exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 12.2s

Alternatives: 4

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 99.5%

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

Alternative 2: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. neg-sub0 99.5%

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

   2. exp-diff 99.5%

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

   3. remove-double-neg 99.5%

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

   4. associate-*l/ 99.5%

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

   5. 1-exp 99.5%

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

   6. *-lft-identity 99.5%

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

   7. remove-double-neg 99.5%

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

3. Simplified 99.5%

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

Alternative 3: 97.4% 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 99.5%

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

   1. neg-sub0 99.5%

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

   2. exp-diff 99.5%

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

   3. remove-double-neg 99.5%

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

   4. associate-*l/ 99.5%

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

   5. 1-exp 99.5%

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

   6. *-lft-identity 99.5%

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

   7. remove-double-neg 99.5%

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

3. Simplified 99.5%

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

   1. frac-2neg 99.5%

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

   2. div-inv 99.5%

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

6. Applied egg-rr 99.5%

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

7. Taylor expanded in w around inf 99.5%

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

   1. add-exp-log 94.9%

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

   2. log-pow 94.9%

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

9. Applied egg-rr 94.9%

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

10. Taylor expanded in w around 0 98.4%

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

11. Final simplification 98.4%

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

Alternative 4: 56.9% 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 99.5%

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

3. Taylor expanded in w around 0 55.1%

   \[\leadsto \color{blue}{\ell} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))