exp-w (used to crash)

Percentage Accurate: 99.3% → 99.3%

Time: 13.2s

Alternatives: 9

Speedup: 1.0×

• 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. 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. Final simplification 99.7%

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

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 99.7%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
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. Taylor expanded in w around 0 98.5%

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

5. Final simplification 98.5%

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

Alternative 3: 82.5% accurate, 23.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.029:\\ \;\;\;\;\ell - \ell \cdot \left(w + \left(w \cdot w\right) \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell}{\ell + \ell \cdot w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 0.029)
   (- l (* l (+ w (* (* w w) -0.5))))
   (/ (* l l) (+ l (* l w)))))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.029) {
		tmp = l - (l * (w + ((w * w) * -0.5)));
	} else {
		tmp = (l * l) / (l + (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 <= 0.029d0) then
        tmp = l - (l * (w + ((w * w) * (-0.5d0))))
    else
        tmp = (l * l) / (l + (l * w))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.029) {
		tmp = l - (l * (w + ((w * w) * -0.5)));
	} else {
		tmp = (l * l) / (l + (l * w));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.029:
		tmp = l - (l * (w + ((w * w) * -0.5)))
	else:
		tmp = (l * l) / (l + (l * w))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.029)
		tmp = Float64(l - Float64(l * Float64(w + Float64(Float64(w * w) * -0.5))));
	else
		tmp = Float64(Float64(l * l) / Float64(l + Float64(l * w)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.029)
		tmp = l - (l * (w + ((w * w) * -0.5)));
	else
		tmp = (l * l) / (l + (l * w));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.029], N[(l - N[(l * N[(w + N[(N[(w * w), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(l * l), $MachinePrecision] / N[(l + N[(l * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 0.0290000000000000015

   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. Taylor expanded in w around 0 98.7%

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

   5. Taylor expanded in w around 0 85.4%

      \[\leadsto \color{blue}{\ell + \left(-1 \cdot \left(\ell \cdot w\right) + -1 \cdot \left({w}^{2} \cdot \left(-1 \cdot \ell + 0.5 \cdot \ell\right)\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out 85.4%

         \[\leadsto \ell + \color{blue}{-1 \cdot \left(\ell \cdot w + {w}^{2} \cdot \left(-1 \cdot \ell + 0.5 \cdot \ell\right)\right)} \]

      2. unpow2 85.4%

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

      3. distribute-rgt-out 85.4%

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

      4. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in l around 0 85.4%

      \[\leadsto \ell + -1 \cdot \color{blue}{\left(\ell \cdot \left(w + -0.5 \cdot {w}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 85.4%

         \[\leadsto \ell + -1 \cdot \left(\ell \cdot \left(w + \color{blue}{{w}^{2} \cdot -0.5}\right)\right) \]

      2. unpow2 85.4%

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

   10. Simplified 85.4%

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

   if 0.0290000000000000015 < 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. Taylor expanded in w around 0 97.1%

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

   5. Taylor expanded in w around 0 3.7%

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

      1. mul-1-neg 3.7%

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

      2. unsub-neg 3.7%

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

   7. Simplified 3.7%

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

      1. sub-neg 3.7%

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

      2. flip-+ 21.3%

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

      3. distribute-rgt-neg-in 21.3%

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

      4. distribute-rgt-neg-in 21.3%

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

      5. distribute-rgt-neg-in 21.3%

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

   9. Applied egg-rr 21.3%

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

   10. Taylor expanded in w around 0 65.5%

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

       1. unpow2 65.5%

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

   12. Simplified 65.5%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 0.029:\\ \;\;\;\;\ell - \ell \cdot \left(w + \left(w \cdot w\right) \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell}{\ell + \ell \cdot w}\\ \end{array} \]

Alternative 4: 70.8% accurate, 27.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 1.2:\\ \;\;\;\;\ell \cdot \left(1 - w\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{\ell} + \frac{w}{\ell}}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 1.2) (* l (- 1.0 w)) (/ 1.0 (+ (/ 1.0 l) (/ w l)))))

C

double code(double w, double l) {
	double tmp;
	if (w <= 1.2) {
		tmp = l * (1.0 - w);
	} else {
		tmp = 1.0 / ((1.0 / l) + (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 <= 1.2d0) then
        tmp = l * (1.0d0 - w)
    else
        tmp = 1.0d0 / ((1.0d0 / l) + (w / l))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 1.2) {
		tmp = l * (1.0 - w);
	} else {
		tmp = 1.0 / ((1.0 / l) + (w / l));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 1.2:
		tmp = l * (1.0 - w)
	else:
		tmp = 1.0 / ((1.0 / l) + (w / l))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 1.2)
		tmp = Float64(l * Float64(1.0 - w));
	else
		tmp = Float64(1.0 / Float64(Float64(1.0 / l) + Float64(w / l)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 1.2)
		tmp = l * (1.0 - w);
	else
		tmp = 1.0 / ((1.0 / l) + (w / l));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 1.2], N[(l * N[(1.0 - w), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(1.0 / l), $MachinePrecision] + N[(w / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 1.19999999999999996

