exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 16.9s

Alternatives: 9

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: 99.4% 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: 99.4% 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 N/A

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

   2. associate-*l/ N/A

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

   3. *-lft-identity N/A

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

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

   5. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

   6. exp-lowering-exp.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

   7. exp-lowering-exp.f64 99.8%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

3. Simplified 99.8%

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

Alternative 2: 97.9% 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 N/A

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

   2. associate-*l/ N/A

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

   3. *-lft-identity N/A

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

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

   5. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

   6. exp-lowering-exp.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

   7. exp-lowering-exp.f64 99.8%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

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

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{\ell}, \mathsf{exp.f64}\left(w\right)\right) \]
6. Step-by-step derivation

7. Simplified 99.0%

   \[\leadsto \frac{\color{blue}{\ell}}{e^{w}} \]
8. Add Preprocessing

Alternative 3: 93.6% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 + w \cdot 0.5\\ t_1 := w \cdot t\_0\\ \mathbf{if}\;w \leq -1.65 \cdot 10^{+77}:\\ \;\;\;\;\ell \cdot \left(-0.16666666666666666 \cdot \left(w \cdot \left(w \cdot w\right)\right)\right)\\ \mathbf{elif}\;w \leq 0.08:\\ \;\;\;\;\frac{\ell \cdot \left(1 + w \cdot \left(\left(w \cdot w\right) \cdot \left(t\_0 \cdot \left(t\_0 \cdot t\_0\right)\right)\right)\right)}{1 + t\_1 \cdot \left(-1 + t\_1\right)}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (let* ((t_0 (+ -1.0 (* w 0.5))) (t_1 (* w t_0)))
   (if (<= w -1.65e+77)
     (* l (* -0.16666666666666666 (* w (* w w))))
     (if (<= w 0.08)
       (/
        (* l (+ 1.0 (* w (* (* w w) (* t_0 (* t_0 t_0))))))
        (+ 1.0 (* t_1 (+ -1.0 t_1))))
       0.0))))

C

double code(double w, double l) {
	double t_0 = -1.0 + (w * 0.5);
	double t_1 = w * t_0;
	double tmp;
	if (w <= -1.65e+77) {
		tmp = l * (-0.16666666666666666 * (w * (w * w)));
	} else if (w <= 0.08) {
		tmp = (l * (1.0 + (w * ((w * w) * (t_0 * (t_0 * t_0)))))) / (1.0 + (t_1 * (-1.0 + t_1)));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-1.0d0) + (w * 0.5d0)
    t_1 = w * t_0
    if (w <= (-1.65d+77)) then
        tmp = l * ((-0.16666666666666666d0) * (w * (w * w)))
    else if (w <= 0.08d0) then
        tmp = (l * (1.0d0 + (w * ((w * w) * (t_0 * (t_0 * t_0)))))) / (1.0d0 + (t_1 * ((-1.0d0) + t_1)))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double t_0 = -1.0 + (w * 0.5);
	double t_1 = w * t_0;
	double tmp;
	if (w <= -1.65e+77) {
		tmp = l * (-0.16666666666666666 * (w * (w * w)));
	} else if (w <= 0.08) {
		tmp = (l * (1.0 + (w * ((w * w) * (t_0 * (t_0 * t_0)))))) / (1.0 + (t_1 * (-1.0 + t_1)));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	t_0 = -1.0 + (w * 0.5)
	t_1 = w * t_0
	tmp = 0
	if w <= -1.65e+77:
		tmp = l * (-0.16666666666666666 * (w * (w * w)))
	elif w <= 0.08:
		tmp = (l * (1.0 + (w * ((w * w) * (t_0 * (t_0 * t_0)))))) / (1.0 + (t_1 * (-1.0 + t_1)))
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	t_0 = Float64(-1.0 + Float64(w * 0.5))
	t_1 = Float64(w * t_0)
	tmp = 0.0
	if (w <= -1.65e+77)
		tmp = Float64(l * Float64(-0.16666666666666666 * Float64(w * Float64(w * w))));
	elseif (w <= 0.08)
		tmp = Float64(Float64(l * Float64(1.0 + Float64(w * Float64(Float64(w * w) * Float64(t_0 * Float64(t_0 * t_0)))))) / Float64(1.0 + Float64(t_1 * Float64(-1.0 + t_1))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	t_0 = -1.0 + (w * 0.5);
	t_1 = w * t_0;
	tmp = 0.0;
	if (w <= -1.65e+77)
		tmp = l * (-0.16666666666666666 * (w * (w * w)));
	elseif (w <= 0.08)
		tmp = (l * (1.0 + (w * ((w * w) * (t_0 * (t_0 * t_0)))))) / (1.0 + (t_1 * (-1.0 + t_1)));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := Block[{t$95$0 = N[(-1.0 + N[(w * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(w * t$95$0), $MachinePrecision]}, If[LessEqual[w, -1.65e+77], N[(l * N[(-0.16666666666666666 * N[(w * N[(w * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[w, 0.08], N[(N[(l * N[(1.0 + N[(w * N[(N[(w * w), $MachinePrecision] * N[(t$95$0 * N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(t$95$1 * N[(-1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]]]

