id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
23,425 |
\cos(-u + w) - \cos\left(w + u\right) = 2*\sin{w}*\sin{u}
|
19,472 |
3^{1/2} \cdot 81 = 3^{\frac{9}{2}}
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-10,512 |
-\frac{1}{n^2*4}\left(n*12 + 4(-1)\right) = \frac{4}{4} (-\frac{n*3 + (-1)}{n * n})
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24,753 |
1/16 = (-3/4 + 7/8)/2
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21,719 |
\cos{t} = \dfrac{\sec^2{t}}{\sec^3{t}}
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-16,550 |
7\cdot 99^{1/2} = 7\cdot (9\cdot 11)^{1/2}
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7,902 |
x^3 - y * y * y = (-y + x) (y^2 + x^2 + xy)
|
8,041 |
\alpha\cdot (x + 1) = x\cdot \alpha + \alpha
|
33,084 |
\sin^2\left(4\cdot \pi/7\right) - \sin^2(\dfrac{2\cdot \pi}{7}) = 2\cdot \sin(\frac{\pi}{7})\cdot \cos(3\cdot \pi/7) \gt 0
|
13,034 |
(1 + x)^2 + (-1) = 2 \cdot x + x \cdot x
|
5,068 |
\mathbb{E}[X] + \mathbb{E}[Q] = \mathbb{E}[X + Q]
|
23,049 |
5 + 2 + 4 \cdot \left(-1\right) = 3
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-9,485 |
y\cdot 2\cdot 2\cdot 3\cdot 3 = y\cdot 36
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30,516 |
24/45 = \frac{1}{10!}\cdot \left(9!\cdot 2 + 8!\cdot 2\cdot 8 + 8!\cdot 2\cdot 7\right)
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-5,344 |
\frac{1}{10}\cdot 15.6 = \frac{15.6}{10}
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15,248 |
\binom{n}{3}\cdot 3 + \binom{n}{4}\cdot 3 = \binom{\binom{n}{2}}{2}
|
12,661 |
(c + b) \cdot a = a \cdot c + b \cdot a
|
25,120 |
\frac{1}{132} \cdot 42 + 20/132 = 62/132 = \frac{1}{66} \cdot 31
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-15,989 |
-\frac{28}{10} = \frac{2}{10}\cdot 10 - 6\cdot 8/10
|
12,406 |
1 = (48 \cdot (-1) + 49)^{1 / 2}
|
7,023 |
x*a^2 = a*x*a
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18,319 |
\sqrt{|a_n|^2} = |a_n|
|
25,994 |
G*B = B*G
|
-545 |
π \times 11 - 10 \times π = π
|
-4,790 |
4.16 \times 10 = \frac{4.16}{10^6} \times 10 = \frac{4.16}{10^5}
|
-20,015 |
\dfrac{1}{-r\cdot 2 + 3}\cdot \left(r + 9\cdot (-1)\right)\cdot 6/6 = \frac{r\cdot 6 + 54\cdot (-1)}{18 - 12\cdot r}
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10,872 |
33! = 2^{33 + 2 \cdot \left(-1\right)} \cdot 4043484860477916195764296875
|
-18,655 |
25/14 = \frac{50}{28}
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7,603 |
21 \cdot 21^2 + 3^3 + 5^3 + 19^3 = 1^3 + 9^3 + 15^3 + 23^3
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22,875 |
z^3 + z*3 + 4\left(-1\right) = (z^2 + z + 4) \left((-1) + z\right)
|
32,140 |
