exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 20.1s

Alternatives: 13

Speedup: 1.0×

• Could not converge on a ground truth

  1. w = -1.1997762332086457e+163
  2. l = -2.4230111893584254e+144

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

\[\begin{array}{l} \\ e^{0 - w} \cdot {\ell}^{\left(e^{w}\right)} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (* (exp (- 0.0 w)) (pow l (exp w))))

C

double code(double w, double l) {
	return exp((0.0 - w)) * pow(l, exp(w));
}

Fortran

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

Java

public static double code(double w, double l) {
	return Math.exp((0.0 - w)) * Math.pow(l, Math.exp(w));
}

Python

def code(w, l):
	return math.exp((0.0 - w)) * math.pow(l, math.exp(w))

Julia

function code(w, l)
	return Float64(exp(Float64(0.0 - w)) * (l ^ exp(w)))
end

MATLAB

function tmp = code(w, l)
	tmp = exp((0.0 - w)) * (l ^ exp(w));
end

Wolfram

code[w_, l_] := N[(N[Exp[N[(0.0 - w), $MachinePrecision]], $MachinePrecision] * N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

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

3. Final simplification 99.7%

   \[\leadsto e^{0 - w} \cdot {\ell}^{\left(e^{w}\right)} \]
4. Add Preprocessing

Alternative 2: 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 99.7%

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

3. Taylor expanded in w around inf

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

   1. *-commutative N/A

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

   2. exp-to-pow N/A

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

   3. remove-double-neg N/A

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

   4. distribute-lft-neg-out N/A

      \[\leadsto e^{\mathsf{neg}\left(\left(\mathsf{neg}\left(\log \ell\right)\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

   5. log-rec N/A

      \[\leadsto e^{\mathsf{neg}\left(\log \left(\frac{1}{\ell}\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

   6. *-commutative N/A

      \[\leadsto e^{\mathsf{neg}\left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

   7. mul-1-neg N/A

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

   8. +-rgt-identity N/A

      \[\leadsto e^{-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0} \cdot e^{\mathsf{neg}\left(\color{blue}{w}\right)} \]

   9. exp-sum N/A

      \[\leadsto e^{\left(-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0\right) + \left(\mathsf{neg}\left(w\right)\right)} \]

   10. +-rgt-identity N/A

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

   11. unsub-neg N/A

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

   12. div-exp N/A

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

   13. /-lowering-/.f64 N/A

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

5. Simplified 99.7%

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

Alternative 3: 99.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -1.6:\\ \;\;\;\;\frac{\ell}{e^{w}}\\ \mathbf{else}:\\ \;\;\;\;{\ell}^{\left(e^{w}\right)} \cdot \frac{1}{1 + w \cdot \left(1 + w \cdot \left(0.5 + w \cdot 0.16666666666666666\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w -1.6)
   (/ l (exp w))
   (*
    (pow l (exp w))
    (/ 1.0 (+ 1.0 (* w (+ 1.0 (* w (+ 0.5 (* w 0.16666666666666666))))))))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -1.6) {
		tmp = l / exp(w);
	} else {
		tmp = pow(l, exp(w)) * (1.0 / (1.0 + (w * (1.0 + (w * (0.5 + (w * 0.16666666666666666)))))));
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-1.6d0)) then
        tmp = l / exp(w)
    else
        tmp = (l ** exp(w)) * (1.0d0 / (1.0d0 + (w * (1.0d0 + (w * (0.5d0 + (w * 0.16666666666666666d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -1.6) {
		tmp = l / Math.exp(w);
	} else {
		tmp = Math.pow(l, Math.exp(w)) * (1.0 / (1.0 + (w * (1.0 + (w * (0.5 + (w * 0.16666666666666666)))))));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -1.6:
		tmp = l / math.exp(w)
	else:
		tmp = math.pow(l, math.exp(w)) * (1.0 / (1.0 + (w * (1.0 + (w * (0.5 + (w * 0.16666666666666666)))))))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -1.6)
		tmp = Float64(l / exp(w));
	else
		tmp = Float64((l ^ exp(w)) * Float64(1.0 / Float64(1.0 + Float64(w * Float64(1.0 + Float64(w * Float64(0.5 + Float64(w * 0.16666666666666666))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -1.6)
		tmp = l / exp(w);
	else
		tmp = (l ^ exp(w)) * (1.0 / (1.0 + (w * (1.0 + (w * (0.5 + (w * 0.16666666666666666)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -1.6], N[(l / N[Exp[w], $MachinePrecision]), $MachinePrecision], N[(N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision] * N[(1.0 / N[(1.0 + N[(w * N[(1.0 + N[(w * N[(0.5 + N[(w * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < -1.6000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in w around inf

