exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 12.0s

Alternatives: 8

Speedup: N/A×

• could not determine a ground truth

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% 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

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

FPCore

(FPCore (w l) :precision binary64 (* (pow l (exp w)) (/ (- -1.0) (exp w))))

C

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

Fortran

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

Java

public static double code(double w, double l) {
	return Math.pow(l, Math.exp(w)) * (-(-1.0) / Math.exp(w));
}

Python

def code(w, l):
	return math.pow(l, math.exp(w)) * (-(-1.0) / math.exp(w))

Julia

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

MATLAB

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

Wolfram

code[w_, l_] := N[(N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision] * N[((--1.0) / N[Exp[w], $MachinePrecision]), $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. Step-by-step derivation

   1. frac-2neg 99.0%

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

   2. div-inv 99.0%

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

5. Applied egg-rr 99.0%

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

6. Taylor expanded in w around inf 99.0%

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

7. Final simplification 99.0%

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

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: 98.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.062:\\ \;\;\;\;e^{-w}\\ \mathbf{elif}\;w \leq 0.0076:\\ \;\;\;\;\left(\ell + \ell \cdot \left(w \cdot \log \ell\right)\right) \cdot \left(\left(-w\right) - -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\log \ell - w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w -0.062)
   (exp (- w))
   (if (<= w 0.0076)
     (* (+ l (* l (* w (log l)))) (- (- w) -1.0))
     (exp (- (log l) w)))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -0.062) {
		tmp = exp(-w);
	} else if (w <= 0.0076) {
		tmp = (l + (l * (w * log(l)))) * (-w - -1.0);
	} else {
		tmp = exp((log(l) - w));
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-0.062d0)) then
        tmp = exp(-w)
    else if (w <= 0.0076d0) then
        tmp = (l + (l * (w * log(l)))) * (-w - (-1.0d0))
    else
        tmp = exp((log(l) - w))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -0.062) {
		tmp = Math.exp(-w);
	} else if (w <= 0.0076) {
		tmp = (l + (l * (w * Math.log(l)))) * (-w - -1.0);
	} else {
		tmp = Math.exp((Math.log(l) - w));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -0.062:
		tmp = math.exp(-w)
	elif w <= 0.0076:
		tmp = (l + (l * (w * math.log(l)))) * (-w - -1.0)
	else:
		tmp = math.exp((math.log(l) - w))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -0.062)
		tmp = exp(Float64(-w));
	elseif (w <= 0.0076)
		tmp = Float64(Float64(l + Float64(l * Float64(w * log(l)))) * Float64(Float64(-w) - -1.0));
	else
		tmp = exp(Float64(log(l) - w));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -0.062)
		tmp = exp(-w);
	elseif (w <= 0.0076)
		tmp = (l + (l * (w * log(l)))) * (-w - -1.0);
	else
		tmp = exp((log(l) - w));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -0.062], N[Exp[(-w)], $MachinePrecision], If[LessEqual[w, 0.0076], N[(N[(l + N[(l * N[(w * N[Log[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[((-w) - -1.0), $MachinePrecision]), $MachinePrecision], N[Exp[N[(N[Log[l], $MachinePrecision] - w), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if w < -0.062

   1. Initial program 99.7%

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

      1. exp-neg 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-lft-identity 99.7%

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

   3. Simplified 99.7%

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

      1. add-exp-log 99.6%

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

      2. log-div 99.6%

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

      3. log-pow 99.6%

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

      4. add-log-exp 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in w around inf 96.4%

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

      1. neg-mul-1 96.4%

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

   8. Simplified 96.4%

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

   if -0.062 < w < 0.00759999999999999998

   1. Initial program 99.7%

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

      1. exp-neg 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-lft-identity 99.7%

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

   3. Simplified 99.7%

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

      1. frac-2neg 99.7%

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

      2. div-inv 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in w around 0 99.3%

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

   7. Taylor expanded in w around 0 99.0%

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

      1. *-commutative 99.0%

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

   9. Simplified 99.0%

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

   if 0.00759999999999999998 < w

   1. Initial program 94.7%

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

      1. exp-neg 94.7%

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

      2. associate-*l/ 94.7%

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

      3. *-lft-identity 94.7%

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

   3. Simplified 94.7%

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

      1. add-exp-log 94.7%

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

      2. log-div 94.6%

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

      3. log-pow 94.6%

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

      4. add-log-exp 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in w around 0 90.3%

      \[\leadsto e^{\color{blue}{\log \ell} - w} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -0.062:\\ \;\;\;\;e^{-w}\\ \mathbf{elif}\;w \leq 0.0076:\\ \;\;\;\;\left(\ell + \ell \cdot \left(w \cdot \log \ell\right)\right) \cdot \left(\left(-w\right) - -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\log \ell - w}\\ \end{array} \]