Derivation

1. Split input into 3 regimes

2. if w < -1.6499999999999999e77

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   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

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\ell}, \mathsf{exp.f64}\left(w\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 100.0%

      \[\leadsto \frac{\color{blue}{\ell}}{e^{w}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{e^{w}}{\ell}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{e^{w}}{\ell}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(e^{w}\right), \color{blue}{\ell}\right)\right) \]

      4. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(w\right), \ell\right)\right) \]

   9. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{e^{w}}{\ell}}} \]

   10. Taylor expanded in w around 0

       \[\leadsto \color{blue}{\ell + w \cdot \left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)} \]
   11. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \color{blue}{\left(w \cdot \left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \color{blue}{\left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)}\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right)\right), \color{blue}{\ell}\right)\right)\right) \]

   12. Simplified 84.9%

       \[\leadsto \color{blue}{\ell + w \cdot \left(w \cdot \left(\ell \cdot 0.5 - w \cdot \left(\ell \cdot 0.16666666666666666 + 0\right)\right) - \ell\right)} \]

   13. Taylor expanded in w around inf

       \[\leadsto \color{blue}{\frac{-1}{6} \cdot \left(\ell \cdot {w}^{3}\right)} \]
   14. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(\ell \cdot {w}^{3}\right) \cdot \color{blue}{\frac{-1}{6}} \]

       2. associate-*l* N/A

          \[\leadsto \ell \cdot \color{blue}{\left({w}^{3} \cdot \frac{-1}{6}\right)} \]

       3. *-commutative N/A

          \[\leadsto \ell \cdot \left(\frac{-1}{6} \cdot \color{blue}{{w}^{3}}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \color{blue}{\left(\frac{-1}{6} \cdot {w}^{3}\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left({w}^{3}\right)}\right)\right) \]

       6. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \left(w \cdot \color{blue}{\left(w \cdot w\right)}\right)\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \left(w \cdot {w}^{\color{blue}{2}}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(w, \color{blue}{\left({w}^{2}\right)}\right)\right)\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(w, \left(w \cdot \color{blue}{w}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 94.8%

           \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(w, \mathsf{*.f64}\left(w, \color{blue}{w}\right)\right)\right)\right) \]

   15. Simplified 94.8%

       \[\leadsto \color{blue}{\ell \cdot \left(-0.16666666666666666 \cdot \left(w \cdot \left(w \cdot w\right)\right)\right)} \]

   if -1.6499999999999999e77 < w < 0.0800000000000000017

   1. Initial program 99.7%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in w around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\ell}, \mathsf{exp.f64}\left(w\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 98.4%

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

   8. Taylor expanded in w around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \color{blue}{\left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \color{blue}{\left(-1 \cdot \left(w \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(\left(\mathsf{neg}\left(w \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right)\right) - \ell\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right)\right) - \ell\right)\right)\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\mathsf{neg}\left(\ell \cdot \left(-1 + \frac{1}{2}\right)\right)\right) - \ell\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\mathsf{neg}\left(\ell \cdot \frac{-1}{2}\right)\right) - \ell\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\mathsf{neg}\left(\frac{-1}{2} \cdot \ell\right)\right) - \ell\right)\right)\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot \ell\right) - \ell\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\frac{1}{2} \cdot \ell\right) - \ell\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\left(w \cdot \left(\frac{1}{2} \cdot \ell\right)\right), \color{blue}{\ell}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(w, \left(\frac{1}{2} \cdot \ell\right)\right), \ell\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(w, \left(\ell \cdot \frac{1}{2}\right)\right), \ell\right)\right)\right) \]

