exp-w (used to crash)

Percentage Accurate: 99.4% → 98.3%

Time: 14.8s

Alternatives: 5

Speedup: 1.0×

• could not determine a ground truth

  1. w = 7.382320303051424e+289
  2. l = 3.7441163756092937e+65

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: 99.4% 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: 98.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq 1.22 \cdot 10^{-8}:\\ \;\;\;\;\left(1 - w\right) \cdot {\ell}^{\left(1 + w\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.5 \cdot w - 1, w, 1\right) \cdot {\ell}^{\left(\mathsf{fma}\left(\mathsf{fma}\left(0.5, w, 1\right), w, 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= l 1.22e-8)
   (* (- 1.0 w) (pow l (+ 1.0 w)))
   (* (fma (- (* 0.5 w) 1.0) w 1.0) (pow l (fma (fma 0.5 w 1.0) w 1.0)))))

C

double code(double w, double l) {
	double tmp;
	if (l <= 1.22e-8) {
		tmp = (1.0 - w) * pow(l, (1.0 + w));
	} else {
		tmp = fma(((0.5 * w) - 1.0), w, 1.0) * pow(l, fma(fma(0.5, w, 1.0), w, 1.0));
	}
	return tmp;
}

Julia

function code(w, l)
	tmp = 0.0
	if (l <= 1.22e-8)
		tmp = Float64(Float64(1.0 - w) * (l ^ Float64(1.0 + w)));
	else
		tmp = Float64(fma(Float64(Float64(0.5 * w) - 1.0), w, 1.0) * (l ^ fma(fma(0.5, w, 1.0), w, 1.0)));
	end
	return tmp
end

Wolfram

code[w_, l_] := If[LessEqual[l, 1.22e-8], N[(N[(1.0 - w), $MachinePrecision] * N[Power[l, N[(1.0 + w), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.5 * w), $MachinePrecision] - 1.0), $MachinePrecision] * w + 1.0), $MachinePrecision] * N[Power[l, N[(N[(0.5 * w + 1.0), $MachinePrecision] * w + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < 1.22e-8

   1. Initial program 99.9%

      \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in w around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in w around 0

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

      1. lower-+.f64 99.9

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

   8. Applied rewrites 99.9%

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

   if 1.22e-8 < l

   1. Initial program 97.8%

      \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in w around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 83.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{0.5 \cdot w} - 1, w, 1\right) \cdot {\ell}^{\left(e^{w}\right)} \]

   5. Applied rewrites 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5 \cdot w - 1, w, 1\right)} \cdot {\ell}^{\left(e^{w}\right)} \]

   6. Taylor expanded in w around 0

      \[\leadsto \mathsf{fma}\left(\frac{1}{2} \cdot w - 1, w, 1\right) \cdot {\ell}^{\color{blue}{\left(1 + w \cdot \left(1 + \frac{1}{2} \cdot w\right)\right)}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2} \cdot w - 1, w, 1\right) \cdot {\ell}^{\color{blue}{\left(w \cdot \left(1 + \frac{1}{2} \cdot w\right) + 1\right)}} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2} \cdot w - 1, w, 1\right) \cdot {\ell}^{\left(\color{blue}{\left(1 + \frac{1}{2} \cdot w\right) \cdot w} + 1\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2} \cdot w - 1, w, 1\right) \cdot {\ell}^{\color{blue}{\left(\mathsf{fma}\left(1 + \frac{1}{2} \cdot w, w, 1\right)\right)}} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2} \cdot w - 1, w, 1\right) \cdot {\ell}^{\left(\mathsf{fma}\left(\color{blue}{\frac{1}{2} \cdot w + 1}, w, 1\right)\right)} \]

      5. lower-fma.f64 99.4

         \[\leadsto \mathsf{fma}\left(0.5 \cdot w - 1, w, 1\right) \cdot {\ell}^{\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(0.5, w, 1\right)}, w, 1\right)\right)} \]

   8. Applied rewrites 99.4%

      \[\leadsto \mathsf{fma}\left(0.5 \cdot w - 1, w, 1\right) \cdot {\ell}^{\color{blue}{\left(\mathsf{fma}\left(\mathsf{fma}\left(0.5, w, 1\right), w, 1\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.4% 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]