   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. Taylor expanded in w around 0 98.3%

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

   5. Taylor expanded in w around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. unsub-neg 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in l around 0 76.5%

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

   if 1.19999999999999996 < 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. Taylor expanded in w around 0 100.0%

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

      1. add-log-exp 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\log \left(e^{\frac{\ell}{e^{w}}}\right)} \]
   7. Step-by-step derivation

      1. add-log-exp 100.0%

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

      2. clear-num 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in w around 0 57.5%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 1.2:\\ \;\;\;\;\ell \cdot \left(1 - w\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{\ell} + \frac{w}{\ell}}\\ \end{array} \]

Alternative 5: 72.5% accurate, 27.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.052:\\ \;\;\;\;\ell \cdot \left(1 - w\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell}{\ell + \ell \cdot w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 0.052) (* l (- 1.0 w)) (/ (* l l) (+ l (* l w)))))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.052) {
		tmp = l * (1.0 - w);
	} else {
		tmp = (l * l) / (l + (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 <= 0.052d0) then
        tmp = l * (1.0d0 - w)
    else
        tmp = (l * l) / (l + (l * w))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.052) {
		tmp = l * (1.0 - w);
	} else {
		tmp = (l * l) / (l + (l * w));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.052:
		tmp = l * (1.0 - w)
	else:
		tmp = (l * l) / (l + (l * w))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.052)
		tmp = Float64(l * Float64(1.0 - w));
	else
		tmp = Float64(Float64(l * l) / Float64(l + Float64(l * w)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.052)
		tmp = l * (1.0 - w);
	else
		tmp = (l * l) / (l + (l * w));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.052], N[(l * N[(1.0 - w), $MachinePrecision]), $MachinePrecision], N[(N[(l * l), $MachinePrecision] / N[(l + N[(l * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 0.0519999999999999976

   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. Taylor expanded in w around 0 98.7%

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

   5. Taylor expanded in w around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

   7. Simplified 76.8%

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

   8. Taylor expanded in l around 0 76.8%

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

   if 0.0519999999999999976 < 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. Taylor expanded in w around 0 97.1%

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

   5. Taylor expanded in w around 0 3.7%

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

      1. mul-1-neg 3.7%

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

      2. unsub-neg 3.7%

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

   7. Simplified 3.7%

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

      1. sub-neg 3.7%

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

      2. flip-+ 21.3%

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

      3. distribute-rgt-neg-in 21.3%

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

      4. distribute-rgt-neg-in 21.3%

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

      5. distribute-rgt-neg-in 21.3%

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

   9. Applied egg-rr 21.3%

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

   10. Taylor expanded in w around 0 65.5%

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

       1. unpow2 65.5%

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

   12. Simplified 65.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 0.052:\\ \;\;\;\;\ell \cdot \left(1 - w\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell}{\ell + \ell \cdot w}\\ \end{array} \]

Alternative 6: 82.5% accurate, 27.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.0295:\\ \;\;\;\;\ell - \left(w \cdot w\right) \cdot \left(\ell \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell}{\ell + \ell \cdot w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 0.0295) (- l (* (* w w) (* l -0.5))) (/ (* l l) (+ l (* l w)))))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.0295) {
		tmp = l - ((w * w) * (l * -0.5));
	} else {
		tmp = (l * l) / (l + (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 <= 0.0295d0) then
        tmp = l - ((w * w) * (l * (-0.5d0)))
    else
        tmp = (l * l) / (l + (l * w))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.0295) {
		tmp = l - ((w * w) * (l * -0.5));
	} else {
		tmp = (l * l) / (l + (l * w));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.0295:
		tmp = l - ((w * w) * (l * -0.5))
	else:
		tmp = (l * l) / (l + (l * w))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.0295)
		tmp = Float64(l - Float64(Float64(w * w) * Float64(l * -0.5)));
	else
		tmp = Float64(Float64(l * l) / Float64(l + Float64(l * w)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.0295)
		tmp = l - ((w * w) * (l * -0.5));
	else
		tmp = (l * l) / (l + (l * w));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.0295], N[(l - N[(N[(w * w), $MachinePrecision] * N[(l * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(l * l), $MachinePrecision] / N[(l + N[(l * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 0.029499999999999998

   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. Taylor expanded in w around 0 98.7%

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

   5. Taylor expanded in w around 0 85.4%

      \[\leadsto \color{blue}{\ell + \left(-1 \cdot \left(\ell \cdot w\right) + -1 \cdot \left({w}^{2} \cdot \left(-1 \cdot \ell + 0.5 \cdot \ell\right)\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out 85.4%

         \[\leadsto \ell + \color{blue}{-1 \cdot \left(\ell \cdot w + {w}^{2} \cdot \left(-1 \cdot \ell + 0.5 \cdot \ell\right)\right)} \]