      13. *-lowering-*.f64 90.6%

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(w, \mathsf{*.f64}\left(\ell, \frac{1}{2}\right)\right), \ell\right)\right)\right) \]

   10. Simplified 90.6%

       \[\leadsto \color{blue}{\ell + w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right)} \]
   11. Step-by-step derivation

       1. flip3-+ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{3} + {\left(w \cdot \left(w \cdot \left(\ell \cdot \frac{1}{2}\right) - \ell\right)\right)}^{3}\right), \color{blue}{\left(\ell \cdot \ell + \left(\left(w \cdot \left(w \cdot \left(\ell \cdot \frac{1}{2}\right) - \ell\right)\right) \cdot \left(w \cdot \left(w \cdot \left(\ell \cdot \frac{1}{2}\right) - \ell\right)\right) - \ell \cdot \left(w \cdot \left(w \cdot \left(\ell \cdot \frac{1}{2}\right) - \ell\right)\right)\right)\right)}\right) \]

   12. Applied egg-rr 34.9%

       \[\leadsto \color{blue}{\frac{\ell \cdot \left(\ell \cdot \ell\right) + \left(w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right)\right) \cdot \left(\left(w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right)\right) \cdot \left(w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right)\right)\right)}{\ell \cdot \ell + \left(w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right)\right) \cdot \left(w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right) - \ell\right)}} \]

   13. Taylor expanded in l around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\ell \cdot \left(1 + {w}^{3} \cdot {\left(\frac{1}{2} \cdot w - 1\right)}^{3}\right)\right), \color{blue}{\left(1 + w \cdot \left(\left(\frac{1}{2} \cdot w - 1\right) \cdot \left(w \cdot \left(\frac{1}{2} \cdot w - 1\right) - 1\right)\right)\right)}\right) \]

   15. Simplified 94.2%

       \[\leadsto \color{blue}{\frac{\ell \cdot \left(1 + w \cdot \left(\left(w \cdot w\right) \cdot \left(\left(-1 + w \cdot 0.5\right) \cdot \left(\left(-1 + w \cdot 0.5\right) \cdot \left(-1 + w \cdot 0.5\right)\right)\right)\right)\right)}{1 + \left(w \cdot \left(-1 + w \cdot 0.5\right)\right) \cdot \left(-1 + w \cdot \left(-1 + w \cdot 0.5\right)\right)}} \]

   if 0.0800000000000000017 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   3. Simplified 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 91.4% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.07:\\ \;\;\;\;\ell \cdot \left(1 + w \cdot \left(-1 + w \cdot \left(0.5 - w \cdot 0.16666666666666666\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 0.07)
   (* l (+ 1.0 (* w (+ -1.0 (* w (- 0.5 (* w 0.16666666666666666)))))))
   0.0))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.07) {
		tmp = l * (1.0 + (w * (-1.0 + (w * (0.5 - (w * 0.16666666666666666))))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 0.07d0) then
        tmp = l * (1.0d0 + (w * ((-1.0d0) + (w * (0.5d0 - (w * 0.16666666666666666d0))))))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.07) {
		tmp = l * (1.0 + (w * (-1.0 + (w * (0.5 - (w * 0.16666666666666666))))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.07:
		tmp = l * (1.0 + (w * (-1.0 + (w * (0.5 - (w * 0.16666666666666666))))))
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.07)
		tmp = Float64(l * Float64(1.0 + Float64(w * Float64(-1.0 + Float64(w * Float64(0.5 - Float64(w * 0.16666666666666666)))))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.07)
		tmp = l * (1.0 + (w * (-1.0 + (w * (0.5 - (w * 0.16666666666666666))))));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.07], N[(l * N[(1.0 + N[(w * N[(-1.0 + N[(w * N[(0.5 - N[(w * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if w < 0.070000000000000007

   1. Initial program 99.8%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 99.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   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