Derivation

1. Initial program 99.0%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 3: 97.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq 1.22 \cdot 10^{-8}:\\ \;\;\;\;\left(1 - w\right) \cdot {\ell}^{\left(1 + w\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - w\right) \cdot {\ell}^{\left(\mathsf{fma}\left(\mathsf{fma}\left(0.5, w, 1\right), w, 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= l 1.22e-8)
   (* (- 1.0 w) (pow l (+ 1.0 w)))
   (* (- 1.0 w) (pow l (fma (fma 0.5 w 1.0) w 1.0)))))

C

double code(double w, double l) {
	double tmp;
	if (l <= 1.22e-8) {
		tmp = (1.0 - w) * pow(l, (1.0 + w));
	} else {
		tmp = (1.0 - w) * pow(l, fma(fma(0.5, w, 1.0), w, 1.0));
	}
	return tmp;
}

Julia

function code(w, l)
	tmp = 0.0
	if (l <= 1.22e-8)
		tmp = Float64(Float64(1.0 - w) * (l ^ Float64(1.0 + w)));
	else
		tmp = Float64(Float64(1.0 - w) * (l ^ fma(fma(0.5, w, 1.0), w, 1.0)));
	end
	return tmp
end

Wolfram

code[w_, l_] := If[LessEqual[l, 1.22e-8], N[(N[(1.0 - w), $MachinePrecision] * N[Power[l, N[(1.0 + w), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - w), $MachinePrecision] * N[Power[l, N[(N[(0.5 * w + 1.0), $MachinePrecision] * w + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < 1.22e-8

   1. Initial program 99.9%

      \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in w around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in w around 0

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

      1. lower-+.f64 99.9

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

   8. Applied rewrites 99.9%

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

   if 1.22e-8 < l

   1. Initial program 97.8%

      \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in w around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 65.4

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

   5. Applied rewrites 65.4%

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

   6. Taylor expanded in w around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(1 - w\right) \cdot {\ell}^{\color{blue}{\left(\mathsf{fma}\left(1 + \frac{1}{2} \cdot w, w, 1\right)\right)}} \]

      4. +-commutative N/A

         \[\leadsto \left(1 - w\right) \cdot {\ell}^{\left(\mathsf{fma}\left(\color{blue}{\frac{1}{2} \cdot w + 1}, w, 1\right)\right)} \]

      5. lower-fma.f64 97.5

         \[\leadsto \left(1 - w\right) \cdot {\ell}^{\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(0.5, w, 1\right)}, w, 1\right)\right)} \]

   8. Applied rewrites 97.5%

      \[\leadsto \left(1 - w\right) \cdot {\ell}^{\color{blue}{\left(\mathsf{fma}\left(\mathsf{fma}\left(0.5, w, 1\right), w, 1\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.6% accurate, 2.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(w, l):
	return (1.0 - w) * math.pow(l, (1.0 + w))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Add Preprocessing

3. Taylor expanded in w around 0

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

   1. fp-cancel-sign-sub-inv N/A

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

   2. metadata-eval N/A

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

   3. *-lft-identity N/A

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

   4. lower--.f64 71.2

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

5. Applied rewrites 71.2%

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

6. Taylor expanded in w around 0

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

   1. lower-+.f64 85.0

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

8. Applied rewrites 85.0%

   \[\leadsto \left(1 - w\right) \cdot {\ell}^{\color{blue}{\left(1 + w\right)}} \]
9. Add Preprocessing

Alternative 5: 31.4% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(w, l):
	return -w * math.pow(l, (1.0 + w))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Add Preprocessing

3. Taylor expanded in w around 0

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

   1. fp-cancel-sign-sub-inv N/A

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

   2. metadata-eval N/A

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

   3. *-lft-identity N/A

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

   4. lower--.f64 71.2

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

5. Applied rewrites 71.2%

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

6. Taylor expanded in w around 0

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

   1. lower-+.f64 85.0

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

8. Applied rewrites 85.0%

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

9. Taylor expanded in w around inf

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

11. Applied rewrites 32.7%

    \[\leadsto \left(-w\right) \cdot {\ell}^{\left(1 + w\right)} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024326 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))