exp-w (used to crash)

Percentage Accurate: 99.5% → 99.5%

Time: 13.5s

Alternatives: 6

Speedup: N/A×

• could not determine a ground truth

  1. w = 2.00000000000000007e154
  2. l = -2

Specification

Math

\[\begin{array}{l} \\ e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \end{array} \]

FPCore

(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));
}

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

Java

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))

Julia

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \end{array} \]

FPCore

(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));
}

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

Java

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))

Julia

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt[3]{e^{w}}\\ \frac{\frac{{\ell}^{\left(e^{w}\right)}}{t_0}}{{t_0}^{2}} \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (let* ((t_0 (cbrt (exp w)))) (/ (/ (pow l (exp w)) t_0) (pow t_0 2.0))))

C

double code(double w, double l) {
	double t_0 = cbrt(exp(w));
	return (pow(l, exp(w)) / t_0) / pow(t_0, 2.0);
}

Java

public static double code(double w, double l) {
	double t_0 = Math.cbrt(Math.exp(w));
	return (Math.pow(l, Math.exp(w)) / t_0) / Math.pow(t_0, 2.0);
}

Julia

function code(w, l)
	t_0 = cbrt(exp(w))
	return Float64(Float64((l ^ exp(w)) / t_0) / (t_0 ^ 2.0))
end

Wolfram

code[w_, l_] := Block[{t$95$0 = N[Power[N[Exp[w], $MachinePrecision], 1/3], $MachinePrecision]}, N[(N[(N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision] / t$95$0), $MachinePrecision] / N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 99.8%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Step-by-step derivation

   1. exp-neg 99.8%

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

   2. associate-*l/ 99.8%

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

   3. *-lft-identity 99.8%

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

3. Simplified 99.8%

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

   1. clear-num 99.6%

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

   2. inv-pow 99.6%

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

   3. add-cube-cbrt 99.6%

      \[\leadsto {\left(\frac{\color{blue}{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right) \cdot \sqrt[3]{e^{w}}}}{{\ell}^{\left(e^{w}\right)}}\right)}^{-1} \]

   4. *-un-lft-identity 99.6%

      \[\leadsto {\left(\frac{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right) \cdot \sqrt[3]{e^{w}}}{\color{blue}{1 \cdot {\ell}^{\left(e^{w}\right)}}}\right)}^{-1} \]

   5. times-frac 99.6%

      \[\leadsto {\color{blue}{\left(\frac{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}{1} \cdot \frac{\sqrt[3]{e^{w}}}{{\ell}^{\left(e^{w}\right)}}\right)}}^{-1} \]

   6. unpow-prod-down 99.6%

      \[\leadsto \color{blue}{{\left(\frac{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}{1}\right)}^{-1} \cdot {\left(\frac{\sqrt[3]{e^{w}}}{{\ell}^{\left(e^{w}\right)}}\right)}^{-1}} \]

   7. pow2 99.6%

      \[\leadsto {\left(\frac{\color{blue}{{\left(\sqrt[3]{e^{w}}\right)}^{2}}}{1}\right)}^{-1} \cdot {\left(\frac{\sqrt[3]{e^{w}}}{{\ell}^{\left(e^{w}\right)}}\right)}^{-1} \]

6. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{{\left(\frac{{\left(\sqrt[3]{e^{w}}\right)}^{2}}{1}\right)}^{-1} \cdot {\left(\frac{\sqrt[3]{e^{w}}}{{\ell}^{\left(e^{w}\right)}}\right)}^{-1}} \]
7. Step-by-step derivation

   1. unpow-1 99.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{e^{w}}\right)}^{2}}{1}}} \cdot {\left(\frac{\sqrt[3]{e^{w}}}{{\ell}^{\left(e^{w}\right)}}\right)}^{-1} \]

   2. /-rgt-identity 99.6%

      \[\leadsto \frac{1}{\color{blue}{{\left(\sqrt[3]{e^{w}}\right)}^{2}}} \cdot {\left(\frac{\sqrt[3]{e^{w}}}{{\ell}^{\left(e^{w}\right)}}\right)}^{-1} \]

