exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 12.8s

Alternatives: 5

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 99.9%

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

   1. exp-neg 99.9%

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

   2. associate-*l/ 99.9%

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

   3. *-lft-identity 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 97.6% 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 99.9%

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

   1. exp-neg 99.9%

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

   2. associate-*l/ 99.9%

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

   3. *-lft-identity 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in w around 0 98.9%

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

6. Final simplification 98.9%

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

Alternative 3: 76.9% accurate, 20.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -5:\\ \;\;\;\;\frac{\ell \cdot \left(\ell + 2\right)}{\ell + 2}\\ \mathbf{elif}\;w \leq 0.055:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;\left(\ell + 1\right) + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w -5.0)
   (/ (* l (+ l 2.0)) (+ l 2.0))
   (if (<= w 0.055) l (+ (+ l 1.0) -1.0))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -5.0) {
		tmp = (l * (l + 2.0)) / (l + 2.0);
	} else if (w <= 0.055) {
		tmp = l;
	} else {
		tmp = (l + 1.0) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-5.0d0)) then
        tmp = (l * (l + 2.0d0)) / (l + 2.0d0)
    else if (w <= 0.055d0) then
        tmp = l
    else
        tmp = (l + 1.0d0) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -5.0) {
		tmp = (l * (l + 2.0)) / (l + 2.0);
	} else if (w <= 0.055) {
		tmp = l;
	} else {
		tmp = (l + 1.0) + -1.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -5.0:
		tmp = (l * (l + 2.0)) / (l + 2.0)
	elif w <= 0.055:
		tmp = l
	else:
		tmp = (l + 1.0) + -1.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -5.0)
		tmp = Float64(Float64(l * Float64(l + 2.0)) / Float64(l + 2.0));
	elseif (w <= 0.055)
		tmp = l;
	else
		tmp = Float64(Float64(l + 1.0) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -5.0)
		tmp = (l * (l + 2.0)) / (l + 2.0);
	elseif (w <= 0.055)
		tmp = l;
	else
		tmp = (l + 1.0) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -5.0], N[(N[(l * N[(l + 2.0), $MachinePrecision]), $MachinePrecision] / N[(l + 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[w, 0.055], l, N[(N[(l + 1.0), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if w < -5

   1. Initial program 100.0%

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

      1. exp-neg 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 100.0%

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

      2. pow3 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in w around 0 3.9%

      \[\leadsto {\color{blue}{\left({\ell}^{0.3333333333333333}\right)}}^{3} \]
   8. Step-by-step derivation

      1. unpow1/3 3.9%

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

      2. rem-cube-cbrt 3.9%

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

      3. expm1-log1p-u 3.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\ell\right)\right)} \]

   9. Applied egg-rr 3.9%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\ell\right)\right)} \]
   10. Step-by-step derivation

       1. expm1-udef 3.6%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\ell\right)} - 1} \]

       2. flip-- 28.5%

          \[\leadsto \color{blue}{\frac{e^{\mathsf{log1p}\left(\ell\right)} \cdot e^{\mathsf{log1p}\left(\ell\right)} - 1 \cdot 1}{e^{\mathsf{log1p}\left(\ell\right)} + 1}} \]

       3. log1p-udef 28.5%

          \[\leadsto \frac{e^{\color{blue}{\log \left(1 + \ell\right)}} \cdot e^{\mathsf{log1p}\left(\ell\right)} - 1 \cdot 1}{e^{\mathsf{log1p}\left(\ell\right)} + 1} \]

       4. rem-exp-log 28.5%

          \[\leadsto \frac{\color{blue}{\left(1 + \ell\right)} \cdot e^{\mathsf{log1p}\left(\ell\right)} - 1 \cdot 1}{e^{\mathsf{log1p}\left(\ell\right)} + 1} \]

       5. +-commutative 28.5%

          \[\leadsto \frac{\color{blue}{\left(\ell + 1\right)} \cdot e^{\mathsf{log1p}\left(\ell\right)} - 1 \cdot 1}{e^{\mathsf{log1p}\left(\ell\right)} + 1} \]

       6. log1p-udef 28.5%

          \[\leadsto \frac{\left(\ell + 1\right) \cdot e^{\color{blue}{\log \left(1 + \ell\right)}} - 1 \cdot 1}{e^{\mathsf{log1p}\left(\ell\right)} + 1} \]

       7. rem-exp-log 28.5%

          \[\leadsto \frac{\left(\ell + 1\right) \cdot \color{blue}{\left(1 + \ell\right)} - 1 \cdot 1}{e^{\mathsf{log1p}\left(\ell\right)} + 1} \]

       8. +-commutative 28.5%

          \[\leadsto \frac{\left(\ell + 1\right) \cdot \color{blue}{\left(\ell + 1\right)} - 1 \cdot 1}{e^{\mathsf{log1p}\left(\ell\right)} + 1} \]

       9. metadata-eval 28.5%

          \[\leadsto \frac{\left(\ell + 1\right) \cdot \left(\ell + 1\right) - \color{blue}{1}}{e^{\mathsf{log1p}\left(\ell\right)} + 1} \]

