exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 13.4s

Alternatives: 6

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

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

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 99.8%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
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. Final simplification 99.8%

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

Alternative 2: 97.4% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Taylor expanded in w around 0 98.1%

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

   1. clear-num 98.2%

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

   2. inv-pow 98.2%

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

6. Applied egg-rr 98.2%

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

   1. unpow-1 98.2%

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

8. Simplified 98.2%

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

9. Final simplification 98.2%

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

Alternative 3: 97.5% accurate, 2.9× speedup

Math

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

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(Float64(-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 99.8%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
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. Taylor expanded in w around 0 98.1%

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

   1. div-inv 98.1%

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

   2. rec-exp 98.1%

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

6. Applied egg-rr 98.1%

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

7. Final simplification 98.1%

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

Alternative 4: 97.5% 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 99.8%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
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. Taylor expanded in w around 0 98.1%

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

5. Final simplification 98.1%

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

Alternative 5: 63.4% accurate, 61.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Taylor expanded in w around 0 98.1%

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

5. Taylor expanded in w around 0 64.3%

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

   1. mul-1-neg 64.3%

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

   2. unsub-neg 64.3%

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

7. Simplified 64.3%

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

8. Final simplification 64.3%

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

Alternative 6: 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 99.8%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
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-cube-cbrt 98.6%

      \[\leadsto \frac{{\color{blue}{\left(\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}\right)}}^{\left(e^{w}\right)}}{e^{w}} \]

   2. unpow-prod-down 98.6%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}^{\left(e^{w}\right)} \cdot {\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}}}{e^{w}} \]

   3. pow2 98.6%

      \[\leadsto \frac{{\color{blue}{\left({\left(\sqrt[3]{\ell}\right)}^{2}\right)}}^{\left(e^{w}\right)} \cdot {\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}}{e^{w}} \]

   4. pow-pow 98.6%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\ell}\right)}^{\left(2 \cdot e^{w}\right)}} \cdot {\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}}{e^{w}} \]

5. Applied egg-rr 98.6%

   \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\ell}\right)}^{\left(2 \cdot e^{w}\right)} \cdot {\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}}}{e^{w}} \]
6. Step-by-step derivation

   1. *-commutative 98.6%

      \[\leadsto \frac{{\left(\sqrt[3]{\ell}\right)}^{\color{blue}{\left(e^{w} \cdot 2\right)}} \cdot {\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}}{e^{w}} \]

7. Simplified 98.6%

   \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\ell}\right)}^{\left(e^{w} \cdot 2\right)} \cdot {\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}}}{e^{w}} \]
8. Step-by-step derivation

   1. pow-unpow 98.6%

      \[\leadsto \frac{\color{blue}{{\left({\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}\right)}^{2}} \cdot {\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}}{e^{w}} \]

   2. pow-plus 98.6%

      \[\leadsto \frac{\color{blue}{{\left({\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}\right)}^{\left(2 + 1\right)}}}{e^{w}} \]

   3. metadata-eval 98.6%

      \[\leadsto \frac{{\left({\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}\right)}^{\color{blue}{3}}}{e^{w}} \]

9. Applied egg-rr 98.6%

   \[\leadsto \frac{\color{blue}{{\left({\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}\right)}^{3}}}{e^{w}} \]
10. Step-by-step derivation

    1. add-cube-cbrt 98.3%

       \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{{\left({\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}\right)}^{3}}{e^{w}}} \cdot \sqrt[3]{\frac{{\left({\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}\right)}^{3}}{e^{w}}}\right) \cdot \sqrt[3]{\frac{{\left({\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}\right)}^{3}}{e^{w}}}} \]

    2. pow3 98.3%

       \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{{\left({\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}\right)}^{3}}{e^{w}}}\right)}^{3}} \]

    3. cbrt-div 98.4%

       \[\leadsto {\color{blue}{\left(\frac{\sqrt[3]{{\left({\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}\right)}^{3}}}{\sqrt[3]{e^{w}}}\right)}}^{3} \]

    4. rem-cbrt-cube 98.6%

       \[\leadsto {\left(\frac{\color{blue}{{\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}}}{\sqrt[3]{e^{w}}}\right)}^{3} \]

11. Applied egg-rr 98.6%

    \[\leadsto \color{blue}{{\left(\frac{{\left(\sqrt[3]{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\right)}^{3}} \]

12. Taylor expanded in w around 0 57.2%

    \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \ell} \]
13. Step-by-step derivation

    1. pow-base-1 57.2%

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

    2. *-lft-identity 57.2%

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

14. Simplified 57.2%

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

15. Final simplification 57.2%

    \[\leadsto \ell \]

Reproduce

herbie shell --seed 2023306 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))