id
int64 -30,985
55.9k
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stringlengths 5
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|---|---|
-3,402 |
13^{1/2}*\left(3 + \left(-1\right)\right) = 13^{1/2}*2
|
7,897 |
(x + 1) x/2 = x \frac{1}{2} ((-1) + x) + x
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35,320 |
\tan\left(\frac{\pi}{2} - x\right) = \cot(x)
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18,719 |
\sec^2(x/2) = \frac{1}{(1 + \cos(x)) \cdot 1/2} = \dfrac{1}{1 + \cos\left(x\right)} \cdot 2
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23,527 |
\theta^2 = 9 \cdot x \cdot x + 6 \cdot x + 1 = 3 \cdot \left(3 \cdot x^2 + 2 \cdot x\right) + 1 \Rightarrow \theta^2 + (-1) = (x \cdot 2 + x^2 \cdot 3) \cdot 3
|
-22,304 |
(x + 6)\times (8 + x) = 48 + x^2 + 14\times x
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7,076 |
\sum_{x=l}^6 (1 - s_x) + l + (-1) = 6\cdot s_l rightarrow l + \sum_{x=l + 1}^6 (-s_x + 1) = s_l\cdot 7
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6,952 |
-1/3 = \frac{1}{5 + 2 \cdot (-1)} \cdot \left(3 + 4 \cdot (-1)\right)
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5,468 |
1 + 3 \cdot t^1 + 5 \cdot t^2 + \ldots = \frac{2}{\left(t + (-1)\right)^2} \cdot t - \frac{1}{t + (-1)} = \dfrac{1}{(t + (-1))^2} \cdot (t + 1)
|
9,560 |
d^k*d^m = d^{m + k}
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17,621 |
E\left[t'\right] \cdot y_0 \cdot E\left[t\right] = E\left[t' + t\right] \cdot y_0
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43,047 |
30 = \dfrac14\cdot 5!
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-11,905 |
0.1575 = 1.575\cdot 0.1
|
25,569 |
z + a = (\sqrt{z + a})^2
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6,223 |
\left(2^{2^k}\right)^2 = 2^{2^k}\cdot 2^{2^k} = 2^{2^k\cdot 2} = 2^{2^{k + 1}}
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6,808 |
z^2 + z + 1 = z^2 - 2 \cdot z + 1 + 3 \cdot z + 3 \cdot (-1) + 3 = (z + \left(-1\right))^2 + 3 \cdot (z + (-1)) + 3
|
-20,746 |
\frac{7}{7}*\dfrac{1}{5*\left(-1\right) - 9*r}*(5*r + 2) = \frac{14 + r*35}{-63*r + 35*(-1)}
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7,651 |
(x + (-1)) \left(x + 1\right) = \left(-1\right) + x x
|
17,266 |
g \cdot h/x = \frac{g}{x} \cdot h
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38,135 |
\binom{1}{1}\cdot \binom{1}{1}\cdot \binom{8}{4} = \binom{8}{4}
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-23,706 |
\dfrac{1}{20} = 1/(4*5)
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-16,512 |
12 \cdot \sqrt{9 \cdot 7} = \sqrt{63} \cdot 12
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23,033 |
(-\frac{y}{z} + 1) \sqrt{y^2 + z^2} \sqrt{y^2 + z^2} = (z^2 + y y) \left(1 - y/z\right)
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50,861 |
-8+24 = 16
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30,464 |
9\cdot x \cdot x + 16\cdot y^2\cdot z^4 = 9\cdot x^2 - -16\cdot y^2\cdot z^4 = \left(3\cdot x\right) \cdot \left(3\cdot x\right) - \left(4\cdot i\cdot y\cdot z \cdot z\right)^2
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22,808 |
x^{x^{x^{x^{\dots}}}} = 2 rightarrow x * x = 2
