exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 11.4s

Alternatives: 6

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 99.1%

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

2. Final simplification 99.1%

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

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 99.1%

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

   1. exp-neg 99.1%

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

   2. associate-*l/ 99.1%

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

   3. *-lft-identity 99.1%

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

3. Simplified 99.1%

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

4. Final simplification 99.1%

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

Alternative 3: 97.8% 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 99.1%

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

   1. exp-neg 99.1%

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

   2. associate-*l/ 99.1%

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

   3. *-lft-identity 99.1%

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

3. Simplified 99.1%

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

4. Taylor expanded in w around 0 96.0%

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

5. Final simplification 96.0%

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

Alternative 4: 63.9% accurate, 50.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.072:\\ \;\;\;\;w \cdot \left(-\ell\right)\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (if (<= w -0.072) (* w (- l)) l))

C

double code(double w, double l) {
	double tmp;
	if (w <= -0.072) {
		tmp = w * -l;
	} 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 <= (-0.072d0)) then
        tmp = w * -l
    else
        tmp = l
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -0.072) {
		tmp = w * -l;
	} else {
		tmp = l;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -0.072:
		tmp = w * -l
	else:
		tmp = l
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -0.072)
		tmp = Float64(w * Float64(-l));
	else
		tmp = l;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -0.072)
		tmp = w * -l;
	else
		tmp = l;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -0.072], N[(w * (-l)), $MachinePrecision], l]

Derivation

1. Split input into 2 regimes

2. if w < -0.0719999999999999946

   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 32.4%

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

      1. +-commutative 32.4%

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

      2. mul-1-neg 32.4%

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

      3. unsub-neg 32.4%

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

      4. *-commutative 32.4%

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

   7. Simplified 32.4%

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

   8. Taylor expanded in w around inf 32.4%

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

      1. associate-*r* 32.4%

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

      2. neg-mul-1 32.4%

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

   10. Simplified 32.4%

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

   if -0.0719999999999999946 < w

   1. Initial program 98.8%

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

      1. *-commutative 98.8%

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

      2. exp-neg 98.8%

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

      3. div-inv 98.8%

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

      4. add-cube-cbrt 98.8%

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

      5. associate-/r* 98.8%

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

      6. cbrt-unprod 98.8%

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

      7. prod-exp 98.8%

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

   3. Applied egg-rr 98.8%

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

      1. associate-/l/ 98.8%

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

   5. Simplified 98.8%

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

   6. Taylor expanded in w around 0 72.4%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -0.072:\\ \;\;\;\;w \cdot \left(-\ell\right)\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \]

Alternative 5: 63.6% 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 99.1%

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

   1. exp-neg 99.1%

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

   2. associate-*l/ 99.1%

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

   3. *-lft-identity 99.1%

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

3. Simplified 99.1%

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

4. Taylor expanded in w around 0 96.0%

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

5. Taylor expanded in w around 0 60.3%

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

   1. +-commutative 60.3%

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

   2. mul-1-neg 60.3%

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

   3. unsub-neg 60.3%

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

   4. *-commutative 60.3%

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

7. Simplified 60.3%

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

8. Taylor expanded in l around 0 60.3%

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

9. Final simplification 60.3%

   \[\leadsto \ell \cdot \left(1 - w\right) \]

Alternative 6: 56.7% 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 99.1%

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

   1. *-commutative 99.1%

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

   2. exp-neg 99.1%

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

   3. div-inv 99.1%

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

   4. add-cube-cbrt 99.1%

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

   5. associate-/r* 99.1%

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

   6. cbrt-unprod 99.1%

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

   7. prod-exp 99.1%

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

3. Applied egg-rr 99.1%

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

   1. associate-/l/ 99.1%

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

5. Simplified 99.1%

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

6. Taylor expanded in w around 0 52.3%

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

7. Final simplification 52.3%

   \[\leadsto \ell \]

Reproduce

herbie shell --seed 2023227 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))