exp-w (used to crash)

Percentage Accurate: 99.5% → 99.5%

Time: 29.5s

Alternatives: 10

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: 99.5% 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: 99.5% 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 99.2%

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

3. Final simplification 99.2%

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

Alternative 2: 99.5% 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 99.2%

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

   1. exp-neg 99.2%

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

   2. remove-double-neg 99.2%

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

   3. associate-*l/ 99.2%

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

   4. *-lft-identity 99.2%

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

   5. remove-double-neg 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 3: 98.0% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[w_, l_] := N[(l * N[((--1.0) / N[Exp[w], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

   1. exp-neg 99.2%

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

   2. remove-double-neg 99.2%

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

   3. associate-*l/ 99.2%

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

   4. *-lft-identity 99.2%

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

   5. remove-double-neg 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in w around 0 96.9%

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

   1. frac-2neg 96.9%

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

   2. div-inv 96.9%

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

7. Applied egg-rr 96.9%

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

8. Taylor expanded in w around inf 96.9%

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

9. Final simplification 96.9%

   \[\leadsto \ell \cdot \frac{--1}{e^{w}} \]
10. Add Preprocessing

Alternative 4: 98.0% 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 99.2%

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

   1. exp-neg 99.2%

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

   2. remove-double-neg 99.2%

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

   3. associate-*l/ 99.2%

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

   4. *-lft-identity 99.2%

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

   5. remove-double-neg 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in w around 0 96.9%

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

6. Final simplification 96.9%

   \[\leadsto \frac{\ell}{e^{w}} \]
7. Add Preprocessing

Alternative 5: 76.8% accurate, 20.3× speedup

Math

\[\begin{array}{l} \\ \ell \cdot \left(w \cdot \left(-1 + w \cdot \left(0.5 - w \cdot 0.16666666666666666\right)\right) - -1\right) \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (* l (- (* w (+ -1.0 (* w (- 0.5 (* w 0.16666666666666666))))) -1.0)))

C

double code(double w, double l) {
	return l * ((w * (-1.0 + (w * (0.5 - (w * 0.16666666666666666))))) - -1.0);
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = l * ((w * ((-1.0d0) + (w * (0.5d0 - (w * 0.16666666666666666d0))))) - (-1.0d0))
end function

Java

public static double code(double w, double l) {
	return l * ((w * (-1.0 + (w * (0.5 - (w * 0.16666666666666666))))) - -1.0);
}

Python

def code(w, l):
	return l * ((w * (-1.0 + (w * (0.5 - (w * 0.16666666666666666))))) - -1.0)

Julia

function code(w, l)
	return Float64(l * Float64(Float64(w * Float64(-1.0 + Float64(w * Float64(0.5 - Float64(w * 0.16666666666666666))))) - -1.0))
end

MATLAB

function tmp = code(w, l)
	tmp = l * ((w * (-1.0 + (w * (0.5 - (w * 0.16666666666666666))))) - -1.0);
end

Wolfram

code[w_, l_] := N[(l * N[(N[(w * N[(-1.0 + N[(w * N[(0.5 - N[(w * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

   1. exp-neg 99.2%

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

   2. remove-double-neg 99.2%

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

   3. associate-*l/ 99.2%

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

   4. *-lft-identity 99.2%

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

   5. remove-double-neg 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in w around 0 96.9%

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

   1. frac-2neg 96.9%

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

   2. div-inv 96.9%

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

7. Applied egg-rr 96.9%

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

8. Taylor expanded in w around 0 79.0%

   \[\leadsto \left(-\ell\right) \cdot \color{blue}{\left(w \cdot \left(1 + w \cdot \left(0.16666666666666666 \cdot w - 0.5\right)\right) - 1\right)} \]

9. Final simplification 79.0%

   \[\leadsto \ell \cdot \left(w \cdot \left(-1 + w \cdot \left(0.5 - w \cdot 0.16666666666666666\right)\right) - -1\right) \]
10. Add Preprocessing

Alternative 6: 69.7% accurate, 27.7× speedup

Math

\[\begin{array}{l} \\ \ell + w \cdot \left(\ell + w \cdot \left(\ell \cdot 0.5\right)\right) \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (+ l (* w (+ l (* w (* l 0.5))))))

C

double code(double w, double l) {
	return l + (w * (l + (w * (l * 0.5))));
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = l + (w * (l + (w * (l * 0.5d0))))
end function

Java

public static double code(double w, double l) {
	return l + (w * (l + (w * (l * 0.5))));
}

Python

def code(w, l):
	return l + (w * (l + (w * (l * 0.5))))

Julia

function code(w, l)
	return Float64(l + Float64(w * Float64(l + Float64(w * Float64(l * 0.5)))))
end

MATLAB

function tmp = code(w, l)
	tmp = l + (w * (l + (w * (l * 0.5))));
end

Wolfram

code[w_, l_] := N[(l + N[(w * N[(l + N[(w * N[(l * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