       10. log1p-udef 28.5%

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

       11. rem-exp-log 28.5%

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

       12. +-commutative 28.5%

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

   11. Applied egg-rr 28.5%

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

       1. difference-of-sqr-1 28.5%

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

       2. associate-+l+ 28.5%

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

       3. metadata-eval 28.5%

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

       4. associate--l+ 28.8%

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

       5. metadata-eval 28.8%

          \[\leadsto \frac{\left(\ell + 2\right) \cdot \left(\ell + \color{blue}{0}\right)}{\left(\ell + 1\right) + 1} \]

       6. associate-+l+ 28.8%

          \[\leadsto \frac{\left(\ell + 2\right) \cdot \left(\ell + 0\right)}{\color{blue}{\ell + \left(1 + 1\right)}} \]

       7. metadata-eval 28.8%

          \[\leadsto \frac{\left(\ell + 2\right) \cdot \left(\ell + 0\right)}{\ell + \color{blue}{2}} \]

   13. Simplified 28.8%

       \[\leadsto \color{blue}{\frac{\left(\ell + 2\right) \cdot \left(\ell + 0\right)}{\ell + 2}} \]

   if -5 < w < 0.0550000000000000003

   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. add-cube-cbrt 97.7%

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

      2. pow3 97.8%

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

      3. add-sqr-sqrt 97.2%

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

      4. unpow-prod-down 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in w around 0 98.6%

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

   if 0.0550000000000000003 < w

   1. Initial program 100.0%

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

      1. exp-neg 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 100.0%

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

      2. pow3 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in w around 0 6.0%

      \[\leadsto {\color{blue}{\left({\ell}^{0.3333333333333333}\right)}}^{3} \]
   8. Step-by-step derivation

      1. unpow1/3 6.0%

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

      2. rem-cube-cbrt 6.0%

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

      3. expm1-log1p-u 6.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\ell\right)\right)} \]

   9. Applied egg-rr 6.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\ell\right)\right)} \]
   10. Step-by-step derivation

       1. expm1-udef 87.5%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\ell\right)} - 1} \]

       2. log1p-udef 87.5%

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

       3. rem-exp-log 87.5%

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

       4. +-commutative 87.5%

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

   11. Applied egg-rr 87.5%

       \[\leadsto \color{blue}{\left(\ell + 1\right) - 1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -5:\\ \;\;\;\;\frac{\ell \cdot \left(\ell + 2\right)}{\ell + 2}\\ \mathbf{elif}\;w \leq 0.055:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;\left(\ell + 1\right) + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.2% accurate, 30.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.053:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;\left(\ell + 1\right) + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w 0.053) l (+ (+ l 1.0) -1.0)))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.053) {
		tmp = l;
	} else {
		tmp = (l + 1.0) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 0.053d0) then
        tmp = l
    else
        tmp = (l + 1.0d0) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.053) {
		tmp = l;
	} else {
		tmp = (l + 1.0) + -1.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.053:
		tmp = l
	else:
		tmp = (l + 1.0) + -1.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.053)
		tmp = l;
	else
		tmp = Float64(Float64(l + 1.0) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.053)
		tmp = l;
	else
		tmp = (l + 1.0) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.053], l, N[(N[(l + 1.0), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 0.0529999999999999985

   1. Initial program 99.8%

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

      1. exp-neg 99.8%

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

      2. associate-*l/ 99.8%

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

      3. *-lft-identity 99.8%

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

   3. Simplified 99.8%

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

      1. add-cube-cbrt 98.6%

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

      2. pow3 98.6%

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

      3. add-sqr-sqrt 98.3%

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

      4. unpow-prod-down 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in w around 0 62.4%

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

   if 0.0529999999999999985 < w

   1. Initial program 100.0%

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

      1. exp-neg 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 100.0%

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

      2. pow3 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in w around 0 6.0%

      \[\leadsto {\color{blue}{\left({\ell}^{0.3333333333333333}\right)}}^{3} \]
   8. Step-by-step derivation

      1. unpow1/3 6.0%

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

      2. rem-cube-cbrt 6.0%

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

      3. expm1-log1p-u 6.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\ell\right)\right)} \]

   9. Applied egg-rr 6.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\ell\right)\right)} \]
   10. Step-by-step derivation

       1. expm1-udef 87.5%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\ell\right)} - 1} \]

       2. log1p-udef 87.5%

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

       3. rem-exp-log 87.5%

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

       4. +-commutative 87.5%

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

   11. Applied egg-rr 87.5%

       \[\leadsto \color{blue}{\left(\ell + 1\right) - 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 0.053:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;\left(\ell + 1\right) + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.5% 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 99.9%

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

   1. exp-neg 99.9%

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

   2. associate-*l/ 99.9%

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

   3. *-lft-identity 99.9%

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

3. Simplified 99.9%

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

   1. add-cube-cbrt 98.8%

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

   2. pow3 98.8%

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

   3. add-sqr-sqrt 98.5%

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

   4. unpow-prod-down 98.6%

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

6. Applied egg-rr 98.6%

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

7. Taylor expanded in w around 0 55.5%

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

8. Final simplification 55.5%

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

Reproduce

herbie shell --seed 2024027 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))