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\ell}, \mathsf{exp.f64}\left(w\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 98.8%

      \[\leadsto \frac{\color{blue}{\ell}}{e^{w}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{e^{w}}{\ell}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{e^{w}}{\ell}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(e^{w}\right), \color{blue}{\ell}\right)\right) \]

      4. exp-lowering-exp.f64 98.7%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(w\right), \ell\right)\right) \]

   9. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{e^{w}}{\ell}}} \]

   10. Taylor expanded in w around 0

       \[\leadsto \color{blue}{\ell + w \cdot \left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)} \]
   11. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \color{blue}{\left(w \cdot \left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \color{blue}{\left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)}\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right)\right), \color{blue}{\ell}\right)\right)\right) \]

   12. Simplified 89.6%

       \[\leadsto \color{blue}{\ell + w \cdot \left(w \cdot \left(\ell \cdot 0.5 - w \cdot \left(\ell \cdot 0.16666666666666666 + 0\right)\right) - \ell\right)} \]

   13. Taylor expanded in l around 0

       \[\leadsto \color{blue}{\ell \cdot \left(1 + w \cdot \left(w \cdot \left(\frac{1}{2} - \frac{1}{6} \cdot w\right) - 1\right)\right)} \]
   14. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \color{blue}{\left(1 + w \cdot \left(w \cdot \left(\frac{1}{2} - \frac{1}{6} \cdot w\right) - 1\right)\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{+.f64}\left(1, \color{blue}{\left(w \cdot \left(w \cdot \left(\frac{1}{2} - \frac{1}{6} \cdot w\right) - 1\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(w, \color{blue}{\left(w \cdot \left(\frac{1}{2} - \frac{1}{6} \cdot w\right) - 1\right)}\right)\right)\right) \]

       4. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(w, \left(w \cdot \left(\frac{1}{2} - \frac{1}{6} \cdot w\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(w, \left(w \cdot \left(\frac{1}{2} - \frac{1}{6} \cdot w\right) + -1\right)\right)\right)\right) \]

       6. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(w, \left(-1 + \color{blue}{w \cdot \left(\frac{1}{2} - \frac{1}{6} \cdot w\right)}\right)\right)\right)\right) \]

       7. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(w, \mathsf{+.f64}\left(-1, \color{blue}{\left(w \cdot \left(\frac{1}{2} - \frac{1}{6} \cdot w\right)\right)}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(w, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(w, \color{blue}{\left(\frac{1}{2} - \frac{1}{6} \cdot w\right)}\right)\right)\right)\right)\right) \]

       9. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(w, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot w\right)}\right)\right)\right)\right)\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(w, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\frac{1}{2}, \left(w \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right)\right) \]

       11. *-lowering-*.f64 92.2%

           \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(w, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(w, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right)\right) \]

   15. Simplified 92.2%

       \[\leadsto \color{blue}{\ell \cdot \left(1 + w \cdot \left(-1 + w \cdot \left(0.5 - w \cdot 0.16666666666666666\right)\right)\right)} \]

   if 0.070000000000000007 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   3. Simplified 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 91.4% accurate, 20.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -12.8:\\ \;\;\;\;\ell \cdot \left(-0.16666666666666666 \cdot \left(w \cdot \left(w \cdot w\right)\right)\right)\\ \mathbf{elif}\;w \leq 0.135:\\ \;\;\;\;\ell - \ell \cdot w\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w -12.8)
   (* l (* -0.16666666666666666 (* w (* w w))))
   (if (<= w 0.135) (- l (* l w)) 0.0)))

C

double code(double w, double l) {
	double tmp;
	if (w <= -12.8) {
		tmp = l * (-0.16666666666666666 * (w * (w * w)));
	} else if (w <= 0.135) {
		tmp = l - (l * w);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-12.8d0)) then
        tmp = l * ((-0.16666666666666666d0) * (w * (w * w)))
    else if (w <= 0.135d0) then
        tmp = l - (l * w)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -12.8) {
		tmp = l * (-0.16666666666666666 * (w * (w * w)));
	} else if (w <= 0.135) {
		tmp = l - (l * w);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -12.8:
		tmp = l * (-0.16666666666666666 * (w * (w * w)))
	elif w <= 0.135:
		tmp = l - (l * w)
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -12.8)
		tmp = Float64(l * Float64(-0.16666666666666666 * Float64(w * Float64(w * w))));
	elseif (w <= 0.135)
		tmp = Float64(l - Float64(l * w));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -12.8)
		tmp = l * (-0.16666666666666666 * (w * (w * w)));
	elseif (w <= 0.135)
		tmp = l - (l * w);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -12.8], N[(l * N[(-0.16666666666666666 * N[(w * N[(w * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[w, 0.135], N[(l - N[(l * w), $MachinePrecision]), $MachinePrecision], 0.0]]

