id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
2,465 |
c^x = 1 + x \cdot \log_e(c) + \frac{\log_e(c)^2}{2} \cdot x \cdot x + \frac{x^3}{6} \cdot \log_e(c)^3 \cdot \cdots
|
22,791 |
C^{\beta + x} = C^x C^\beta
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-20,090 |
\dfrac{1}{r + (-1)}\cdot 1 = \frac{1}{5\cdot r + 5\cdot (-1)}\cdot 5
|
294 |
\frac{2\cdot x}{x + 2\cdot (-1)}\cdot 1 = \frac{1}{x + 2\cdot \left(-1\right)}\cdot \left(2\cdot x + 4\cdot (-1) + 4\right) = 2 + \dfrac{1}{x + 2\cdot \left(-1\right)}\cdot 4
|
-3,119 |
\sqrt{2}*(4 + 3*\left(-1\right) + 2) = \sqrt{2}*3
|
4,608 |
-(x + \left(-1\right)) + K = 1 + K - x
|
-21,671 |
\frac{1}{3}*2 = 2/3
|
-5,972 |
\frac{1}{30 + q^2 + 11\cdot q}\cdot q = \frac{q}{(6 + q)\cdot (q + 5)}
|
494 |
(-y + x) (y^2 + x^2 + xy) = x \cdot x^2 - y^3
|
21,087 |
1 + x + 0(-1) = x + 1
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-7,079 |
1/12 = \frac38 \cdot 2/9
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-7,999 |
\dfrac{3}{-3i} - \dfrac{12i}{-3i} = \dfrac 1i \left(\dfrac{3}{-3} - \dfrac{12i}{-3} \right)= \dfrac 1i (-1+4i)
|
2,807 |
\dfrac{1}{1 - z}\cdot (4\cdot z + 3\cdot (-1)) = -\frac{1}{z + (-1)}\cdot (4\cdot (z + (-1)) + 1) = -4 + \frac{1}{1 - z}
|
38,800 |
\binom{9}{2} - \binom{3}{2} \cdot \binom{3}{1} = 27
|
13,924 |
4*(x + 1)^2 + 1 = 4*x^2 + 8*x + 4 + 1 = 4*x^2 + 1 + 8*x + 4 < 3*2^x + 8*x + 4
|
-18,258 |
\frac{x \cdot (x + 6 \cdot (-1))}{(x + 6 \cdot (-1)) \cdot (6 \cdot \left(-1\right) + x)} = \frac{-6 \cdot x + x^2}{x^2 - 12 \cdot x + 36}
|
-28,997 |
3 = \frac{1}{2}*\left(3 - -3\right)
|
12,110 |
\sin(\alpha) \cos(\beta) + \sin\left(\beta\right) \cos(\alpha) = \sin\left(\beta + \alpha\right)
|
27,878 |
g^k\cdot g^l = g^{l + k}
|
29,781 |
(y + 1)*(1 + y) = y^2 + y*2 + 1
|
-15,711 |
\dfrac{{(p^{5})^{2}}}{{(p^{4}t^{-4})^{-3}}} = \dfrac{{p^{10}}}{{p^{-12}t^{12}}}
|
1,674 |
(-1) + \sqrt{2} = (2^{1/4} + (-1)) \left(1 + 2^{\frac14}\right)
|
22,406 |
(u_1 + u_2) dR = u_1 Rd + u_2 Rd
|
35,763 |
1 - \frac{\sin(2\cdot x)}{2} = 1 - \sin(x)\cdot \cos(x) = \sin^2(x) + \cos^2\left(x\right) - \sin(x)\cdot \cos\left(x\right)
|
14,622 |
(c_1 c_2) (c_1 c_2) (c_1 c_2) = 1 = 1 = c_1^3 c_2^3
|
-639 |
(e^{\frac{7πi}{6}})^5 = e^{5iπ*7/6}
|
-1,792 |
\pi \dfrac{1}{12}7 - \frac{1}{12}7 \pi = 0
|
26,478 |
p^2 + 2qp + q^2\cdot 2 = q \cdot q + (q + p)^2
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-26,201 |
