exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 22.5s

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: 99.4% 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 99.4%

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

   1. exp-neg 99.4%

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

   2. associate-*l/ 99.4%

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

   3. *-lft-identity 99.4%

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

3. Simplified 99.4%

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

5. Final simplification 99.4%

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

Alternative 2: 97.7% 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 99.4%

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

   1. exp-neg 99.4%

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

   2. associate-*l/ 99.4%

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

   3. *-lft-identity 99.4%

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

3. Simplified 99.4%

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

   1. *-un-lft-identity 99.4%

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

   2. add-sqr-sqrt 40.9%

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

   3. sqrt-unprod 85.0%

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

   4. sqr-neg 85.0%

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

   5. sqrt-unprod 44.2%

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

   6. add-sqr-sqrt 83.9%

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

   7. add-sqr-sqrt 83.9%

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

   8. sqrt-unprod 83.9%

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

   9. exp-neg 83.9%

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

   10. inv-pow 83.9%

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

   11. add-sqr-sqrt 44.2%

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

   12. sqrt-unprod 69.5%

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

   13. sqr-neg 69.5%

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

   14. sqrt-unprod 25.3%

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

   15. add-sqr-sqrt 55.4%

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

   16. pow1 55.4%

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

   17. pow-prod-up 98.0%

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

   18. metadata-eval 98.0%

       \[\leadsto e^{-w} \cdot {\left(1 \cdot \ell\right)}^{\left(\sqrt{{\left(e^{w}\right)}^{\color{blue}{0}}}\right)} \]

   19. metadata-eval 98.0%

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

   20. metadata-eval 98.0%

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

6. Applied egg-rr 98.0%

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

7. Taylor expanded in l around 0 98.0%

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

8. Final simplification 98.0%

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

Alternative 3: 70.7% accurate, 30.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.98:\\ \;\;\;\;\ell - \ell \cdot w\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w 0.98) (- l (* l w)) (/ l w)))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.98) {
		tmp = l - (l * w);
	} else {
		tmp = l / w;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 0.98d0) then
        tmp = l - (l * w)
    else
        tmp = l / w
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.98) {
		tmp = l - (l * w);
	} else {
		tmp = l / w;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.98:
		tmp = l - (l * w)
	else:
		tmp = l / w
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.98)
		tmp = Float64(l - Float64(l * w));
	else
		tmp = Float64(l / w);
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.98)
		tmp = l - (l * w);
	else
		tmp = l / w;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.98], N[(l - N[(l * w), $MachinePrecision]), $MachinePrecision], N[(l / w), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 0.97999999999999998

   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. *-un-lft-identity 99.7%

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

      2. add-sqr-sqrt 30.7%

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

      3. sqrt-unprod 82.8%

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

      4. sqr-neg 82.8%

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

      5. sqrt-unprod 52.1%

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

      6. add-sqr-sqrt 81.9%

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

      7. add-sqr-sqrt 81.9%

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

      8. sqrt-unprod 81.9%

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

      9. exp-neg 81.9%

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

      10. inv-pow 81.9%

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

      11. add-sqr-sqrt 52.1%

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

      12. sqrt-unprod 82.0%

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

      13. sqr-neg 82.0%

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

      14. sqrt-unprod 29.8%

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

      15. add-sqr-sqrt 65.4%

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

      16. pow1 65.4%

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

      17. pow-prod-up 98.6%

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

      18. metadata-eval 98.6%

          \[\leadsto e^{-w} \cdot {\left(1 \cdot \ell\right)}^{\left(\sqrt{{\left(e^{w}\right)}^{\color{blue}{0}}}\right)} \]

      19. metadata-eval 98.6%

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

      20. metadata-eval 98.6%

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

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in w around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

   9. Simplified 73.9%

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

   if 0.97999999999999998 < w

   1. Initial program 97.4%

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

      1. *-un-lft-identity 97.4%

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

      2. add-sqr-sqrt 97.4%

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

      3. sqrt-unprod 97.4%

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

      4. sqr-neg 97.4%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 95.0%

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

      7. add-sqr-sqrt 95.0%

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

      8. sqrt-unprod 95.0%

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

      9. exp-neg 95.0%

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

      10. inv-pow 95.0%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 0.2%

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

      13. sqr-neg 0.2%

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

      14. sqrt-unprod 0.2%

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

      15. add-sqr-sqrt 0.2%

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

      16. pow1 0.2%

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

      17. pow-prod-up 95.1%

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

      18. metadata-eval 95.1%

          \[\leadsto e^{-w} \cdot {\left(1 \cdot \ell\right)}^{\left(\sqrt{{\left(e^{w}\right)}^{\color{blue}{0}}}\right)} \]

      19. metadata-eval 95.1%

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

      20. metadata-eval 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. exp-neg 95.1%