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

      1. *-commutative N/A

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

      2. exp-to-pow N/A

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

      3. remove-double-neg N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto e^{\mathsf{neg}\left(\left(\mathsf{neg}\left(\log \ell\right)\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      5. log-rec N/A

         \[\leadsto e^{\mathsf{neg}\left(\log \left(\frac{1}{\ell}\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      6. *-commutative N/A

         \[\leadsto e^{\mathsf{neg}\left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      7. mul-1-neg N/A

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

      8. +-rgt-identity N/A

         \[\leadsto e^{-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0} \cdot e^{\mathsf{neg}\left(\color{blue}{w}\right)} \]

      9. exp-sum N/A

         \[\leadsto e^{\left(-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0\right) + \left(\mathsf{neg}\left(w\right)\right)} \]

      10. +-rgt-identity N/A

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

      11. unsub-neg N/A

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

      12. div-exp N/A

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

      13. /-lowering-/.f64 N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in w around 0

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

   8. Simplified 100.0%

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

   if -1.6000000000000001 < w

   1. Initial program 99.6%

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

   3. Taylor expanded in w around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(e^{\mathsf{neg}\left(w\right)}\right)}, \mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right)\right) \]
   4. Step-by-step derivation

      1. exp-neg N/A

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

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

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

      3. exp-lowering-exp.f64 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in w around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \color{blue}{\left(1 + w \cdot \left(1 + w \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot w\right)\right)\right)}\right), \mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right)\right) \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 99.1%

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

   8. Simplified 99.1%

      \[\leadsto \frac{1}{\color{blue}{1 + w \cdot \left(1 + w \cdot \left(0.5 + w \cdot 0.16666666666666666\right)\right)}} \cdot {\ell}^{\left(e^{w}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -1.6:\\ \;\;\;\;\frac{\ell}{e^{w}}\\ \mathbf{else}:\\ \;\;\;\;{\ell}^{\left(e^{w}\right)} \cdot \frac{1}{1 + w \cdot \left(1 + w \cdot \left(0.5 + w \cdot 0.16666666666666666\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -1.6:\\ \;\;\;\;\frac{\ell}{e^{w}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\ell}^{\left(e^{w}\right)}}{1 + w \cdot \left(1 + w \cdot \left(0.5 + w \cdot 0.16666666666666666\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w -1.6)
   (/ l (exp w))
   (/
    (pow l (exp w))
    (+ 1.0 (* w (+ 1.0 (* w (+ 0.5 (* w 0.16666666666666666)))))))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -1.6) {
		tmp = l / exp(w);
	} else {
		tmp = pow(l, exp(w)) / (1.0 + (w * (1.0 + (w * (0.5 + (w * 0.16666666666666666))))));
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-1.6d0)) then
        tmp = l / exp(w)
    else
        tmp = (l ** exp(w)) / (1.0d0 + (w * (1.0d0 + (w * (0.5d0 + (w * 0.16666666666666666d0))))))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -1.6) {
		tmp = l / Math.exp(w);
	} else {
		tmp = Math.pow(l, Math.exp(w)) / (1.0 + (w * (1.0 + (w * (0.5 + (w * 0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -1.6:
		tmp = l / math.exp(w)
	else:
		tmp = math.pow(l, math.exp(w)) / (1.0 + (w * (1.0 + (w * (0.5 + (w * 0.16666666666666666))))))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -1.6)
		tmp = Float64(l / exp(w));
	else
		tmp = Float64((l ^ exp(w)) / Float64(1.0 + Float64(w * Float64(1.0 + Float64(w * Float64(0.5 + Float64(w * 0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -1.6)
		tmp = l / exp(w);
	else
		tmp = (l ^ exp(w)) / (1.0 + (w * (1.0 + (w * (0.5 + (w * 0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -1.6], N[(l / N[Exp[w], $MachinePrecision]), $MachinePrecision], N[(N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision] / N[(1.0 + N[(w * N[(1.0 + N[(w * N[(0.5 + N[(w * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < -1.6000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in w around inf

