot \left(1 - w\right) - \left(w \cdot w\right) \cdot \left(\ell \cdot -0.5 + w \cdot \left(\ell \cdot 0.16666666666666666\right)\right) \]
Alternative 4
Accuracy75.0%
Cost704
\[\ell - \ell \cdot \left(w + \left(w \cdot w\right) \cdot -0.5\right) \]
Alternative 5
Accuracy64.7%
Cost388
\[\begin{array}{l} \mathbf{if}\;w \leq -9:\\ \;\;\;\;\ell \cdot \left(-w\right)\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \]
Alternative 6
Accuracy64.4%
Cost320
\[\ell - \ell \cdot w \]
Alternative 7
Accuracy57.9%
Cost64
\[\ell \]

Error

Reproduce?

herbie shell --seed 2023160 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))