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

      2. *-rgt-identity 95.1%

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

      3. associate-/r/ 95.1%

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

   6. Applied egg-rr 95.1%

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

   7. Taylor expanded in w around 0 52.2%

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

   8. Taylor expanded in w around inf 51.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 0.98:\\ \;\;\;\;\ell - \ell \cdot w\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{w}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.9% accurate, 30.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.31:\\ \;\;\;\;\ell - \ell \cdot w\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{w}{\ell}}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 0.31) (- l (* l w)) (/ 1.0 (/ w l))))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.31) {
		tmp = l - (l * w);
	} else {
		tmp = 1.0 / (w / 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 <= 0.31d0) then
        tmp = l - (l * w)
    else
        tmp = 1.0d0 / (w / l)
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.31) {
		tmp = l - (l * w);
	} else {
		tmp = 1.0 / (w / l);
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.31:
		tmp = l - (l * w)
	else:
		tmp = 1.0 / (w / l)
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.31)
		tmp = Float64(l - Float64(l * w));
	else
		tmp = Float64(1.0 / Float64(w / l));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.31)
		tmp = l - (l * w);
	else
		tmp = 1.0 / (w / l);
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.31], N[(l - N[(l * w), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(w / l), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 0.309999999999999998

   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. *-un-lft-identity 99.7%

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

      2. add-sqr-sqrt 30.7%

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

      3. sqrt-unprod 82.8%

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

      4. sqr-neg 82.8%

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

      5. sqrt-unprod 52.1%

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

      6. add-sqr-sqrt 81.9%

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

      7. add-sqr-sqrt 81.9%

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

      8. sqrt-unprod 81.9%

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

      9. exp-neg 81.9%

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

      10. inv-pow 81.9%

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

      11. add-sqr-sqrt 52.1%

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

      12. sqrt-unprod 82.0%

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

      13. sqr-neg 82.0%

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

      14. sqrt-unprod 29.8%

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

      15. add-sqr-sqrt 65.4%

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

      16. pow1 65.4%

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

      17. pow-prod-up 98.6%

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

      18. metadata-eval 98.6%

          \[\leadsto e^{-w} \cdot {\left(1 \cdot \ell\right)}^{\left(\sqrt{{\left(e^{w}\right)}^{\color{blue}{0}}}\right)} \]

      19. metadata-eval 98.6%

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

      20. metadata-eval 98.6%

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

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in w around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

   9. Simplified 73.9%

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

   if 0.309999999999999998 < w

   1. Initial program 97.4%

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

      1. *-un-lft-identity 97.4%

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

      2. add-sqr-sqrt 97.4%

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

      3. sqrt-unprod 97.4%

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

      4. sqr-neg 97.4%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 95.0%

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

      7. add-sqr-sqrt 95.0%

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

      8. sqrt-unprod 95.0%

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

      9. exp-neg 95.0%

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

      10. inv-pow 95.0%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 0.2%

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

      13. sqr-neg 0.2%

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

      14. sqrt-unprod 0.2%

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

      15. add-sqr-sqrt 0.2%

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

      16. pow1 0.2%

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

      17. pow-prod-up 95.1%

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

      18. metadata-eval 95.1%

          \[\leadsto e^{-w} \cdot {\left(1 \cdot \ell\right)}^{\left(\sqrt{{\left(e^{w}\right)}^{\color{blue}{0}}}\right)} \]

      19. metadata-eval 95.1%

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

      20. metadata-eval 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. exp-neg 95.1%

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

      2. *-rgt-identity 95.1%

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

      3. associate-/r/ 95.1%

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

   6. Applied egg-rr 95.1%

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

   7. Taylor expanded in w around 0 52.2%

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

   8. Taylor expanded in w around inf 52.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{w}{\ell}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 0.31:\\ \;\;\;\;\ell - \ell \cdot w\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{w}{\ell}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.3% accurate, 38.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 6200000:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w 6200000.0) l (/ l w)))

C

double code(double w, double l) {
	double tmp;
	if (w <= 6200000.0) {
		tmp = l;
	} else {
		tmp = l / w;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 6200000.0d0) then
        tmp = l
    else
        tmp = l / w
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 6200000.0) {
		tmp = l;
	} else {
		tmp = l / w;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 6200000.0:
		tmp = l
	else:
		tmp = l / w
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 6200000.0)
		tmp = l;
	else
		tmp = Float64(l / w);
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 6200000.0)
		tmp = l;
	else
		tmp = l / w;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 6200000.0], l, N[(l / w), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 6.2e6

   1. Initial program 99.3%

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

   3. Taylor expanded in w around 0 65.8%

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

   if 6.2e6 < w

   1. Initial program 100.0%

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

      1. *-un-lft-identity 100.0%

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

      2. add-sqr-sqrt 100.0%

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

      3. sqrt-unprod 100.0%

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

      4. sqr-neg 100.0%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 100.0%

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

      7. add-sqr-sqrt 100.0%

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

      8. sqrt-unprod 100.0%

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

      9. exp-neg 100.0%

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

      10. inv-pow 100.0%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 0.0%

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

      13. sqr-neg 0.0%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 0.0%

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

      16. pow1 0.0%

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

      17. pow-prod-up 100.0%

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

      18. metadata-eval 100.0%

          \[\leadsto e^{-w} \cdot {\left(1 \cdot \ell\right)}^{\left(\sqrt{{\left(e^{w}\right)}^{\color{blue}{0}}}\right)} \]

      19. metadata-eval 100.0%

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

      20. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. exp-neg 100.0%

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

      2. *-rgt-identity 100.0%

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

      3. associate-/r/ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in w around 0 56.1%

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

   8. Taylor expanded in w around inf 55.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 6200000:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{w}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.4% 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 99.4%

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

3. Taylor expanded in w around 0 57.3%

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

4. Final simplification 57.3%

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

Reproduce

herbie shell --seed 2024041 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))