\sqrt{9*\left(-1\right)} = \sqrt{9}*\sqrt{-1} = 3*i
|
38,933 |
\frac{20}{50} \cdot 7 = 2.8
|
2,824 |
z^{1/3} z^{1/6} = z^{\frac{1}{3} + 1/6} = z^{1/2}
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43,837 |
\sin{\frac{1}{2} \cdot \pi} = 1
|
838 |
\frac{1}{\binom{5}{2}} \binom{4}{2} = 6/10 = 3/5
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7,035 |
y \cdot z = 1 \implies \frac1z = y
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27,833 |
\dfrac{2}{16} + 1/17 = \dfrac{1}{16} + \frac{1}{16} + \tfrac{1}{17}
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-4,387 |
\frac{p^5}{p^2}\cdot 8/14 = \frac{p^5}{14\cdot p^2}\cdot 8
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-10,601 |
\frac{35}{5 \cdot t + 15 \cdot (-1)} = \frac{7}{t + 3 \cdot (-1)} \cdot \frac55
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35,741 |
0 = -|x|^{p + 2 \cdot (-1)} \cdot x + a \Rightarrow |x|^{2 \cdot (-1) + p} \cdot x = a
|
11,148 |
\frac{\epsilon^2}{1 + \epsilon} = -(1 - \epsilon) + \dfrac{1}{1 + \epsilon}
|
17,574 |
6 \cdot (-1) + x \cdot x - x = 0 rightarrow 3 = x
|
519 |
\frac{1}{\mathbb{E}\left[T_2\right]} \cdot \mathbb{E}\left[T_1\right] = \mathbb{E}\left[\dfrac{1}{T_2} \cdot T_1\right]
|
-3,022 |
2\sqrt{10} = \left(4 + 2(-1)\right) \sqrt{10}
|
-4,673 |
\frac{1}{z \cdot z + (-1)}\cdot \left(-4\cdot z + 2\cdot \left(-1\right)\right) = -\frac{1}{1 + z} - \frac{3}{(-1) + z}
|
-4,210 |
\dfrac52 \cdot a^3 = \frac{5}{2} \cdot a^3
|
24,691 |
-1^2 + \left(x^2\right)^2 = (-1) + x^4
|
18,575 |
1/9 + \frac18 = 17/72
|
11,620 |
(\sqrt{5})^2 = 5 + \sqrt{30}\cdot 0
|
-22,298 |
(1 + x)\cdot (x + 7\cdot (-1)) = 7\cdot (-1) + x \cdot x - 6\cdot x
|
-19,920 |
-\frac{29}{20} = -1.45
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22,678 |
1 - \frac{1}{z^4 + 1} = \frac{z^4}{z^4 + 1}
|
5,060 |
\frac{1}{-1} \cdot \left(-\left(-1\right)^2 + 2 \cdot |-1|\right)^{1/2} = -1
|
21,744 |
0 = (-1) + 2 \cdot \sin{z} \Rightarrow 1/2 = \sin{z}
|
36,840 |
exp(x) = \frac{d}{dx} exp(x)
|
31,822 |
n \cdot n + 1 = 2n \cdot n - n^2 + \left(-1\right)
|
16,993 |
\frac{\sin(y^2 \cdot z)}{z \cdot y^2} \cdot \dfrac{y^2 \cdot z}{z^2 + y^2} = \frac{1}{z^2 + y^2} \cdot \sin(z \cdot y^2)
|
-20,006 |
\frac{y\cdot 80 + 48 (-1)}{90 y + 54 \left(-1\right)} = \frac89 \frac{10 y + 6\left(-1\right)}{10 y + 6(-1)}
|
21,889 |
a_{2*k + 1} = \frac{1}{a_{\left(-1\right) + k*2}}*(1 + a_{k*2} * a_{k*2}) \implies a_{(-1) + k*2}*a_{2*k + 1} + (-1) = a_{2*k}^2
|
23,828 |
2*\left((-1)*0.5 + 2.5\right) = 4
|
24,710 |
(2 + y)*((-1) + y) = y^2 + y + 2*(-1)
|
8,192 |
(d\cdot c)^{\frac{1}{2}} = (c\cdot d)^{1 / 2}
|
1,539 |
x^2 - x \cdot 3 + 6 = 8 + x^2 - x \cdot 3 + 2 \cdot (-1)