   1. exp-neg 99.2%

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

   2. remove-double-neg 99.2%

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

   3. associate-*l/ 99.2%

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

   4. *-lft-identity 99.2%

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

   5. remove-double-neg 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in w around 0 96.9%

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

   1. clear-num 96.8%

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

   2. associate-/r/ 96.9%

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

   3. exp-neg 96.9%

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

   4. add-sqr-sqrt 57.9%

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

   5. sqrt-unprod 85.0%

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

   6. sqr-neg 85.0%

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

   7. sqrt-unprod 27.1%

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

   8. add-sqr-sqrt 58.1%

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

7. Applied egg-rr 58.1%

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

8. Taylor expanded in w around 0 72.4%

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

   1. associate-*r* 72.4%

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

   2. *-commutative 72.4%

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

10. Simplified 72.4%

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

11. Final simplification 72.4%

    \[\leadsto \ell + w \cdot \left(\ell + w \cdot \left(\ell \cdot 0.5\right)\right) \]
12. Add Preprocessing

Alternative 7: 73.4% accurate, 27.7× speedup

Math

\[\begin{array}{l} \\ \ell \cdot \left(w \cdot \left(-1 - w \cdot -0.5\right) - -1\right) \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (* l (- (* w (- -1.0 (* w -0.5))) -1.0)))

C

double code(double w, double l) {
	return l * ((w * (-1.0 - (w * -0.5))) - -1.0);
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = l * ((w * ((-1.0d0) - (w * (-0.5d0)))) - (-1.0d0))
end function

Java

public static double code(double w, double l) {
	return l * ((w * (-1.0 - (w * -0.5))) - -1.0);
}

Python

def code(w, l):
	return l * ((w * (-1.0 - (w * -0.5))) - -1.0)

Julia

function code(w, l)
	return Float64(l * Float64(Float64(w * Float64(-1.0 - Float64(w * -0.5))) - -1.0))
end

MATLAB

function tmp = code(w, l)
	tmp = l * ((w * (-1.0 - (w * -0.5))) - -1.0);
end

Wolfram

code[w_, l_] := N[(l * N[(N[(w * N[(-1.0 - N[(w * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

   1. exp-neg 99.2%

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

   2. remove-double-neg 99.2%

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

   3. associate-*l/ 99.2%

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

   4. *-lft-identity 99.2%

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

   5. remove-double-neg 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in w around 0 96.9%

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

   1. frac-2neg 96.9%

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

   2. div-inv 96.9%

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

7. Applied egg-rr 96.9%

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

8. Taylor expanded in w around 0 76.8%

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

9. Final simplification 76.8%

   \[\leadsto \ell \cdot \left(w \cdot \left(-1 - w \cdot -0.5\right) - -1\right) \]
10. Add Preprocessing

Alternative 8: 63.3% accurate, 61.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. exp-neg 99.2%

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

   2. remove-double-neg 99.2%

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

   3. associate-*l/ 99.2%

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

   4. *-lft-identity 99.2%

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

   5. remove-double-neg 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in w around 0 96.9%

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

   1. frac-2neg 96.9%

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

   2. div-inv 96.9%

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

7. Applied egg-rr 96.9%

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

8. Taylor expanded in w around inf 96.9%

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

9. Taylor expanded in w around 0 65.1%

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

    1. neg-mul-1 65.1%

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

    2. sub-neg 65.1%

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

    3. *-lft-identity 65.1%

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

    4. *-commutative 65.1%

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

    5. distribute-rgt-out-- 65.1%

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

11. Simplified 65.1%

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

12. Final simplification 65.1%

    \[\leadsto \ell \cdot \left(1 - w\right) \]
13. Add Preprocessing

Alternative 9: 63.3% 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 99.2%

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

   1. exp-neg 99.2%

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

   2. remove-double-neg 99.2%

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

   3. associate-*l/ 99.2%

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

   4. *-lft-identity 99.2%

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

   5. remove-double-neg 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in w around 0 96.9%

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

   1. frac-2neg 96.9%

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

   2. div-inv 96.9%

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

7. Applied egg-rr 96.9%

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

8. Taylor expanded in w around 0 65.1%

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

   1. mul-1-neg 65.1%

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

   2. unsub-neg 65.1%

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

10. Simplified 65.1%

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

11. Final simplification 65.1%

    \[\leadsto \ell - w \cdot \ell \]
12. Add Preprocessing

Alternative 10: 56.4% 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 99.2%

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

   1. exp-neg 99.2%

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

   2. remove-double-neg 99.2%

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

   3. associate-*l/ 99.2%

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

   4. *-lft-identity 99.2%

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

   5. remove-double-neg 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in w around 0 96.9%

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

6. Taylor expanded in w around 0 58.8%

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

7. Final simplification 58.8%

   \[\leadsto \ell \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024112 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))