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

      1. *-commutative N/A

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

      2. exp-to-pow N/A

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

      3. remove-double-neg N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto e^{\mathsf{neg}\left(\left(\mathsf{neg}\left(\log \ell\right)\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      5. log-rec N/A

         \[\leadsto e^{\mathsf{neg}\left(\log \left(\frac{1}{\ell}\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      6. *-commutative N/A

         \[\leadsto e^{\mathsf{neg}\left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      7. mul-1-neg N/A

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

      8. +-rgt-identity N/A

         \[\leadsto e^{-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0} \cdot e^{\mathsf{neg}\left(\color{blue}{w}\right)} \]

      9. exp-sum N/A

         \[\leadsto e^{\left(-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0\right) + \left(\mathsf{neg}\left(w\right)\right)} \]

      10. +-rgt-identity N/A

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

      11. unsub-neg N/A

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

      12. div-exp N/A

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

      13. /-lowering-/.f64 N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in w around 0

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

   8. Simplified 100.0%

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

   if -1.6000000000000001 < w

   1. Initial program 99.6%

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

   3. Taylor expanded in w around inf

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

      1. *-commutative N/A

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

      2. exp-to-pow N/A

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

      3. remove-double-neg N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto e^{\mathsf{neg}\left(\left(\mathsf{neg}\left(\log \ell\right)\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      5. log-rec N/A

         \[\leadsto e^{\mathsf{neg}\left(\log \left(\frac{1}{\ell}\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      6. *-commutative N/A

         \[\leadsto e^{\mathsf{neg}\left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      7. mul-1-neg N/A

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

      8. +-rgt-identity N/A

         \[\leadsto e^{-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0} \cdot e^{\mathsf{neg}\left(\color{blue}{w}\right)} \]

      9. exp-sum N/A

         \[\leadsto e^{\left(-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0\right) + \left(\mathsf{neg}\left(w\right)\right)} \]

      10. +-rgt-identity N/A

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

      11. unsub-neg N/A

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

      12. div-exp N/A

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

      13. /-lowering-/.f64 N/A

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

   5. Simplified 99.6%

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

   6. Taylor expanded in w around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right), \color{blue}{\left(1 + w \cdot \left(1 + w \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot w\right)\right)\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 99.1%

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

   8. Simplified 99.1%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\color{blue}{1 + w \cdot \left(1 + w \cdot \left(0.5 + w \cdot 0.16666666666666666\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 97.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ e^{0 - w} \cdot \ell \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (* (exp (- 0.0 w)) l))

C

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

Fortran

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

Java

public static double code(double w, double l) {
	return Math.exp((0.0 - w)) * l;
}

Python

def code(w, l):
	return math.exp((0.0 - w)) * l

Julia

function code(w, l)
	return Float64(exp(Float64(0.0 - w)) * l)
end

MATLAB

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

Wolfram

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

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

5. Simplified 97.7%

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

6. Final simplification 97.7%

   \[\leadsto e^{0 - w} \cdot \ell \]
7. Add Preprocessing

Alternative 6: 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. Add Preprocessing