Alternative 4: 98.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -4.1:\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;{\ell}^{\left(e^{w}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w -4.1) (exp (- w)) (pow l (exp w))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -4.1) {
		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 <= (-4.1d0)) 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 <= -4.1) {
		tmp = Math.exp(-w);
	} else {
		tmp = Math.pow(l, Math.exp(w));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -4.1:
		tmp = math.exp(-w)
	else:
		tmp = math.pow(l, math.exp(w))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -4.1)
		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 <= -4.1)
		tmp = exp(-w);
	else
		tmp = l ^ exp(w);
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -4.1], N[Exp[(-w)], $MachinePrecision], N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < -4.0999999999999996

   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. add-exp-log 99.9%

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

      2. log-div 99.9%

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

      3. log-pow 99.9%

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

      4. add-log-exp 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in w around inf 99.0%

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

      1. neg-mul-1 99.0%

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

   8. Simplified 99.0%

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

   if -4.0999999999999996 < 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 97.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -4.1:\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;{\ell}^{\left(e^{w}\right)}\\ \end{array} \]

Alternative 5: 97.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.122 \lor \neg \left(w \leq 5000000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell + w \cdot \left(\ell \cdot \log \ell - \ell\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (or (<= w -0.122) (not (<= w 5000000.0)))
   (exp (- w))
   (+ l (* w (- (* l (log l)) l)))))

C

double code(double w, double l) {
	double tmp;
	if ((w <= -0.122) || !(w <= 5000000.0)) {
		tmp = exp(-w);
	} else {
		tmp = l + (w * ((l * log(l)) - 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 <= (-0.122d0)) .or. (.not. (w <= 5000000.0d0))) then
        tmp = exp(-w)
    else
        tmp = l + (w * ((l * log(l)) - l))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if ((w <= -0.122) || !(w <= 5000000.0)) {
		tmp = Math.exp(-w);
	} else {
		tmp = l + (w * ((l * Math.log(l)) - l));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if (w <= -0.122) or not (w <= 5000000.0):
		tmp = math.exp(-w)
	else:
		tmp = l + (w * ((l * math.log(l)) - l))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if ((w <= -0.122) || !(w <= 5000000.0))
		tmp = exp(Float64(-w));
	else
		tmp = Float64(l + Float64(w * Float64(Float64(l * log(l)) - l)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if ((w <= -0.122) || ~((w <= 5000000.0)))
		tmp = exp(-w);
	else
		tmp = l + (w * ((l * log(l)) - l));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[Or[LessEqual[w, -0.122], N[Not[LessEqual[w, 5000000.0]], $MachinePrecision]], N[Exp[(-w)], $MachinePrecision], N[(l + N[(w * N[(N[(l * N[Log[l], $MachinePrecision]), $MachinePrecision] - l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < -0.122 or 5e6 < w

   1. Initial program 99.8%

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

      1. exp-neg 99.8%

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

      2. associate-*l/ 99.8%

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

      3. *-lft-identity 99.8%

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

   3. Simplified 99.8%

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

      1. add-exp-log 99.8%

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

      2. log-div 99.8%

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

      3. log-pow 99.7%

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

      4. add-log-exp 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in w around inf 97.6%

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

      1. neg-mul-1 97.6%

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

   8. Simplified 97.6%

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

   if -0.122 < w < 5e6

   1. Initial program 98.3%

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

      1. exp-neg 98.3%

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

      2. associate-*l/ 98.3%

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

      3. *-lft-identity 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in w around 0 95.9%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -0.122 \lor \neg \left(w \leq 5000000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell + w \cdot \left(\ell \cdot \log \ell - \ell\right)\\ \end{array} \]

Alternative 6: 98.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.075 \lor \neg \left(w \leq 5000000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell + \left(-1 + \log \ell\right) \cdot \left(\ell \cdot w\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (or (<= w -0.075) (not (<= w 5000000.0)))
   (exp (- w))
   (+ l (* (+ -1.0 (log l)) (* l w)))))