Derivation

1. Split input into 3 regimes

2. if w < -12.800000000000001

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   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

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\ell}, \mathsf{exp.f64}\left(w\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 100.0%

      \[\leadsto \frac{\color{blue}{\ell}}{e^{w}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{e^{w}}{\ell}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{e^{w}}{\ell}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(e^{w}\right), \color{blue}{\ell}\right)\right) \]

      4. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(w\right), \ell\right)\right) \]

   9. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{e^{w}}{\ell}}} \]

   10. Taylor expanded in w around 0

       \[\leadsto \color{blue}{\ell + w \cdot \left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)} \]
   11. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \color{blue}{\left(w \cdot \left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \color{blue}{\left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)}\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right) + \left(\frac{-1}{2} \cdot \ell + \frac{1}{6} \cdot \ell\right)\right)\right) - \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right)\right), \color{blue}{\ell}\right)\right)\right) \]

   12. Simplified 71.8%

       \[\leadsto \color{blue}{\ell + w \cdot \left(w \cdot \left(\ell \cdot 0.5 - w \cdot \left(\ell \cdot 0.16666666666666666 + 0\right)\right) - \ell\right)} \]

   13. Taylor expanded in w around inf

       \[\leadsto \color{blue}{\frac{-1}{6} \cdot \left(\ell \cdot {w}^{3}\right)} \]
   14. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(\ell \cdot {w}^{3}\right) \cdot \color{blue}{\frac{-1}{6}} \]

       2. associate-*l* N/A

          \[\leadsto \ell \cdot \color{blue}{\left({w}^{3} \cdot \frac{-1}{6}\right)} \]

       3. *-commutative N/A

          \[\leadsto \ell \cdot \left(\frac{-1}{6} \cdot \color{blue}{{w}^{3}}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \color{blue}{\left(\frac{-1}{6} \cdot {w}^{3}\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left({w}^{3}\right)}\right)\right) \]

       6. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \left(w \cdot \color{blue}{\left(w \cdot w\right)}\right)\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \left(w \cdot {w}^{\color{blue}{2}}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(w, \color{blue}{\left({w}^{2}\right)}\right)\right)\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(w, \left(w \cdot \color{blue}{w}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 79.7%

           \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(w, \mathsf{*.f64}\left(w, \color{blue}{w}\right)\right)\right)\right) \]

   15. Simplified 79.7%

       \[\leadsto \color{blue}{\ell \cdot \left(-0.16666666666666666 \cdot \left(w \cdot \left(w \cdot w\right)\right)\right)} \]

   if -12.800000000000001 < w < 0.13500000000000001

   1. Initial program 99.7%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in w around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\ell}, \mathsf{exp.f64}\left(w\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 98.3%

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

   8. Taylor expanded in w around 0

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

      1. mul-1-neg N/A

         \[\leadsto \ell + \left(\mathsf{neg}\left(\ell \cdot w\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\ell, \color{blue}{\left(\ell \cdot w\right)}\right) \]

      4. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{\_.f64}\left(\ell, \mathsf{*.f64}\left(\ell, \color{blue}{w}\right)\right) \]

   10. Simplified 98.3%

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

   if 0.13500000000000001 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   3. Simplified 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 87.8% accurate, 20.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -13.6:\\ \;\;\;\;\ell \cdot \left(\left(w \cdot w\right) \cdot 0.5\right)\\ \mathbf{elif}\;w \leq 0.235:\\ \;\;\;\;\ell - \ell \cdot w\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w -13.6) (* l (* (* w w) 0.5)) (if (<= w 0.235) (- l (* l w)) 0.0)))