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35,185 |
3 = 4/2 + 2/2
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6,966 |
A - \theta A \theta = A \theta^2 - \theta A \theta = \left(A,\theta\right)
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-12,059 |
\frac{8}{15} = \mu/(6\cdot \pi)\cdot 6\cdot \pi = \mu
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39,383 |
\sin(m \cdot \pi + \frac{\pi}{2}) = \sin{m \cdot \pi} \cdot \cos{\frac{1}{2} \cdot \pi} + \cos{m \cdot \pi} \cdot \sin{\pi/2} = 0 \cdot 0 + (-1)^m
|
1,391 |
2^{n/2} \cdot 2^n = 2^{n + \dfrac{1}{2} \cdot n} = 2^{\frac32 \cdot n}
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34,550 |
\sec(\arctan\left(x\right)) = (x^2 + 1)^{1/2}
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33,160 |
D = \left(C \cap D\right) \cup (D \cap x) = D \cap \left(C \cup x\right)
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-9,952 |
0.01 \times (-48) = -\frac{48}{100} = -0.48
|
8,313 |
|c_2 + y| = |y - c_1 + c_1 + c_2| \leq |y - c_1| + |c_1 + c_2|
|
14,113 |
\tan{z} = \cot\left(\tfrac{\pi}{2} - z\right) = \frac{1}{\tan\left(\pi/2 - z\right)}
|
24,377 |
(b - y)^2 = y^2 + y = b^2 - 2\cdot b\cdot y + y \cdot y
|
21,831 |
d + 0 + 0 = 0 \Rightarrow d = 0
|
30,144 |
2\times 3\times 3/2 - 16/3 - \tfrac23 = 9 + 6\times \left(-1\right) = 3
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-17,279 |
1.252 = \tfrac{125.2}{100}
|
936 |
\dfrac{1}{6^3} \cdot (91 + 1050 + 1134) = \frac{1}{216} \cdot 2275 \approx 10.53
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31,783 |
3 + 5 \cdot x = (x \cdot 2 + 1) \cdot 4 - 3 \cdot x + \left(-1\right)
|
24,351 |
\frac12 \cdot (\cos\left(2 \cdot r\right) + 1) = \cos^2(r)
|
51,009 |
\binom{4+2}{2}=\binom{6}{2}=15
|
38,875 |
\dfrac{1}{\frac10} = \dfrac{1}{\frac10}
|
11,406 |
(g_2 + g_1)\cdot a = a\cdot g_2 + g_1\cdot a
|
5,814 |
\frac{1}{31} \cdot 10 \cdot 2 \cdot C - 21/31 \cdot C = \frac{1}{31} \cdot ((-1) \cdot C)
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10,174 |
2*3^0 + 3^1*2 + 2*3 * 3 + ... + 2*3^{k + (-1)} = \left(-1\right) + 3^k
|
8,030 |
\frac14\pi + \tfrac{\pi}{3} = \frac{7\pi}{12}1
|
230 |
(A \cdot A - B \cdot A + B \cdot B) \cdot \left(A + B\right) = A^3 + B^3
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24,375 |
(-1) + p^{2^{k_0}} = (\left(-1\right) + p)*(1 + p)*(1 + p^2)*(p^{2^2} + 1)*...*(p^{2^{(-1) + k_0}} + 1)
|
5,464 |
-a^2/2 + \dfrac{f^2}{2} = -\dfrac{aa}{2} + \dfrac{ff}{2}
|
985 |
d^{x_2} \cdot d^{x_1} \cdot ... \cdot d^{x_l} = d^{x_1 + x_2 + ... + x_l}
|
13,095 |
i=\{cos\frac{\pi}{2}+ isin\frac{\pi}{2}\}
|
20,999 |
\dfrac{y^{1/2}}{e^{-3\cdot y}} = y^{1/2}\cdot e^{y\cdot 3}
|
4,285 |
1/n + 1/\left(x\cdot n\right) = \tfrac1n\cdot \left(1 + \dfrac{1}{x}\right)
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22,456 |
E[Y\cdot 2] = 2\cdot E[Y]
|
35,170 |
0\le(\lvert a_k\rvert - \lvert b_k \rvert)^2 = \lvert a_k\rvert^2 - 2\lvert a_k\rvert \lvert b_k\rvert + \lvert b_k\rvert^2 = a_k^2 - 2\lvert a_k b_k\rvert + b_k^2
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39,317 |
\left(1 + 2 + 3 + 4 + 5 + 6\right)/6 = 3.5
|
-7,081 |
\frac17*3*0 = 0
|
8,921 |
