exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 13.7s

Alternatives: 8

Speedup: 1.0×

• could not determine a ground truth

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% 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

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

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]

Derivation

1. Initial program 99.6%

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

2. Final simplification 99.6%

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

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 99.6%

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

   1. exp-neg 99.6%

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

   2. associate-*l/ 99.6%

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

   3. *-lft-identity 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 3: 97.6% accurate, 3.0× speedup

Math

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

FPCore

(FPCore (w l) :precision binary64 (/ l (exp w)))

C

double code(double w, double l) {
	return l / exp(w);
}

Fortran

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

Java

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

Python

def code(w, l):
	return l / math.exp(w)

Julia

function code(w, l)
	return Float64(l / exp(w))
end

MATLAB

function tmp = code(w, l)
	tmp = l / exp(w);
end

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. exp-neg 99.6%

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

   2. associate-*l/ 99.6%

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

   3. *-lft-identity 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in w around 0 97.4%

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

5. Final simplification 97.4%

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

Alternative 4: 71.2% accurate, 27.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq 1.25 \cdot 10^{-5}:\\ \;\;\;\;\ell - w \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{w}{\ell} + \frac{1}{\ell}}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w 1.25e-5) (- l (* w l)) (/ 1.0 (+ (/ w l) (/ 1.0 l)))))

C

double code(double w, double l) {
	double tmp;
	if (w <= 1.25e-5) {
		tmp = l - (w * l);
	} else {
		tmp = 1.0 / ((w / l) + (1.0 / l));
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= 1.25d-5) then
        tmp = l - (w * l)
    else
        tmp = 1.0d0 / ((w / l) + (1.0d0 / l))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= 1.25e-5) {
		tmp = l - (w * l);
	} else {
		tmp = 1.0 / ((w / l) + (1.0 / l));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= 1.25e-5:
		tmp = l - (w * l)
	else:
		tmp = 1.0 / ((w / l) + (1.0 / l))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= 1.25e-5)
		tmp = Float64(l - Float64(w * l));
	else
		tmp = Float64(1.0 / Float64(Float64(w / l) + Float64(1.0 / l)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= 1.25e-5)
		tmp = l - (w * l);
	else
		tmp = 1.0 / ((w / l) + (1.0 / l));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, 1.25e-5], N[(l - N[(w * l), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(w / l), $MachinePrecision] + N[(1.0 / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < 1.25000000000000006e-5

   1. Initial program 99.6%

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

      1. exp-neg 99.6%

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

      2. associate-*l/ 99.6%

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

      3. *-lft-identity 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in w around 0 98.0%

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

   5. Taylor expanded in w around 0 70.9%

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

      1. +-commutative 70.9%

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

      2. mul-1-neg 70.9%

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

      3. unsub-neg 70.9%

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

   7. Simplified 70.9%

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

   if 1.25000000000000006e-5 < w

   1. Initial program 99.6%

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

      1. exp-neg 99.6%

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

      2. associate-*l/ 99.6%

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

      3. *-lft-identity 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in w around 0 94.9%

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

      1. clear-num 94.9%

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

      2. inv-pow 94.9%

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

   6. Applied egg-rr 94.9%

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

      1. unpow-1 94.9%

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

   8. Simplified 94.9%

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

   9. Taylor expanded in w around 0 50.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq 1.25 \cdot 10^{-5}:\\ \;\;\;\;\ell - w \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{w}{\ell} + \frac{1}{\ell}}\\ \end{array} \]

Alternative 5: 64.2% accurate, 43.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.4:\\ \;\;\;\;w \cdot \left(-\ell\right)\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(w + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w -0.4) (* w (- l)) (* l (+ w 1.0))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -0.4) {
		tmp = w * -l;
	} else {
		tmp = l * (w + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-0.4d0)) then
        tmp = w * -l
    else
        tmp = l * (w + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -0.4) {
		tmp = w * -l;
	} else {
		tmp = l * (w + 1.0);
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -0.4:
		tmp = w * -l
	else:
		tmp = l * (w + 1.0)
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -0.4)
		tmp = Float64(w * Float64(-l));
	else
		tmp = Float64(l * Float64(w + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -0.4)
		tmp = w * -l;
	else
		tmp = l * (w + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -0.4], N[(w * (-l)), $MachinePrecision], N[(l * N[(w + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < -0.40000000000000002