C

double code(double w, double l) {
	double tmp;
	if (w <= -13.6) {
		tmp = l * ((w * w) * 0.5);
	} else if (w <= 0.235) {
		tmp = l - (l * w);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-13.6d0)) then
        tmp = l * ((w * w) * 0.5d0)
    else if (w <= 0.235d0) then
        tmp = l - (l * w)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -13.6) {
		tmp = l * ((w * w) * 0.5);
	} else if (w <= 0.235) {
		tmp = l - (l * w);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -13.6:
		tmp = l * ((w * w) * 0.5)
	elif w <= 0.235:
		tmp = l - (l * w)
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -13.6)
		tmp = Float64(l * Float64(Float64(w * w) * 0.5));
	elseif (w <= 0.235)
		tmp = Float64(l - Float64(l * w));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -13.6)
		tmp = l * ((w * w) * 0.5);
	elseif (w <= 0.235)
		tmp = l - (l * w);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -13.6], N[(l * N[(N[(w * w), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[w, 0.235], N[(l - N[(l * w), $MachinePrecision]), $MachinePrecision], 0.0]]

Derivation

1. Split input into 3 regimes

2. if w < -13.5999999999999996

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   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

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\ell}, \mathsf{exp.f64}\left(w\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 100.0%

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

   8. Taylor expanded in w around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \color{blue}{\left(w \cdot \left(-1 \cdot \left(w \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \color{blue}{\left(-1 \cdot \left(w \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right) - \ell\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(\left(\mathsf{neg}\left(w \cdot \left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right)\right) - \ell\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \ell + \frac{1}{2} \cdot \ell\right)\right)\right) - \ell\right)\right)\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\mathsf{neg}\left(\ell \cdot \left(-1 + \frac{1}{2}\right)\right)\right) - \ell\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\mathsf{neg}\left(\ell \cdot \frac{-1}{2}\right)\right) - \ell\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\mathsf{neg}\left(\frac{-1}{2} \cdot \ell\right)\right) - \ell\right)\right)\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot \ell\right) - \ell\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \left(w \cdot \left(\frac{1}{2} \cdot \ell\right) - \ell\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\left(w \cdot \left(\frac{1}{2} \cdot \ell\right)\right), \color{blue}{\ell}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(w, \left(\frac{1}{2} \cdot \ell\right)\right), \ell\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(w, \left(\ell \cdot \frac{1}{2}\right)\right), \ell\right)\right)\right) \]

      13. *-lowering-*.f64 54.3%

          \[\leadsto \mathsf{+.f64}\left(\ell, \mathsf{*.f64}\left(w, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(w, \mathsf{*.f64}\left(\ell, \frac{1}{2}\right)\right), \ell\right)\right)\right) \]

   10. Simplified 54.3%

       \[\leadsto \color{blue}{\ell + w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right)} \]
   11. Step-by-step derivation

       1. flip3-+ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{3} + {\left(w \cdot \left(w \cdot \left(\ell \cdot \frac{1}{2}\right) - \ell\right)\right)}^{3}\right), \color{blue}{\left(\ell \cdot \ell + \left(\left(w \cdot \left(w \cdot \left(\ell \cdot \frac{1}{2}\right) - \ell\right)\right) \cdot \left(w \cdot \left(w \cdot \left(\ell \cdot \frac{1}{2}\right) - \ell\right)\right) - \ell \cdot \left(w \cdot \left(w \cdot \left(\ell \cdot \frac{1}{2}\right) - \ell\right)\right)\right)\right)}\right) \]

   12. Applied egg-rr 7.6%

       \[\leadsto \color{blue}{\frac{\ell \cdot \left(\ell \cdot \ell\right) + \left(w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right)\right) \cdot \left(\left(w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right)\right) \cdot \left(w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right)\right)\right)}{\ell \cdot \ell + \left(w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right)\right) \cdot \left(w \cdot \left(w \cdot \left(\ell \cdot 0.5\right) - \ell\right) - \ell\right)}} \]

   13. Taylor expanded in w around inf

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

       3. associate-*l* N/A

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

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \color{blue}{\left(\frac{1}{2} \cdot {w}^{2}\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({w}^{2}\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{1}{2}, \left(w \cdot \color{blue}{w}\right)\right)\right) \]

       7. *-lowering-*.f64 67.6%

          \[\leadsto \mathsf{*.f64}\left(\ell, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(w, \color{blue}{w}\right)\right)\right) \]