C

double code(double w, double l) {
	double tmp;
	if ((w <= -0.075) || !(w <= 5000000.0)) {
		tmp = exp(-w);
	} else {
		tmp = l + ((-1.0 + log(l)) * (l * w));
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if ((w <= (-0.075d0)) .or. (.not. (w <= 5000000.0d0))) then
        tmp = exp(-w)
    else
        tmp = l + (((-1.0d0) + log(l)) * (l * w))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if ((w <= -0.075) || !(w <= 5000000.0)) {
		tmp = Math.exp(-w);
	} else {
		tmp = l + ((-1.0 + Math.log(l)) * (l * w));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if (w <= -0.075) or not (w <= 5000000.0):
		tmp = math.exp(-w)
	else:
		tmp = l + ((-1.0 + math.log(l)) * (l * w))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if ((w <= -0.075) || !(w <= 5000000.0))
		tmp = exp(Float64(-w));
	else
		tmp = Float64(l + Float64(Float64(-1.0 + log(l)) * Float64(l * w)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if ((w <= -0.075) || ~((w <= 5000000.0)))
		tmp = exp(-w);
	else
		tmp = l + ((-1.0 + log(l)) * (l * w));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[Or[LessEqual[w, -0.075], N[Not[LessEqual[w, 5000000.0]], $MachinePrecision]], N[Exp[(-w)], $MachinePrecision], N[(l + N[(N[(-1.0 + N[Log[l], $MachinePrecision]), $MachinePrecision] * N[(l * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < -0.0749999999999999972 or 5e6 < w

   1. Initial program 99.8%

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

      1. exp-neg 99.8%

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

      2. associate-*l/ 99.8%

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

      3. *-lft-identity 99.8%

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

   3. Simplified 99.8%

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

      1. add-exp-log 99.8%

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

      2. log-div 99.8%

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

      3. log-pow 99.7%

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

      4. add-log-exp 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in w around inf 97.6%

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

      1. neg-mul-1 97.6%

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

   8. Simplified 97.6%

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

   if -0.0749999999999999972 < w < 5e6

   1. Initial program 98.3%

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

      1. exp-neg 98.3%

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

      2. associate-*l/ 98.3%

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

      3. *-lft-identity 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in w around 0 95.9%

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

   5. Taylor expanded in l around 0 96.4%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -0.075 \lor \neg \left(w \leq 5000000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell + \left(-1 + \log \ell\right) \cdot \left(\ell \cdot w\right)\\ \end{array} \]

Alternative 7: 97.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.69 \lor \neg \left(w \leq 5000000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (or (<= w -0.69) (not (<= w 5000000.0))) (exp (- w)) l))

C

double code(double w, double l) {
	double tmp;
	if ((w <= -0.69) || !(w <= 5000000.0)) {
		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 <= (-0.69d0)) .or. (.not. (w <= 5000000.0d0))) 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 <= -0.69) || !(w <= 5000000.0)) {
		tmp = Math.exp(-w);
	} else {
		tmp = l;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if (w <= -0.69) or not (w <= 5000000.0):
		tmp = math.exp(-w)
	else:
		tmp = l
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if ((w <= -0.69) || !(w <= 5000000.0))
		tmp = exp(Float64(-w));
	else
		tmp = l;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if ((w <= -0.69) || ~((w <= 5000000.0)))
		tmp = exp(-w);
	else
		tmp = l;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[Or[LessEqual[w, -0.69], N[Not[LessEqual[w, 5000000.0]], $MachinePrecision]], N[Exp[(-w)], $MachinePrecision], l]

Derivation

1. Split input into 2 regimes

2. if w < -0.68999999999999995 or 5e6 < 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. add-exp-log 100.0%

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

      2. log-div 100.0%

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

      3. log-pow 100.0%

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

      4. add-log-exp 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in w around inf 99.3%

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

      1. neg-mul-1 99.3%

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

   8. Simplified 99.3%

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

   if -0.68999999999999995 < w < 5e6

   1. Initial program 98.2%

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

      1. exp-neg 98.2%

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

      2. associate-*l/ 98.2%

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

      3. *-lft-identity 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in w around 0 94.5%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -0.69 \lor \neg \left(w \leq 5000000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \]

Alternative 8: 56.6% 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. 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. Taylor expanded in w around 0 57.6%

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

5. Final simplification 57.6%

   \[\leadsto \ell \]

Reproduce

herbie shell --seed 2023215 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))