   3. associate-*l/ 99.6%

      \[\leadsto \color{blue}{\frac{1 \cdot {\left(\frac{\sqrt[3]{e^{w}}}{{\ell}^{\left(e^{w}\right)}}\right)}^{-1}}{{\left(\sqrt[3]{e^{w}}\right)}^{2}}} \]

   4. *-lft-identity 99.6%

      \[\leadsto \frac{\color{blue}{{\left(\frac{\sqrt[3]{e^{w}}}{{\ell}^{\left(e^{w}\right)}}\right)}^{-1}}}{{\left(\sqrt[3]{e^{w}}\right)}^{2}} \]

   5. unpow-1 99.6%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{\sqrt[3]{e^{w}}}{{\ell}^{\left(e^{w}\right)}}}}}{{\left(\sqrt[3]{e^{w}}\right)}^{2}} \]

   6. associate-/l* 99.8%

      \[\leadsto \frac{\color{blue}{\frac{1 \cdot {\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}}}{{\left(\sqrt[3]{e^{w}}\right)}^{2}} \]

   7. *-lft-identity 99.8%

      \[\leadsto \frac{\frac{\color{blue}{{\ell}^{\left(e^{w}\right)}}}{\sqrt[3]{e^{w}}}}{{\left(\sqrt[3]{e^{w}}\right)}^{2}} \]

8. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{\frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}}{{\left(\sqrt[3]{e^{w}}\right)}^{2}}} \]

9. Final simplification 99.8%

   \[\leadsto \frac{\frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}}{{\left(\sqrt[3]{e^{w}}\right)}^{2}} \]
10. Add Preprocessing

Alternative 2: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = (l ** exp(w)) / exp(w)
end function

Java

public static double code(double w, double l) {
	return Math.pow(l, Math.exp(w)) / Math.exp(w);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Step-by-step derivation

   1. exp-neg 99.8%

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

   2. associate-*l/ 99.8%

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

   3. *-lft-identity 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]
4. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \]
6. Add Preprocessing

Alternative 3: 98.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \frac{\ell}{e^{w}} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (/ l (exp w)))

C

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

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = l / exp(w)
end function

Java

public static double code(double w, double l) {
	return l / Math.exp(w);
}

Python

def code(w, l):
	return l / math.exp(w)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Step-by-step derivation

   1. exp-neg 99.8%

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

   2. associate-*l/ 99.8%

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

   3. *-lft-identity 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 98.2%

   \[\leadsto \frac{\color{blue}{\ell}}{e^{w}} \]

6. Final simplification 98.2%

   \[\leadsto \frac{\ell}{e^{w}} \]
7. Add Preprocessing

Alternative 4: 64.1% accurate, 50.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.0145:\\ \;\;\;\;-\ell \cdot w\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w -0.0145) (- (* l w)) l))

C

double code(double w, double l) {
	double tmp;
	if (w <= -0.0145) {
		tmp = -(l * w);
	} else {
		tmp = l;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-0.0145d0)) then
        tmp = -(l * w)
    else
        tmp = l
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -0.0145) {
		tmp = -(l * w);
	} else {
		tmp = l;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -0.0145:
		tmp = -(l * w)
	else:
		tmp = l
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -0.0145)
		tmp = Float64(-Float64(l * w));
	else
		tmp = l;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -0.0145)
		tmp = -(l * w);
	else
		tmp = l;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -0.0145], (-N[(l * w), $MachinePrecision]), l]

Derivation

1. Split input into 2 regimes

2. if w < -0.0145000000000000007

   1. Initial program 100.0%

      \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
   2. Step-by-step derivation

      1. exp-neg 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-lft-identity 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]
   4. Add Preprocessing

   5. Taylor expanded in w around 0 98.8%

      \[\leadsto \frac{\color{blue}{\ell}}{e^{w}} \]

   6. Taylor expanded in w around 0 28.9%

      \[\leadsto \color{blue}{\ell + -1 \cdot \left(\ell \cdot w\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 28.9%

         \[\leadsto \ell + \color{blue}{\left(-\ell \cdot w\right)} \]

      2. unsub-neg 28.9%

         \[\leadsto \color{blue}{\ell - \ell \cdot w} \]