   15. Simplified 67.6%

       \[\leadsto \color{blue}{\ell \cdot \left(0.5 \cdot \left(w \cdot w\right)\right)} \]

   if -13.5999999999999996 < w < 0.23499999999999999

   1. Initial program 99.7%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in w around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\ell}, \mathsf{exp.f64}\left(w\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 98.3%

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

   8. Taylor expanded in w around 0

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

      1. mul-1-neg N/A

         \[\leadsto \ell + \left(\mathsf{neg}\left(\ell \cdot w\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\ell, \color{blue}{\left(\ell \cdot w\right)}\right) \]

      4. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{\_.f64}\left(\ell, \mathsf{*.f64}\left(\ell, \color{blue}{w}\right)\right) \]

   10. Simplified 98.3%

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

   if 0.23499999999999999 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   3. Simplified 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -13.6:\\ \;\;\;\;\ell \cdot \left(\left(w \cdot w\right) \cdot 0.5\right)\\ \mathbf{elif}\;w \leq 0.235:\\ \;\;\;\;\ell - \ell \cdot w\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.8% accurate, 30.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.215:\\ \;\;\;\;\ell - \ell \cdot w\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w 0.215) (- l (* l w)) 0.0))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.215) {
		tmp = l - (l * w);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 0.215d0) then
        tmp = l - (l * w)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.215) {
		tmp = l - (l * w);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.215:
		tmp = l - (l * w)
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.215)
		tmp = Float64(l - Float64(l * w));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.215)
		tmp = l - (l * w);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.215], N[(l - N[(l * w), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if w < 0.214999999999999997

   1. Initial program 99.8%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 99.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   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

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\ell}, \mathsf{exp.f64}\left(w\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 98.8%

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

   8. Taylor expanded in w around 0

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

      1. mul-1-neg N/A

         \[\leadsto \ell + \left(\mathsf{neg}\left(\ell \cdot w\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\ell, \color{blue}{\left(\ell \cdot w\right)}\right) \]

      4. *-lowering-*.f64 73.7%

         \[\leadsto \mathsf{\_.f64}\left(\ell, \mathsf{*.f64}\left(\ell, \color{blue}{w}\right)\right) \]

   10. Simplified 73.7%

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

   if 0.214999999999999997 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   3. Simplified 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 70.7% accurate, 50.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.1:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w 0.1) l 0.0))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.1) {
		tmp = l;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 0.1d0) then
        tmp = l
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.1) {
		tmp = l;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.1:
		tmp = l
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.1)
		tmp = l;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.1)
		tmp = l;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.1], l, 0.0]

Derivation

1. Split input into 2 regimes

2. if w < 0.10000000000000001

   1. Initial program 99.8%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 99.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   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

      \[\leadsto \color{blue}{\ell} \]
   6. Step-by-step derivation

   7. Simplified 67.1%

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

   if 0.10000000000000001 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. associate-*l/ N/A

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

      3. *-lft-identity N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

      7. exp-lowering-exp.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

   3. Simplified 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 16.9% accurate, 305.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (w l) :precision binary64 0.0)

C

double code(double w, double l) {
	return 0.0;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = 0.0d0
end function

Java

public static double code(double w, double l) {
	return 0.0;
}

Python

def code(w, l):
	return 0.0

Julia

function code(w, l)
	return 0.0
end

MATLAB

function tmp = code(w, l)
	tmp = 0.0;
end

Wolfram

code[w_, l_] := 0.0

Derivation

1. Initial program 99.8%

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

   1. exp-neg N/A

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

   2. associate-*l/ N/A

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

   3. *-lft-identity N/A

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

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left({\ell}^{\left(e^{w}\right)}\right), \color{blue}{\left(e^{w}\right)}\right) \]

   5. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \left(e^{w}\right)\right), \left(e^{\color{blue}{w}}\right)\right) \]

   6. exp-lowering-exp.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \left(e^{w}\right)\right) \]

   7. exp-lowering-exp.f64 99.8%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \mathsf{exp.f64}\left(w\right)\right) \]

3. Simplified 99.8%

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

6. Applied egg-rr 18.2%

   \[\leadsto \color{blue}{0} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024158 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))