5 \cdot 6 - \frac126 = 30 + 3\left(-1\right) = 27
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34,360 |
-p + p^3 + p * p = (-1) + p^2 + p^2 - p + p^2 - p + p^2 - p*2 + 1 + p^3 - p^2*3 + p*3
|
3,571 |
1 + x^4 = 1 + 2x^2 + x^4 - 2x^2 = \left(1 + x^2\right)^2 - (\sqrt{2} x) \cdot (\sqrt{2} x)
|
26,102 |
a_n + a_{\left(-1\right) + n} + \dots + a_2 + a_1 = a_1 + a_2 + \dots + a_{(-1) + n} + a_n
|
3,268 |
z - \tfrac{z^3}{3!} + \dfrac{z^5}{5!} - z^7/7! - \cdots = \sin{z}
|
10,535 |
\frac{n^2}{1 + n^2} = -\frac{1}{n^2 + 1} + 1
|
33,741 |
\frac{1}{9}*7 = -\frac{10}{9} + \frac{1}{9}*17
|
5,563 |
6\cdot (-1) + 3\cdot x = x + 2\cdot (x + 3\cdot (-1))
|
-6,745 |
40/100 + \frac{1}{100}*6 = \frac{1}{100}*6 + 4/10
|
143 |
r*(y_1 + \lambda*y_0) = r*\lambda*y_0 + r*y_1
|
-7,008 |
3/8\cdot \frac17\cdot 6 = \frac{9}{28}
|
45,752 |
2^2\times 11\times 131 = 5764
|
-1,454 |
\frac{1}{63} \cdot 72 = \tfrac{8}{63 \cdot \dfrac19} \cdot 1 = \frac{8}{7}
|
10,360 |
(\sqrt{2} + 2) (11 - 7 \sqrt{2}) = \left(2 - \sqrt{2}\right) \left(5 + \sqrt{2}\right)
|
-30,269 |
\frac{1}{c + \left(-1\right)}\left(c * c + 2c + 3(-1)\right) = \frac{(c + 3) (c + \left(-1\right))}{c + (-1)} = c + 3
|
-20,247 |
42 q/(q*(-24)) = ((-6) q)/(q*(-6)) (-\dfrac{1}{4}7)
|
-1,704 |
\frac{11}{6} \pi - \pi*4/3 = \frac{\pi}{2}
|
7,707 |
-n^2 + \left(n + 1\right)^2 = n \cdot 2 + 1
|
-4,335 |
\dfrac{x\times 60}{x^2 \times x\times 50}\times 1 = \frac{x}{x^3}\times 60/50
|
-28,842 |
\tfrac{1}{7} - n\cdot 9/7 + 6/7 = 6/7 + \frac17 - n\cdot 9/7
|
-3,056 |
\sqrt{175} - \sqrt{28} = -\sqrt{4 \cdot 7} + \sqrt{25 \cdot 7}
|
-8,792 |
25 = 1/2*10*5
|
10,637 |
E_{i,j} Z = E_{i,j} Z
|
38,027 |
48\cdot 16/24 = 32
|
-5,179 |
3.360 \times 10 = {3.360 \times 10} \times 10^{2} = 3.360\times 10^{3}
|
23,104 |
1 + 4*r = -7 + 4*\left(r + 2\right)
|
29,480 |
9*(-1) + 121 = 112
|
817 |
0 = a + b*x \implies x = -a/b = b*1/2/b = \frac{1}{2}
|
43,185 |
8\cdot 2 + 1 = 17
|
2,624 |
(\dfrac{z}{-z + 4 \cdot (-1)})^{1/2} = (\frac{(-1) \cdot z}{z + 4})^{1/2} = \frac{\left(-z\right)^{1/2}}{(4 + z)^{1/2}}
|
-19,023 |
23/30 = A_s/\left(25\cdot \pi\right)\cdot 25\cdot \pi = A_s
|
11,910 |
\cos\left(\tfrac{\pi}{2} - w\right) = \sin(w)
|
23,487 |
2^g + 3^f = (1 + 1)^g + \left(1 + 2\right)^f \leq 1 + g + 1 + f\cdot 2
|
2,148 |
(t^2 + q^2 + t*q)*\left(-t + q\right) = -t^3 + q^3
|
30,308 |
5^{n*2} = (5^n)^2 + 0 * 0
|
558 |