3. Taylor expanded in w around inf

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

   1. *-commutative N/A

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

   2. exp-to-pow N/A

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

   3. remove-double-neg N/A

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

   4. distribute-lft-neg-out N/A

      \[\leadsto e^{\mathsf{neg}\left(\left(\mathsf{neg}\left(\log \ell\right)\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

   5. log-rec N/A

      \[\leadsto e^{\mathsf{neg}\left(\log \left(\frac{1}{\ell}\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

   6. *-commutative N/A

      \[\leadsto e^{\mathsf{neg}\left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

   7. mul-1-neg N/A

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

   8. +-rgt-identity N/A

      \[\leadsto e^{-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0} \cdot e^{\mathsf{neg}\left(\color{blue}{w}\right)} \]

   9. exp-sum N/A

      \[\leadsto e^{\left(-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0\right) + \left(\mathsf{neg}\left(w\right)\right)} \]

   10. +-rgt-identity N/A

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

   11. unsub-neg N/A

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

   12. div-exp N/A

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

   13. /-lowering-/.f64 N/A

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

5. Simplified 99.7%

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

6. Taylor expanded in w around 0

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

8. Simplified 97.7%

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

Alternative 7: 88.6% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.74:\\ \;\;\;\;\ell + w \cdot \left(w \cdot \left(\ell \cdot 0.5 - w \cdot \left(\ell \cdot 0.16666666666666666\right)\right) - \ell\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 0.74)
   (+ l (* w (- (* w (- (* l 0.5) (* w (* l 0.16666666666666666)))) l)))
   0.0))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.74) {
		tmp = l + (w * ((w * ((l * 0.5) - (w * (l * 0.16666666666666666)))) - l));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 0.74d0) then
        tmp = l + (w * ((w * ((l * 0.5d0) - (w * (l * 0.16666666666666666d0)))) - l))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.74) {
		tmp = l + (w * ((w * ((l * 0.5) - (w * (l * 0.16666666666666666)))) - l));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.74:
		tmp = l + (w * ((w * ((l * 0.5) - (w * (l * 0.16666666666666666)))) - l))
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.74)
		tmp = Float64(l + Float64(w * Float64(Float64(w * Float64(Float64(l * 0.5) - Float64(w * Float64(l * 0.16666666666666666)))) - l)));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.74)
		tmp = l + (w * ((w * ((l * 0.5) - (w * (l * 0.16666666666666666)))) - l));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.74], N[(l + N[(w * N[(N[(w * N[(N[(l * 0.5), $MachinePrecision] - N[(w * N[(l * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if w < 0.73999999999999999

   1. Initial program 99.6%

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

   3. Taylor expanded in w around inf

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

      1. *-commutative N/A

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

      2. exp-to-pow N/A

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

      3. remove-double-neg N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto e^{\mathsf{neg}\left(\left(\mathsf{neg}\left(\log \ell\right)\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      5. log-rec N/A

         \[\leadsto e^{\mathsf{neg}\left(\log \left(\frac{1}{\ell}\right) \cdot e^{w}\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      6. *-commutative N/A

         \[\leadsto e^{\mathsf{neg}\left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right)} \cdot e^{\mathsf{neg}\left(w\right)} \]

      7. mul-1-neg N/A

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

      8. +-rgt-identity N/A

         \[\leadsto e^{-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0} \cdot e^{\mathsf{neg}\left(\color{blue}{w}\right)} \]

      9. exp-sum N/A

         \[\leadsto e^{\left(-1 \cdot \left(e^{w} \cdot \log \left(\frac{1}{\ell}\right)\right) + 0\right) + \left(\mathsf{neg}\left(w\right)\right)} \]