      3. *-commutative 28.9%

         \[\leadsto \ell - \color{blue}{w \cdot \ell} \]

   8. Simplified 28.9%

      \[\leadsto \color{blue}{\ell - w \cdot \ell} \]

   9. Taylor expanded in w around inf 28.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\ell \cdot w\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 28.9%

          \[\leadsto \color{blue}{\left(-1 \cdot \ell\right) \cdot w} \]

       2. neg-mul-1 28.9%

          \[\leadsto \color{blue}{\left(-\ell\right)} \cdot w \]

       3. *-commutative 28.9%

          \[\leadsto \color{blue}{w \cdot \left(-\ell\right)} \]

   11. Simplified 28.9%

       \[\leadsto \color{blue}{w \cdot \left(-\ell\right)} \]

   if -0.0145000000000000007 < w

   1. Initial program 99.7%

      \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
   2. Step-by-step derivation

      1. exp-neg 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-lft-identity 99.7%

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

   3. Simplified 99.7%

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

      1. frac-2neg 99.7%

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

      2. div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in w around inf 99.7%

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

   8. Taylor expanded in w around 0 79.2%

      \[\leadsto \color{blue}{\ell} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -0.0145:\\ \;\;\;\;-\ell \cdot w\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.8% accurate, 61.0× speedup

Math

\[\begin{array}{l} \\ \ell \cdot \left(1 - w\right) \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (* l (- 1.0 w)))

C

double code(double w, double l) {
	return l * (1.0 - w);
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = l * (1.0d0 - w)
end function

Java

public static double code(double w, double l) {
	return l * (1.0 - w);
}

Python

def code(w, l):
	return l * (1.0 - w)

Julia

function code(w, l)
	return Float64(l * Float64(1.0 - w))
end

MATLAB

function tmp = code(w, l)
	tmp = l * (1.0 - w);
end

Wolfram

code[w_, l_] := N[(l * N[(1.0 - w), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Step-by-step derivation

   1. exp-neg 99.8%

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

   2. associate-*l/ 99.8%

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

   3. *-lft-identity 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 98.2%

   \[\leadsto \frac{\color{blue}{\ell}}{e^{w}} \]

6. Taylor expanded in w around 0 64.2%

   \[\leadsto \color{blue}{\ell + -1 \cdot \left(\ell \cdot w\right)} \]
7. Step-by-step derivation

   1. mul-1-neg 64.2%

      \[\leadsto \ell + \color{blue}{\left(-\ell \cdot w\right)} \]

   2. unsub-neg 64.2%

      \[\leadsto \color{blue}{\ell - \ell \cdot w} \]

   3. *-commutative 64.2%

      \[\leadsto \ell - \color{blue}{w \cdot \ell} \]

8. Simplified 64.2%

   \[\leadsto \color{blue}{\ell - w \cdot \ell} \]

9. Taylor expanded in l around 0 64.2%

   \[\leadsto \color{blue}{\ell \cdot \left(1 - w\right)} \]

10. Final simplification 64.2%

    \[\leadsto \ell \cdot \left(1 - w\right) \]
11. Add Preprocessing

Alternative 6: 57.0% accurate, 305.0× speedup

Math

\[\begin{array}{l} \\ \ell \end{array} \]

FPCore

(FPCore (w l) :precision binary64 l)

C

double code(double w, double l) {
	return l;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = l
end function

Java

public static double code(double w, double l) {
	return l;
}

Python

def code(w, l):
	return l

Julia

function code(w, l)
	return l
end

MATLAB

function tmp = code(w, l)
	tmp = l;
end

Wolfram

code[w_, l_] := l

Derivation

1. Initial program 99.8%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Step-by-step derivation

   1. exp-neg 99.8%

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

   2. associate-*l/ 99.8%

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

   3. *-lft-identity 99.8%

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

3. Simplified 99.8%

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

   1. frac-2neg 99.8%

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

   2. div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Taylor expanded in w around inf 99.8%

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

8. Taylor expanded in w around 0 57.1%

   \[\leadsto \color{blue}{\ell} \]

9. Final simplification 57.1%

   \[\leadsto \ell \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))