h f h = f h^2
|
4,833 |
2\cdot x^2 + 7 = 5 \cdot 5\cdot \left(x + 2\cdot (-1)\right)^2 = 25\cdot x^2 - 100\cdot x + 100
|
18,289 |
\pi \cdot 2 \cdot \frac{p^3}{2} + 0 = \pi \cdot p^3
|
-21,013 |
-\frac14 \cdot \frac{1}{(-1) + r} \cdot (\left(-1\right) + r) = \frac{1}{4 \cdot r + 4 \cdot (-1)} \cdot \left(1 - r\right)
|
8,995 |
(z^3 + 1)/z = \dfrac{1}{z} + z^2
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-11,605 |
-16 + 8 + i \cdot 24 = 24 \cdot i - 8
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37,707 |
x \cdot Q = x \cdot Q
|
-7,598 |
\frac{6 - i*14}{2 - i*2}*\tfrac{2 + i*2}{2 + i*2} = \frac{-14*i + 6}{-i*2 + 2}
|
11,333 |
|X \cdot x| = |X| \cdot |x|
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-23,322 |
\frac{1}{2 \cdot 3} = \frac16
|
31,892 |
2\cdot (1 - \sqrt{x}) = (1 - \sqrt{x})/1 + \dfrac{1}{\sqrt{x}}\cdot (\sqrt{x} - x)
|
12,982 |
0 = 3*x + e + d*4 \Rightarrow e = -d*4 - 3*x
|
54,131 |
{12 \choose 2} = 66
|
-2,877 |
(25 \cdot 13)^{1/2} - (9 \cdot 13)^{1/2} = -117^{1/2} + 325^{1/2}
|
-13,789 |
9 + 3 \cdot \frac{40}{10} = 9 + 3 \cdot 4 = 9 + 3 \cdot 4 = 9 + 12 = 21
|
15,203 |
\dfrac{x!}{s! (-s + x)!} = {x \choose s}
|
11,435 |
a \cdot a + b \cdot b - b\cdot a\cdot 2 = (-b + a) \cdot (-b + a)
|
4,772 |
\left(z - \lambda\right)^l = (z - \lambda)^{\left(-1\right) + l} \cdot (-\lambda + z)
|
-9,436 |
-27*U + 54*(-1) = -U*3*3*3 - 2*3*3*3
|
14,848 |
14^2 + 8 \cdot 8 = 2^2 + 16 \cdot 16
|
27,459 |
y*A = \lambda*y\Longrightarrow \frac{A*y}{A} = \frac{\lambda*y}{A}
|
8,316 |
(m + g)^2 = m^2 \cdot 2\Longrightarrow (m - g)^2 = g^2 \cdot 2
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-30,262 |
\frac{x^2 - 12 \cdot x + 20}{x + 10 \cdot (-1)} = \dfrac{1}{x + 10 \cdot (-1)} \cdot \left(x + 2 \cdot \left(-1\right)\right) \cdot \left(x + 10 \cdot (-1)\right) = x + 2 \cdot \left(-1\right)
|
36,137 |
\binom{n + 1}{n} = n + 1
|
6,024 |
\frac{1}{4}\cdot (3\cdot (x + y) \cdot (x + y) + (x - y)^2) = y \cdot y + x^2 + y\cdot x
|
19,683 |
\int \sum_{i=1}^\infty b_i\,\mathrm{d}x = \sum_{i=1}^\infty \int b_i\,\mathrm{d}x
|
8,947 |
Var\left(B\right) = Var\left(-B\right)
|
22,723 |
1 + 2\cdot m = (1 + m)^2 - m^2
|
13,541 |
19 = 5^2 + 2^2 - 5\cdot 2
|
-2,621 |
((-1) + 3)*\sqrt{7} = \sqrt{7}*2
|
21,558 |
(-1)^{x + 2\left(-1\right)} = (-1)^x
|
19,266 |
\frac{1}{1}\cdot 5 = \tfrac12\cdot 10
|
-17,333 |
0.654 = \dfrac{65.4}{100}
|
8,524 |
( c, h_b \cdot B) = h_b \cdot B \cdot c
|
38,909 |
\int_{0}^{\pi/2}\sin\left(\frac{1}{\cos x}\right)\,dx = \int_{0}^{\pi/2}\sin\left(\frac{1}{\sin x}\right)\,dx = \int_{0}^{1}\frac{\sin(1/x)}{\sqrt{1-x^2}}\,dx =\int_{1}^{+\infty}\frac{\sin(x)}{x\sqrt{x^2-1}}
|
22,918 |
y = \left(y \cdot 20 + 3 + 3(-1)\right)/20
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-21,026 |
\dfrac{10}{10} \cdot \dfrac{4 + 4 \cdot l}{9 \cdot l} = \frac{1}{l \cdot 90} \cdot (40 + l \cdot 40)
|
-20,290 |
\frac{x \cdot 3 + 3}{-x \cdot 6 + 18} = 3/3 \dfrac{1}{-2 x + 6} (1 + x)
|
-20,296 |
\frac{8}{8} \frac{1}{r + 6(-1)}\left(5\left(-1\right) - r\right) = \frac{1}{8r + 48 (-1)}(-8r + 40 (-1))
|
-4,622 |
2*(-1) + x^2 - x = (x + 2*(-1))*(x + 1)
|
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