|
23,320 |
6^{1/3} \cdot 6^{1/3} = (2^{\frac13})^2 \cdot 3^{1/3} \cdot 3^{1/3}
|
-9,453 |
z \cdot 36 + 84 \cdot (-1) = -7 \cdot 2 \cdot 2 \cdot 3 + z \cdot 2 \cdot 2 \cdot 3 \cdot 3
|
11,566 |
x^2 = \frac{1}{2}*x^2 + \frac{x^2}{2}
|
-27,099 |
\sum_{x=1}^\infty \frac{1}{x\cdot 4^x}\cdot (-8 + 4)^x = \sum_{x=1}^\infty \frac{(-4)^x}{x\cdot 4^x} = \sum_{x=1}^\infty \frac{(-1)^x\cdot 4^x}{x\cdot 4^x} = \sum_{x=1}^\infty \left(-1\right)^x/x
|
-1,740 |
\pi \cdot 5/4 = \pi \cdot 5/4 + 0
|
12,610 |
k\cdot \left(m + (-1)\right) - m = -k + k\cdot m - m
|
36,124 |
|1/x + x| = |\frac{1}{x \cdot (-1)} - x|
|
29,229 |
0\cdot x + x\cdot 0 + 0\cdot x = x\cdot 0 + x\cdot 0
|
2,843 |
\frac12\cdot 4 + \frac12\cdot 8 = (4 + 8)/2 = 12/2
|
20,083 |
(-p + x) \times 16 = -p \Rightarrow 15 \times p = 16 \times x
|
2,177 |
n!! = n \cdot (n - 2) \cdot ... \cdot 3 \cdot 1
|
8,604 |
\frac{1}{1 + x}\left(2(-1) + x \cdot x \cdot x + x^2\cdot 4 + x\right) = x^2 + x\cdot 3 + 2(-1)
|
-22,800 |
\frac{1}{32}*24 = \frac{8*3}{4*8}
|
14,692 |
\|v\|^2 = (\sqrt{v_1^2 + v_2^2 + v_3^2})^2 = v_1^2 + v_2^2 + v_3 \cdot v_3
|
24,626 |
790 = 250\cdot 3 + ((-1) + 3)\cdot 20
|
-1,549 |
\dfrac98 = 9/8
|
-18,338 |
\frac{1}{s^2 - 10*s + 24}*(s^2 + 36*\left(-1\right)) = \frac{(s + 6)*(6*(-1) + s)}{(s + 6*(-1))*(s + 4*(-1))}
|
-22,965 |
\frac{91}{4 \cdot 13} \cdot 1 = \dfrac{91}{52}
|
18,919 |
(1 + r)^3 - (1 - r)^3 = 2 \cdot \left(3 \cdot r + r^3\right) = 2 \cdot r \cdot (3 + r^2)
|
42,402 |
1 + (-1) + 1 + (-1) + \ldots = 0 + 0 + \ldots = 0
|
-20,095 |
\dfrac{r + 5(-1)}{r + 5\left(-1\right)}*9/4 = \frac{1}{20 \left(-1\right) + 4r}(45 (-1) + r*9)
|
-14,089 |
5 - 4 \cdot 8 + 80/8 = 5 - 4 \cdot 8 + 10 = 5 + 32 \cdot (-1) + 10 = -27 + 10 = -17
|
10,341 |
r = \frac{1}{r x r^2 x} = \tfrac{1}{r r x r x} = r^2 x r x
|
49,132 |
\tfrac{1}{e^y} = e^{-y}
|
19,490 |
\left(800^2 + 800 \cdot 800\right)^{1/2} = 2^{1/2} \cdot 800 \approx 1131
|
7,600 |
7\cdot 3^2 + 1^2 = 8^2
|
-15,856 |
6\times 6/10 - \tfrac{4}{10}\times 10 = -4/10
|
14,807 |
\left(3 * 3 + (-1)\right) (3^2 + 3(-1)) = 48 = 3*2^4
|
-11,986 |
\dfrac{29}{30} = \dfrac{s}{10\pi} \times 10\pi = s
|
18,022 |
\left(A*z = b \Rightarrow \frac{z*A}{A} = b/A\right) \Rightarrow z = b/A
|
-23,394 |
\frac{3}{20} = \frac15\cdot 2\cdot 3/8
|
22,652 |
-a\cdot x = x\cdot \left(-a\right)
|
18,714 |
x_1*g_1 = x_1*g_1
|
12,154 |
\left((2*n)!\right)! = 2*n*2*(n + (-1))*2*(n + 2*(-1))*\dotsm*2 = 2^n*n!
|
34,656 |
3 = \frac{2}{2}\cdot 3
|
6,327 |
\cos(-u + \pi\cdot 4) = \cos(2\cdot \pi - u)
|
-10,565 |
5/5\cdot (-\frac{6}{y\cdot 4 + 8}) = -\frac{30}{40 + 20\cdot y}
|
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