exp-w (used to crash)

Percentage Accurate: 99.3% → 99.3%

Time: 13.8s

Alternatives: 8

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: 99.3% 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: 99.3% 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 99.7%

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

   1. exp-neg 99.7%

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

   2. remove-double-neg 99.7%

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

   3. associate-*l/ 99.7%

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

   4. *-lft-identity 99.7%

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

   5. remove-double-neg 99.7%

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

3. Simplified 99.7%

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

Alternative 2: 97.6% accurate, 2.9× speedup

Math

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

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(Float64(-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 99.7%

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

3. Taylor expanded in w around 0 98.1%

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

4. Final simplification 98.1%

   \[\leadsto \ell \cdot e^{-w} \]
5. Add Preprocessing

Alternative 3: 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 99.7%

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

   1. exp-neg 99.7%

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

   2. remove-double-neg 99.7%

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

   3. associate-*l/ 99.7%

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

   4. *-lft-identity 99.7%

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

   5. remove-double-neg 99.7%

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

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 98.1%

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

Alternative 4: 84.5% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.9:\\ \;\;\;\;\ell + \ell \cdot \left(w \cdot \left(w \cdot \left(0.5 + w \cdot -0.16666666666666666\right) + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;w \cdot \frac{\ell}{w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 0.9)
   (+ l (* l (* w (+ (* w (+ 0.5 (* w -0.16666666666666666))) -1.0))))
   (* w (/ l w))))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.9) {
		tmp = l + (l * (w * ((w * (0.5 + (w * -0.16666666666666666))) + -1.0)));
	} else {
		tmp = w * (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 <= 0.9d0) then
        tmp = l + (l * (w * ((w * (0.5d0 + (w * (-0.16666666666666666d0)))) + (-1.0d0))))
    else
        tmp = w * (l / w)
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.9) {
		tmp = l + (l * (w * ((w * (0.5 + (w * -0.16666666666666666))) + -1.0)));
	} else {
		tmp = w * (l / w);
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.9:
		tmp = l + (l * (w * ((w * (0.5 + (w * -0.16666666666666666))) + -1.0)))
	else:
		tmp = w * (l / w)
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.9)
		tmp = Float64(l + Float64(l * Float64(w * Float64(Float64(w * Float64(0.5 + Float64(w * -0.16666666666666666))) + -1.0))));
	else
		tmp = Float64(w * Float64(l / w));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.9)
		tmp = l + (l * (w * ((w * (0.5 + (w * -0.16666666666666666))) + -1.0)));
	else
		tmp = w * (l / w);
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.9], N[(l + N[(l * N[(w * N[(N[(w * N[(0.5 + N[(w * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(w * N[(l / w), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 0.900000000000000022

   1. Initial program 99.6%

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

   3. Taylor expanded in w around 0 98.2%

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

   4. Taylor expanded in w around 0 91.2%

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

   5. Taylor expanded in l around 0 93.3%

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

   if 0.900000000000000022 < w

   1. Initial program 100.0%

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

   3. Taylor expanded in w around 0 3.5%

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

      1. neg-mul-1 3.5%

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

      2. +-commutative 3.5%

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

      3. sub-neg 3.5%

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

   5. Simplified 3.5%

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

   6. Taylor expanded in w around inf 3.5%

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

   7. Taylor expanded in w around 0 43.5%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 0.9:\\ \;\;\;\;\ell + \ell \cdot \left(w \cdot \left(w \cdot \left(0.5 + w \cdot -0.16666666666666666\right) + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;w \cdot \frac{\ell}{w}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.3% accurate, 19.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 11500:\\ \;\;\;\;\ell + \ell \cdot \left(w \cdot \left(w \cdot 0.5 + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;w \cdot \frac{\ell}{w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 11500.0) (+ l (* l (* w (+ (* w 0.5) -1.0)))) (* w (/ l w))))