      10. +-rgt-identity N/A

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

      11. unsub-neg N/A

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

      12. div-exp N/A

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

      13. /-lowering-/.f64 N/A

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

   5. Simplified 99.6%

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

   6. Taylor expanded in w around 0

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

   8. Simplified 97.7%

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

   9. Taylor expanded in w around 0

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

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

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

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

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

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

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

   11. Simplified 88.2%

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

   if 0.73999999999999999 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. sqr-pow N/A

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

      3. pow-prod-up N/A

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

      4. flip-+ N/A

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

      5. +-inverses N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      6. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 - 0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      7. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{\color{blue}{e^{w}}}{2} - \frac{e^{w}}{2}}\right)} \]

      8. mul0-lft N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      9. *-commutative N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - w \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      11. mul0-lft N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      12. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      13. +-inverses N/A

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

      14. metadata-eval N/A

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

      15. flip-- N/A

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

      16. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{0} \]

      17. metadata-eval N/A

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

      18. associate-/r/ N/A

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

      19. div-inv N/A

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

      20. metadata-eval N/A

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

      21. metadata-eval N/A

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

      22. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w} \cdot \left(\frac{1}{2} + \frac{1}{2}\right)} \]

      23. metadata-eval N/A

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

   4. Applied egg-rr 97.3%

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

Alternative 8: 87.3% accurate, 19.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 245:\\ \;\;\;\;\ell \cdot \left(1 + w \cdot \left(-1 + w \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 245.0) (* l (+ 1.0 (* w (+ -1.0 (* w 0.5))))) 0.0))

C

double code(double w, double l) {
	double tmp;
	if (w <= 245.0) {
		tmp = l * (1.0 + (w * (-1.0 + (w * 0.5))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 245.0d0) then
        tmp = l * (1.0d0 + (w * ((-1.0d0) + (w * 0.5d0))))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 245.0) {
		tmp = l * (1.0 + (w * (-1.0 + (w * 0.5))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 245.0:
		tmp = l * (1.0 + (w * (-1.0 + (w * 0.5))))
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 245.0)
		tmp = Float64(l * Float64(1.0 + Float64(w * Float64(-1.0 + Float64(w * 0.5)))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 245.0)
		tmp = l * (1.0 + (w * (-1.0 + (w * 0.5))));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 245.0], N[(l * N[(1.0 + N[(w * N[(-1.0 + N[(w * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if w < 245

   1. Initial program 99.6%

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

   3. Taylor expanded in w around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(1 + w \cdot \left(\frac{1}{2} \cdot w - 1\right)\right)}, \mathsf{pow.f64}\left(\ell, \mathsf{exp.f64}\left(w\right)\right)\right) \]
   4. Step-by-step derivation

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in w around 0

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

   8. Simplified 86.5%

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

   if 245 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. sqr-pow N/A

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

      3. pow-prod-up N/A

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

      4. flip-+ N/A

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

      5. +-inverses N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      6. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 - 0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      7. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{\color{blue}{e^{w}}}{2} - \frac{e^{w}}{2}}\right)} \]

      8. mul0-lft N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      9. *-commutative N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - w \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      11. mul0-lft N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      12. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      13. +-inverses N/A

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

      14. metadata-eval N/A

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

      15. flip-- N/A

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

      16. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{0} \]

      17. metadata-eval N/A

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

      18. associate-/r/ N/A

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

      19. div-inv N/A

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

      20. metadata-eval N/A

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

      21. metadata-eval N/A

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

      22. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w} \cdot \left(\frac{1}{2} + \frac{1}{2}\right)} \]

