exp-w (used to crash)

Percentage Accurate: 99.4% → 98.7%

Time: 11.0s

Alternatives: 5

Speedup: N/A×

• could not determine a ground truth

  1. w = 2.00000000000000007e154
  2. l = -2

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -4.2:\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;{\ell}^{\left(e^{w}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w -4.2) (exp (- w)) (pow l (exp w))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -4.2) {
		tmp = exp(-w);
	} else {
		tmp = pow(l, exp(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 <= (-4.2d0)) then
        tmp = exp(-w)
    else
        tmp = l ** exp(w)
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -4.2) {
		tmp = Math.exp(-w);
	} else {
		tmp = Math.pow(l, Math.exp(w));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -4.2:
		tmp = math.exp(-w)
	else:
		tmp = math.pow(l, math.exp(w))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -4.2)
		tmp = exp(Float64(-w));
	else
		tmp = l ^ exp(w);
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -4.2)
		tmp = exp(-w);
	else
		tmp = l ^ exp(w);
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -4.2], N[Exp[(-w)], $MachinePrecision], N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < -4.20000000000000018

   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. Step-by-step derivation

      1. frac-2neg 100.0%

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

      2. div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. add-exp-log 100.0%

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

      2. un-div-inv 100.0%

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

      3. log-div 0.0%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 98.7%

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

      6. sqr-neg 98.7%

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

      7. sqrt-unprod 98.7%

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

      8. add-sqr-sqrt 98.7%

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

      9. log-pow 98.7%

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

      10. add-sqr-sqrt 98.7%

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

      11. sqrt-unprod 100.0%

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

      12. sqr-neg 100.0%

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

      13. sqrt-unprod 100.0%

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

      14. add-sqr-sqrt 100.0%

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

      15. add-log-exp 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in w around inf 99.8%

      \[\leadsto e^{\color{blue}{-1 \cdot w}} \]
   9. Step-by-step derivation

      1. neg-mul-1 99.8%

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

   10. Simplified 99.8%

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

   if -4.20000000000000018 < w

   1. Initial program 98.6%

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

      1. exp-neg 98.6%

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

      2. associate-*l/ 98.6%

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

      3. *-lft-identity 98.6%

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

   3. Simplified 98.6%

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

      1. frac-2neg 98.6%

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

      2. div-inv 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in w around 0 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -4.2:\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;{\ell}^{\left(e^{w}\right)}\\ \end{array} \]

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 99.0%

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

   1. exp-neg 99.0%

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

   2. associate-*l/ 99.0%

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

   3. *-lft-identity 99.0%

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

3. Simplified 99.0%

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

4. Final simplification 99.0%

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

Alternative 3: 98.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.14 \lor \neg \left(w \leq 63000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(1 + w \cdot \left(-1 + \log \ell\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (or (<= w -0.14) (not (<= w 63000.0)))
   (exp (- w))
   (* l (+ 1.0 (* w (+ -1.0 (log l)))))))

C

double code(double w, double l) {
	double tmp;
	if ((w <= -0.14) || !(w <= 63000.0)) {
		tmp = exp(-w);
	} else {
		tmp = l * (1.0 + (w * (-1.0 + log(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 <= (-0.14d0)) .or. (.not. (w <= 63000.0d0))) then
        tmp = exp(-w)
    else
        tmp = l * (1.0d0 + (w * ((-1.0d0) + log(l))))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if ((w <= -0.14) || !(w <= 63000.0)) {
		tmp = Math.exp(-w);
	} else {
		tmp = l * (1.0 + (w * (-1.0 + Math.log(l))));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if (w <= -0.14) or not (w <= 63000.0):
		tmp = math.exp(-w)
	else:
		tmp = l * (1.0 + (w * (-1.0 + math.log(l))))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if ((w <= -0.14) || !(w <= 63000.0))
		tmp = exp(Float64(-w));
	else
		tmp = Float64(l * Float64(1.0 + Float64(w * Float64(-1.0 + log(l)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if ((w <= -0.14) || ~((w <= 63000.0)))
		tmp = exp(-w);
	else
		tmp = l * (1.0 + (w * (-1.0 + log(l))));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[Or[LessEqual[w, -0.14], N[Not[LessEqual[w, 63000.0]], $MachinePrecision]], N[Exp[(-w)], $MachinePrecision], N[(l * N[(1.0 + N[(w * N[(-1.0 + N[Log[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < -0.14000000000000001 or 63000 < 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. Step-by-step derivation