C

double code(double w, double l) {
	double tmp;
	if (w <= 11500.0) {
		tmp = l + (l * (w * ((w * 0.5) + -1.0)));
	} else {
		tmp = w * (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 <= 11500.0d0) then
        tmp = l + (l * (w * ((w * 0.5d0) + (-1.0d0))))
    else
        tmp = w * (l / w)
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 11500.0) {
		tmp = l + (l * (w * ((w * 0.5) + -1.0)));
	} else {
		tmp = w * (l / w);
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 11500.0:
		tmp = l + (l * (w * ((w * 0.5) + -1.0)))
	else:
		tmp = w * (l / w)
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 11500.0)
		tmp = Float64(l + Float64(l * Float64(w * Float64(Float64(w * 0.5) + -1.0))));
	else
		tmp = Float64(w * Float64(l / w));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 11500.0)
		tmp = l + (l * (w * ((w * 0.5) + -1.0)));
	else
		tmp = w * (l / w);
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 11500.0], N[(l + N[(l * N[(w * N[(N[(w * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(w * N[(l / w), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 11500

   1. Initial program 99.6%

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

   3. Taylor expanded in w around 0 97.8%

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

   4. Taylor expanded in w around 0 90.8%

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

   5. Taylor expanded in l around 0 92.9%

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

   6. Taylor expanded in w around 0 88.2%

      \[\leadsto \ell + \ell \cdot \left(w \cdot \left(\color{blue}{0.5 \cdot w} - 1\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 88.2%

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

   8. Simplified 88.2%

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

   if 11500 < w

   1. Initial program 100.0%

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

   3. Taylor expanded in w around 0 3.4%

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

      1. neg-mul-1 3.4%

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

      2. +-commutative 3.4%

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

      3. sub-neg 3.4%

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

   5. Simplified 3.4%

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

   6. Taylor expanded in w around inf 3.4%

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

   7. Taylor expanded in w around 0 44.5%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 11500:\\ \;\;\;\;\ell + \ell \cdot \left(w \cdot \left(w \cdot 0.5 + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;w \cdot \frac{\ell}{w}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.1% accurate, 30.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if w < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in w around 0 98.2%

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

   4. Taylor expanded in w around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

   6. Simplified 76.2%

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

   if 1 < w

   1. Initial program 100.0%

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

   3. Taylor expanded in w around 0 3.5%

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

      1. neg-mul-1 3.5%

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

      2. +-commutative 3.5%

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

      3. sub-neg 3.5%

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

   5. Simplified 3.5%

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

   6. Taylor expanded in w around inf 3.5%

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

   7. Taylor expanded in w around 0 43.5%

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

Alternative 7: 63.5% accurate, 30.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 10^{-16}:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;w \cdot \frac{\ell}{w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w 1e-16) l (* w (/ l w))))

C

double code(double w, double l) {
	double tmp;
	if (w <= 1e-16) {
		tmp = l;
	} else {
		tmp = w * (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 <= 1d-16) then
        tmp = l
    else
        tmp = w * (l / w)
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 1e-16) {
		tmp = l;
	} else {
		tmp = w * (l / w);
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 1e-16:
		tmp = l
	else:
		tmp = w * (l / w)
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 1e-16)
		tmp = l;
	else
		tmp = Float64(w * Float64(l / w));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 1e-16)
		tmp = l;
	else
		tmp = w * (l / w);
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 1e-16], l, N[(w * N[(l / w), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 9.9999999999999998e-17

   1. Initial program 99.8%

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

   3. Taylor expanded in w around 0 99.4%

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

   4. Taylor expanded in w around 0 67.3%

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

   if 9.9999999999999998e-17 < w

   1. Initial program 99.0%

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

   3. Taylor expanded in w around 0 7.5%

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

      1. neg-mul-1 7.5%

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

      2. +-commutative 7.5%

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

      3. sub-neg 7.5%

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

   5. Simplified 7.5%

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

   6. Taylor expanded in w around inf 7.5%

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

   7. Taylor expanded in w around 0 42.5%

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

Alternative 8: 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 99.7%

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

3. Taylor expanded in w around 0 98.1%

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

4. Taylor expanded in w around 0 57.4%

   \[\leadsto \color{blue}{\ell} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))