      23. metadata-eval N/A

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

   4. Applied egg-rr 100.0%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 245:\\ \;\;\;\;\ell \cdot \left(1 + w \cdot \left(-1 + w \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.4% accurate, 21.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.74:\\ \;\;\;\;\ell \cdot \frac{1}{\frac{1}{1 - w}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 0.74) (* l (/ 1.0 (/ 1.0 (- 1.0 w)))) 0.0))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.74) {
		tmp = l * (1.0 / (1.0 / (1.0 - w)));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 0.74d0) then
        tmp = l * (1.0d0 / (1.0d0 / (1.0d0 - w)))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.74) {
		tmp = l * (1.0 / (1.0 / (1.0 - w)));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.74:
		tmp = l * (1.0 / (1.0 / (1.0 - w)))
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.74)
		tmp = Float64(l * Float64(1.0 / Float64(1.0 / Float64(1.0 - w))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.74)
		tmp = l * (1.0 / (1.0 / (1.0 - w)));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.74], N[(l * N[(1.0 / N[(1.0 / N[(1.0 - w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if w < 0.73999999999999999

   1. Initial program 99.6%

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

   3. Taylor expanded in w around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{exp.f64}\left(\mathsf{neg.f64}\left(w\right)\right), \color{blue}{\left(\ell + w \cdot \left(\ell \cdot \log \ell + \ell \cdot \left(w \cdot \left(\frac{1}{2} \cdot \log \ell + \frac{1}{2} \cdot {\log \ell}^{2}\right)\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt1-in N/A

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

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

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

   5. Simplified 98.8%

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

   6. Taylor expanded in w around 0

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

      1. neg-mul-1 N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 90.1%

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

   8. Simplified 90.1%

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

   9. Taylor expanded in w around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, w\right), \color{blue}{\ell}\right) \]
   10. Step-by-step derivation

   11. Simplified 73.3%

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

       1. flip3-- N/A

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

       2. clear-num N/A

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

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

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

       4. clear-num N/A

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

       5. flip3-- N/A

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

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

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

       7. --lowering--.f64 73.3%

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

   13. Applied egg-rr 73.3%

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

   if 0.73999999999999999 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. sqr-pow N/A

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

      3. pow-prod-up N/A

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

      4. flip-+ N/A

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

      5. +-inverses N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      6. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 - 0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      7. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{\color{blue}{e^{w}}}{2} - \frac{e^{w}}{2}}\right)} \]

      8. mul0-lft N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      9. *-commutative N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - w \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      11. mul0-lft N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      12. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      13. +-inverses N/A

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

      14. metadata-eval N/A

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

      15. flip-- N/A

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

      16. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{0} \]

      17. metadata-eval N/A

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

      18. associate-/r/ N/A

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

      19. div-inv N/A

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

      20. metadata-eval N/A

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

      21. metadata-eval N/A

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

      22. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w} \cdot \left(\frac{1}{2} + \frac{1}{2}\right)} \]

      23. metadata-eval N/A

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

   4. Applied egg-rr 97.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 0.74:\\ \;\;\;\;\ell \cdot \frac{1}{\frac{1}{1 - w}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.4% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.74:\\ \;\;\;\;\frac{\ell}{\frac{1}{1 - w}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w 0.74) (/ l (/ 1.0 (- 1.0 w))) 0.0))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.74) {
		tmp = l / (1.0 / (1.0 - w));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 0.74d0) then
        tmp = l / (1.0d0 / (1.0d0 - w))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.74) {
		tmp = l / (1.0 / (1.0 - w));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.74:
		tmp = l / (1.0 / (1.0 - w))
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.74)
		tmp = Float64(l / Float64(1.0 / Float64(1.0 - w)));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.74)
		tmp = l / (1.0 / (1.0 - w));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.74], N[(l / N[(1.0 / N[(1.0 - w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if w < 0.73999999999999999

   1. Initial program 99.6%

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

   3. Taylor expanded in w around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{exp.f64}\left(\mathsf{neg.f64}\left(w\right)\right), \color{blue}{\left(\ell + w \cdot \left(\ell \cdot \log \ell + \ell \cdot \left(w \cdot \left(\frac{1}{2} \cdot \log \ell + \frac{1}{2} \cdot {\log \ell}^{2}\right)\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt1-in N/A