      1. frac-2neg 100.0%

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

      2. div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. add-exp-log 100.0%

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

      2. un-div-inv 100.0%

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

      3. log-div 0.0%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 64.7%

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

      6. sqr-neg 64.7%

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

      7. sqrt-unprod 64.7%

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

      8. add-sqr-sqrt 64.7%

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

      9. log-pow 64.7%

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

      10. add-sqr-sqrt 64.7%

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

      11. sqrt-unprod 100.0%

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

      12. sqr-neg 100.0%

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

      13. sqrt-unprod 100.0%

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

      14. add-sqr-sqrt 100.0%

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

      15. add-log-exp 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in w around inf 99.9%

      \[\leadsto e^{\color{blue}{-1 \cdot w}} \]
   9. Step-by-step derivation

      1. neg-mul-1 99.9%

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

   10. Simplified 99.9%

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

   if -0.14000000000000001 < w < 63000

   1. Initial program 98.2%

      \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]

   2. Taylor expanded in w around 0 97.6%

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

      1. *-commutative 97.6%

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

      2. mul-1-neg 97.6%

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

      3. +-commutative 97.6%

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

      4. sub-neg 97.6%

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

   4. Simplified 97.6%

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

   5. Taylor expanded in l around 0 97.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -0.14 \lor \neg \left(w \leq 63000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(1 + w \cdot \left(-1 + \log \ell\right)\right)\\ \end{array} \]

Alternative 4: 97.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.7 \lor \neg \left(w \leq 63000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (or (<= w -0.7) (not (<= w 63000.0))) (exp (- w)) l))

C

double code(double w, double l) {
	double tmp;
	if ((w <= -0.7) || !(w <= 63000.0)) {
		tmp = exp(-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 <= (-0.7d0)) .or. (.not. (w <= 63000.0d0))) then
        tmp = exp(-w)
    else
        tmp = l
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if ((w <= -0.7) || !(w <= 63000.0)) {
		tmp = Math.exp(-w);
	} else {
		tmp = l;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if (w <= -0.7) or not (w <= 63000.0):
		tmp = math.exp(-w)
	else:
		tmp = l
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if ((w <= -0.7) || !(w <= 63000.0))
		tmp = exp(Float64(-w));
	else
		tmp = l;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if ((w <= -0.7) || ~((w <= 63000.0)))
		tmp = exp(-w);
	else
		tmp = l;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[Or[LessEqual[w, -0.7], N[Not[LessEqual[w, 63000.0]], $MachinePrecision]], N[Exp[(-w)], $MachinePrecision], l]

Derivation

1. Split input into 2 regimes

2. if w < -0.69999999999999996 or 63000 < 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. Step-by-step derivation

      1. frac-2neg 100.0%

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

      2. div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. add-exp-log 100.0%

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

      2. un-div-inv 100.0%

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

      3. log-div 0.0%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 64.7%

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

      6. sqr-neg 64.7%

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

      7. sqrt-unprod 64.7%

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

      8. add-sqr-sqrt 64.7%

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

      9. log-pow 64.7%

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

      10. add-sqr-sqrt 64.7%

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

      11. sqrt-unprod 100.0%

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

      12. sqr-neg 100.0%

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

      13. sqrt-unprod 100.0%

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

      14. add-sqr-sqrt 100.0%

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

      15. add-log-exp 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in w around inf 99.9%

      \[\leadsto e^{\color{blue}{-1 \cdot w}} \]
   9. Step-by-step derivation

      1. neg-mul-1 99.9%

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

   10. Simplified 99.9%

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

   if -0.69999999999999996 < w < 63000

   1. Initial program 98.2%

      \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]

   2. Taylor expanded in w around 0 96.7%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -0.7 \lor \neg \left(w \leq 63000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \]

Alternative 5: 58.0% 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 99.0%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]

2. Taylor expanded in w around 0 55.1%

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

3. Final simplification 55.1%

   \[\leadsto \ell \]

Reproduce

herbie shell --seed 2023173 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))