exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 11.0s

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 99.6%

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

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: 97.7% 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: 73.7% accurate, 27.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[w_, l_] := N[(l - N[(l * N[(w + N[(N[(w * w), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $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 76.7%

   \[\leadsto \color{blue}{\ell + \left(-1 \cdot \left(\ell \cdot w\right) + -1 \cdot \left({w}^{2} \cdot \left(-1 \cdot \ell + 0.5 \cdot \ell\right)\right)\right)} \]
6. Step-by-step derivation

   1. distribute-lft-out 76.7%

      \[\leadsto \ell + \color{blue}{-1 \cdot \left(\ell \cdot w + {w}^{2} \cdot \left(-1 \cdot \ell + 0.5 \cdot \ell\right)\right)} \]

   2. *-commutative 76.7%

      \[\leadsto \ell + -1 \cdot \left(\color{blue}{w \cdot \ell} + {w}^{2} \cdot \left(-1 \cdot \ell + 0.5 \cdot \ell\right)\right) \]

   3. unpow2 76.7%

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

   4. distribute-rgt-out 76.7%

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

   5. metadata-eval 76.7%

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

7. Simplified 76.7%

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

8. Taylor expanded in l around 0 76.7%

   \[\leadsto \ell + -1 \cdot \color{blue}{\left(\ell \cdot \left(w + -0.5 \cdot {w}^{2}\right)\right)} \]
9. Step-by-step derivation

   1. *-commutative 76.7%

      \[\leadsto \ell + -1 \cdot \left(\ell \cdot \left(w + \color{blue}{{w}^{2} \cdot -0.5}\right)\right) \]

   2. unpow2 76.7%

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

10. Simplified 76.7%

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

11. Final simplification 76.7%

    \[\leadsto \ell - \ell \cdot \left(w + \left(w \cdot w\right) \cdot -0.5\right) \]

Alternative 5: 63.5% 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 99.6%

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

   1. *-commutative 99.6%

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

   2. exp-neg 99.6%

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

   3. div-inv 99.6%

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

   4. add-cube-cbrt 99.6%

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

   5. associate-/r* 99.6%

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

   6. cbrt-unprod 99.6%

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

   7. prod-exp 99.6%

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

3. Applied egg-rr 99.6%

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

   1. associate-/l/ 99.6%

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

5. Simplified 99.6%

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

6. Taylor expanded in l around 0 99.5%

   \[\leadsto \color{blue}{{\left(\frac{1}{e^{w} \cdot e^{2 \cdot w}}\right)}^{0.3333333333333333} \cdot {\ell}^{\left(e^{w}\right)}} \]
7. Step-by-step derivation

   1. unpow1/3 99.6%

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

   2. prod-exp 99.6%

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

   3. count-2 99.6%

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

   4. count-2 99.6%

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

   5. metadata-eval 99.6%

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

   6. distribute-lft-neg-in 99.6%

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

   7. rec-exp 99.6%

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

   8. distribute-lft-neg-in 99.6%

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

   9. metadata-eval 99.6%

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

   10. distribute-rgt1-in 99.6%

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

   11. metadata-eval 99.6%

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

8. Simplified 99.6%

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

9. Taylor expanded in w around 0 67.4%

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

    1. neg-mul-1 67.4%

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

    2. unsub-neg 67.4%

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

11. Simplified 67.4%

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

12. Taylor expanded in w around 0 64.5%

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

13. Final simplification 64.5%

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

Alternative 6: 57.1% 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 99.6%

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

   1. *-commutative 99.6%

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

   2. exp-neg 99.6%

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

   3. div-inv 99.6%

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

   4. add-cube-cbrt 99.6%

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

   5. associate-/r* 99.6%

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

   6. cbrt-unprod 99.6%

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

   7. prod-exp 99.6%

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

3. Applied egg-rr 99.6%

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

   1. associate-/l/ 99.6%

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

5. Simplified 99.6%

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

6. Taylor expanded in w around 0 57.0%

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

7. Final simplification 57.0%

   \[\leadsto \ell \]

Reproduce

herbie shell --seed 2023291 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))