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

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

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

   5. Simplified 98.8%

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

   6. Taylor expanded in w around 0

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

      1. neg-mul-1 N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 90.1%

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

   8. Simplified 90.1%

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

   9. Taylor expanded in w around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, w\right), \color{blue}{\ell}\right) \]
   10. Step-by-step derivation

   11. Simplified 73.3%

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

       1. *-commutative N/A

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

       2. flip3-- N/A

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

       3. clear-num N/A

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

       4. un-div-inv N/A

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

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

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

       6. clear-num N/A

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

       7. flip3-- N/A

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

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

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

       9. --lowering--.f64 73.3%

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

   13. Applied egg-rr 73.3%

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

   if 0.73999999999999999 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. sqr-pow N/A

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

      3. pow-prod-up N/A

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

      4. flip-+ N/A

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

      5. +-inverses N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      6. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 - 0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      7. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{\color{blue}{e^{w}}}{2} - \frac{e^{w}}{2}}\right)} \]

      8. mul0-lft N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      9. *-commutative N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - w \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      11. mul0-lft N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      12. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      13. +-inverses N/A

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

      14. metadata-eval N/A

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

      15. flip-- N/A

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

      16. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{0} \]

      17. metadata-eval N/A

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

      18. associate-/r/ N/A

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

      19. div-inv N/A

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

      20. metadata-eval N/A

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

      21. metadata-eval N/A

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

      22. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w} \cdot \left(\frac{1}{2} + \frac{1}{2}\right)} \]

      23. metadata-eval N/A

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

   4. Applied egg-rr 97.3%

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

Alternative 11: 77.4% accurate, 30.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 0.74:\\ \;\;\;\;\ell \cdot \left(1 - w\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w 0.74) (* l (- 1.0 w)) 0.0))

C

double code(double w, double l) {
	double tmp;
	if (w <= 0.74) {
		tmp = l * (1.0 - w);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 0.74d0) then
        tmp = l * (1.0d0 - w)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 0.74) {
		tmp = l * (1.0 - w);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 0.74:
		tmp = l * (1.0 - w)
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 0.74)
		tmp = Float64(l * Float64(1.0 - w));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 0.74)
		tmp = l * (1.0 - w);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 0.74], N[(l * N[(1.0 - w), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if w < 0.73999999999999999

   1. Initial program 99.6%

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

   3. Taylor expanded in w around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{exp.f64}\left(\mathsf{neg.f64}\left(w\right)\right), \color{blue}{\left(\ell + w \cdot \left(\ell \cdot \log \ell + \ell \cdot \left(w \cdot \left(\frac{1}{2} \cdot \log \ell + \frac{1}{2} \cdot {\log \ell}^{2}\right)\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt1-in N/A

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

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

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

   5. Simplified 98.8%

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

   6. Taylor expanded in w around 0

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

      1. neg-mul-1 N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 90.1%

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

   8. Simplified 90.1%

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

   9. Taylor expanded in w around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, w\right), \color{blue}{\ell}\right) \]
   10. Step-by-step derivation

   11. Simplified 73.3%

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

   if 0.73999999999999999 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. sqr-pow N/A

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

      3. pow-prod-up N/A

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

      4. flip-+ N/A

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

      5. +-inverses N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      6. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 - 0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      7. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{\color{blue}{e^{w}}}{2} - \frac{e^{w}}{2}}\right)} \]

      8. mul0-lft N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      9. *-commutative N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - w \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      11. mul0-lft N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      12. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      13. +-inverses N/A

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

      14. metadata-eval N/A

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

      15. flip-- N/A

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

      16. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{0} \]

      17. metadata-eval N/A

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

      18. associate-/r/ N/A

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

      19. div-inv N/A

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

      20. metadata-eval N/A

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

      21. metadata-eval N/A

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

      22. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w} \cdot \left(\frac{1}{2} + \frac{1}{2}\right)} \]