\left(1 + y^3 = 0 \Rightarrow -2 = y \cdot y \cdot y + (-1)\right) \Rightarrow -2 = (y + \left(-1\right)) \cdot (1 + y^2 + y)
|
17,016 |
E[\sum_{k=1}^x Q_k] = \sum_{k=1}^x E[Q_k]
|
-19,463 |
\frac{9}{5} \cdot 3/4 = \tfrac{3 / 4}{5 \cdot 1/9} \cdot 1
|
25,441 |
\mathbb{E}\left(Z_1\right) \mathbb{E}\left(Z_2\right) = \mathbb{E}\left(Z_1 \mathbb{E}\left(Z_2\right)\right)
|
30,726 |
2x^2 + 3x + 1 = (2x + 1) (1 + x)
|
15,176 |
z_x = x*2 f' y \implies y^2 z_x = x f' y y y*2
|
3,899 |
(2*\sqrt{2} + 5)*\left(5 - 2*\sqrt{2}\right) = 17
|
43,262 |
\left\lceil{\tfrac{6*75}{100}}\right\rceil = 5
|
11,140 |
x^2 + z^2 = 0.5\cdot \left(\left(x - z\right) \cdot \left(x - z\right) + \left(x + z\right)^2\right)
|
22,680 |
1 + 27 - 2\cdot 8 = 12
|
-15,298 |
\dfrac{{y^{4}}}{{y^{8}z^{-2}}} = \dfrac{{y^{4}}}{{y^{8}}} \cdot \dfrac{{1}}{{z^{-2}}} = y^{{4} - {8}} \cdot z^{- {(-2)}} = y^{-4}z^{2}
|
-19,738 |
\frac{35}{8} = 5 \cdot 7/(8)
|
178 |
x = x \times 0 \Rightarrow x = 0
|
-1,495 |
-\dfrac75\cdot 5/2 = \frac{\frac{1}{2}\cdot 5}{\left(-5\right)\cdot 1/7}
|
9,566 |
\frac{2*y}{\sqrt{1 + y^2} + y + (-1)} = \dfrac{1}{y + (-1) + \sqrt{1 + y^2}}*(y * y + 1 - y^2 + y*2 + (-1))
|
7,056 |
\sin(\arccos(z)) = (1 - z^2)^{1/2}
|
25,122 |
8!/(2!*3!) = 3360
|
20,087 |
\binom{4}{2}*2*9! - 24*8! = 8!*84
|
22,914 |
N \cdot A = N \cdot A
|
-2,005 |
\pi/2 = \pi/12 + \pi \cdot 5/12
|
21,764 |
2*(1 + n*2) = n*4 + 2
|
12,237 |
2*\pi + 0 = 2*\pi
|
15,648 |
\left(\tfrac{1}{e^0} + 0\right)*2 + 0 + 0 = 2
|
11,732 |
x * x * x + \left(-1\right) = ((-1) + x)*(1 + x^2 + x)
|
18,025 |
1 = det\left(A\cdot F\right) = det\left(A\right)\cdot det\left(F\right)
|
16,869 |
h \cdot m = h_1 \cdot m_1 \Rightarrow h_1 = m/(m_1) \cdot h
|
4,149 |
(n + 1) \cdot (2 + n) = 2 + n^2 + n \cdot 3
|
10,404 |
(\frac{1}{2}(1 + 5^{1/2}))^2 = \left(5^{1/2} + 3\right)/2
|
23,554 |
8 = 2 + 3*2
|
-12,128 |
\frac{1}{36}31 = \dfrac{1}{18 \pi}s*18 \pi = s
|
15,532 |
b = \arcsin{a}\Longrightarrow \sin{b} = a
|
-26,401 |
\gamma^l \gamma^n = \gamma^{l + n}
|
20,666 |
\frac{\mathrm{d}}{\mathrm{d}z} 1/z = -\dfrac{1}{z \cdot z} = -\frac{1}{z \cdot z}
|
23,692 |
\left(1 + x^k\right) \cdot (x^k + \left(-1\right)) = x^{k \cdot 2} + (-1)
|
4,827 |
(-1) + \int\limits_0^1 \frac{1}{x^2}\,dx = \lim_{x \to 0^+} \frac1x - 1 + (-1)
|
28,787 |
\dfrac{1}{2^{1/2}} \cdot 2^{(j + 1)/2} = 2^{j/2}
|
-13,232 |
\frac{0.000243}{-0.0009} = -0.27
|
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