   1. Initial program 100.0%

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

      1. exp-neg 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in w around 0 98.7%

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

   5. Taylor expanded in w around 0 23.9%

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

      1. +-commutative 23.9%

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

      2. mul-1-neg 23.9%

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

      3. unsub-neg 23.9%

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

   7. Simplified 23.9%

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

   8. Taylor expanded in w around inf 23.9%

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

      1. associate-*r* 23.9%

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

      2. neg-mul-1 23.9%

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

   10. Simplified 23.9%

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

   if -0.40000000000000002 < w

   1. Initial program 99.5%

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

      1. exp-neg 99.5%

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

      2. associate-*l/ 99.5%

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

      3. *-lft-identity 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in w around 0 96.8%

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

   5. Taylor expanded in w around 0 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

   7. Simplified 70.8%

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

      1. cancel-sign-sub-inv 70.8%

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

      2. distribute-lft-neg-in 70.8%

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

      3. *-commutative 70.8%

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

      4. distribute-lft-neg-in 70.8%

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

      5. add-sqr-sqrt 33.1%

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

      6. sqrt-unprod 70.7%

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

      7. sqr-neg 70.7%

         \[\leadsto \ell + \sqrt{\color{blue}{w \cdot w}} \cdot \ell \]

      8. sqrt-unprod 37.7%

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

      9. add-sqr-sqrt 70.8%

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

      10. distribute-rgt1-in 70.8%

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

   9. Applied egg-rr 70.8%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -0.4:\\ \;\;\;\;w \cdot \left(-\ell\right)\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(w + 1\right)\\ \end{array} \]

Alternative 6: 64.2% accurate, 61.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. exp-neg 99.6%

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

   2. associate-*l/ 99.6%

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

   3. *-lft-identity 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in w around 0 97.4%

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

5. Taylor expanded in w around 0 57.2%

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

   1. +-commutative 57.2%

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

   2. mul-1-neg 57.2%

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

   3. unsub-neg 57.2%

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

7. Simplified 57.2%

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

8. Final simplification 57.2%

   \[\leadsto \ell - w \cdot \ell \]

Alternative 7: 10.7% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. exp-neg 99.6%

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

   2. associate-*l/ 99.6%

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

   3. *-lft-identity 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in w around 0 97.4%

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

5. Taylor expanded in w around 0 57.2%

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

   1. +-commutative 57.2%

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

   2. mul-1-neg 57.2%

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

   3. unsub-neg 57.2%

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

7. Simplified 57.2%

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

8. Taylor expanded in w around inf 9.8%

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

   1. associate-*r* 9.8%

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

   2. neg-mul-1 9.8%

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

10. Simplified 9.8%

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

11. Final simplification 9.8%

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

Alternative 8: 3.2% accurate, 101.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. exp-neg 99.6%

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

   2. associate-*l/ 99.6%

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

   3. *-lft-identity 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in w around 0 97.4%

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

5. Taylor expanded in w around 0 57.2%

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

   1. +-commutative 57.2%

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

   2. mul-1-neg 57.2%

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

   3. unsub-neg 57.2%

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

7. Simplified 57.2%

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

   1. cancel-sign-sub-inv 57.2%

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

   2. distribute-lft-neg-in 57.2%

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

   3. distribute-rgt-neg-in 57.2%

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

   4. add-sqr-sqrt 30.4%

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

   5. sqrt-unprod 66.5%

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

   6. sqr-neg 66.5%

      \[\leadsto \ell + \ell \cdot \sqrt{\color{blue}{w \cdot w}} \]

   7. sqrt-unprod 26.8%

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

   8. add-sqr-sqrt 50.5%

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

   9. log1p-expm1-u 27.9%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\ell + \ell \cdot w\right)\right)} \]

9. Applied egg-rr 27.9%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\ell + \ell \cdot w\right)\right)} \]

10. Taylor expanded in w around inf 3.1%

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

11. Final simplification 3.1%

    \[\leadsto w \cdot \ell \]

Reproduce

herbie shell --seed 2023243 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))