      23. metadata-eval N/A

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

   4. Applied egg-rr 97.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 0.74:\\ \;\;\;\;\ell \cdot \left(1 - w\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.5% accurate, 50.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 245:\\ \;\;\;\;\ell\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w 245.0) l 0.0))

C

double code(double w, double l) {
	double tmp;
	if (w <= 245.0) {
		tmp = l;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 245.0d0) then
        tmp = l
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 245.0) {
		tmp = l;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 245.0:
		tmp = l
	else:
		tmp = 0.0
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 245.0)
		tmp = l;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 245.0)
		tmp = l;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 245.0], l, 0.0]

Derivation

1. Split input into 2 regimes

2. if w < 245

   1. Initial program 99.6%

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

   3. Taylor expanded in w around 0

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

   5. Simplified 67.5%

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

   if 245 < w

   1. Initial program 100.0%

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

      1. exp-neg N/A

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

      2. sqr-pow N/A

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

      3. pow-prod-up N/A

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

      4. flip-+ N/A

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

      5. +-inverses N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      6. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 - 0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

      7. metadata-eval N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{\color{blue}{e^{w}}}{2} - \frac{e^{w}}{2}}\right)} \]

      8. mul0-lft N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      9. *-commutative N/A

         \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - w \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      11. mul0-lft N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      12. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

      13. +-inverses N/A

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

      14. metadata-eval N/A

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

      15. flip-- N/A

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

      16. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{0} \]

      17. metadata-eval N/A

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

      18. associate-/r/ N/A

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

      19. div-inv N/A

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

      20. metadata-eval N/A

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

      21. metadata-eval N/A

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

      22. metadata-eval N/A

          \[\leadsto \frac{1}{e^{w} \cdot \left(\frac{1}{2} + \frac{1}{2}\right)} \]

      23. metadata-eval N/A

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

   4. Applied egg-rr 100.0%

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

Alternative 13: 16.5% accurate, 305.0× speedup

Math

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

FPCore

(FPCore (w l) :precision binary64 0.0)

C

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

Fortran

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

Java

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

Python

def code(w, l):
	return 0.0

Julia

function code(w, l)
	return 0.0
end

MATLAB

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

Wolfram

code[w_, l_] := 0.0

Derivation

1. Initial program 99.7%

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

   1. exp-neg N/A

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

   2. sqr-pow N/A

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

   3. pow-prod-up N/A

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

   4. flip-+ N/A

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

   5. +-inverses N/A

      \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

   6. metadata-eval N/A

      \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 - 0}{\color{blue}{\frac{e^{w}}{2}} - \frac{e^{w}}{2}}\right)} \]

   7. metadata-eval N/A

      \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{\color{blue}{e^{w}}}{2} - \frac{e^{w}}{2}}\right)} \]

   8. mul0-lft N/A

      \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

   9. *-commutative N/A

      \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - w \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

   10. *-commutative N/A

       \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot w}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

   11. mul0-lft N/A

       \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

   12. metadata-eval N/A

       \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{\left(\frac{0 \cdot 0 - 0 \cdot 0}{\frac{e^{w}}{\color{blue}{2}} - \frac{e^{w}}{2}}\right)} \]

   13. +-inverses N/A

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

   14. metadata-eval N/A

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

   15. flip-- N/A

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

   16. metadata-eval N/A

       \[\leadsto \frac{1}{e^{w}} \cdot {\ell}^{0} \]

   17. metadata-eval N/A

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

   18. associate-/r/ N/A

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

   19. div-inv N/A

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

   20. metadata-eval N/A

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

   21. metadata-eval N/A

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

   22. metadata-eval N/A

       \[\leadsto \frac{1}{e^{w} \cdot \left(\frac{1}{2} + \frac{1}{2}\right)} \]

   23. metadata-eval N/A

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

4. Applied egg-rr 16.7%

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

Reproduce

herbie shell --seed 2024192 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))