      2. unpow2 85.4%

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

      3. distribute-rgt-out 85.4%

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

      4. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in l around 0 85.4%

      \[\leadsto \ell + -1 \cdot \color{blue}{\left(\ell \cdot \left(w + -0.5 \cdot {w}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 85.4%

         \[\leadsto \ell + -1 \cdot \left(\ell \cdot \left(w + \color{blue}{{w}^{2} \cdot -0.5}\right)\right) \]

      2. unpow2 85.4%

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

   10. Simplified 85.4%

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

   11. Taylor expanded in w around inf 85.4%

       \[\leadsto \ell + -1 \cdot \color{blue}{\left(-0.5 \cdot \left(\ell \cdot {w}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. unpow2 85.4%

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

       2. associate-*r* 85.4%

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

       3. *-commutative 85.4%

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

   13. Simplified 85.4%

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

   if 0.029499999999999998 < 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. Taylor expanded in w around 0 97.1%

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

   5. Taylor expanded in w around 0 3.7%

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

      1. mul-1-neg 3.7%

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

      2. unsub-neg 3.7%

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

   7. Simplified 3.7%

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

      1. sub-neg 3.7%

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

      2. flip-+ 21.3%

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

      3. distribute-rgt-neg-in 21.3%

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

      4. distribute-rgt-neg-in 21.3%

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

      5. distribute-rgt-neg-in 21.3%

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

   9. Applied egg-rr 21.3%

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

   10. Taylor expanded in w around 0 65.5%

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

       1. unpow2 65.5%

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

   12. Simplified 65.5%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 0.0295:\\ \;\;\;\;\ell - \left(w \cdot w\right) \cdot \left(\ell \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \ell}{\ell + \ell \cdot w}\\ \end{array} \]

Alternative 7: 64.1% accurate, 50.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.027:\\ \;\;\;\;\ell \cdot \left(-w\right)\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w -0.027) (* l (- w)) l))

C

double code(double w, double l) {
	double tmp;
	if (w <= -0.027) {
		tmp = l * -w;
	} else {
		tmp = 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 <= (-0.027d0)) then
        tmp = l * -w
    else
        tmp = l
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -0.027) {
		tmp = l * -w;
	} else {
		tmp = l;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -0.027:
		tmp = l * -w
	else:
		tmp = l
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -0.027)
		tmp = Float64(l * Float64(-w));
	else
		tmp = l;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -0.027)
		tmp = l * -w;
	else
		tmp = l;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -0.027], N[(l * (-w)), $MachinePrecision], l]

Derivation

1. Split input into 2 regimes

2. if w < -0.0269999999999999997

   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. Taylor expanded in w around 0 100.0%

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

   5. Taylor expanded in w around 0 19.8%

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

      1. mul-1-neg 19.8%

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

      2. unsub-neg 19.8%

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

   7. Simplified 19.8%

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

   8. Taylor expanded in w around inf 19.8%

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

      1. mul-1-neg 19.8%

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

      2. *-commutative 19.8%

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

      3. distribute-rgt-neg-in 19.8%

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

   10. Simplified 19.8%

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

   if -0.0269999999999999997 < w

   1. Initial program 99.6%

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

      1. exp-neg 99.6%

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

      2. associate-*l/ 99.6%

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

      3. *-lft-identity 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in w around 0 98.0%

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

      1. add-log-exp 21.9%

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

   6. Applied egg-rr 21.9%

      \[\leadsto \color{blue}{\log \left(e^{\frac{\ell}{e^{w}}}\right)} \]
   7. Step-by-step derivation

      1. add-log-exp 98.0%

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

      2. clear-num 97.8%

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

   8. Applied egg-rr 97.8%

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

   9. Taylor expanded in w around 0 83.1%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -0.027:\\ \;\;\;\;\ell \cdot \left(-w\right)\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \]

Alternative 8: 63.8% accurate, 61.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(w, l):
	return l * (1.0 - w)

Julia

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

MATLAB

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

Wolfram

code[w_, l_] := N[(l * N[(1.0 - 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. 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. Taylor expanded in w around 0 98.5%

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

5. Taylor expanded in w around 0 67.7%

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

   1. mul-1-neg 67.7%

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

   2. unsub-neg 67.7%

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

7. Simplified 67.7%

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

8. Taylor expanded in l around 0 67.7%

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

9. Final simplification 67.7%

   \[\leadsto \ell \cdot \left(1 - w\right) \]

Alternative 9: 57.8% 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. 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. Taylor expanded in w around 0 98.5%

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

   1. add-log-exp 40.5%

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

6. Applied egg-rr 40.5%

   \[\leadsto \color{blue}{\log \left(e^{\frac{\ell}{e^{w}}}\right)} \]
7. Step-by-step derivation

   1. add-log-exp 98.5%

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

   2. clear-num 98.3%

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

8. Applied egg-rr 98.3%

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

9. Taylor expanded in w around 0 64.2%

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

10. Final simplification 64.2%

    \[\leadsto \ell \]

Reproduce

herbie shell --seed 2023272 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))