id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-4,129 |
\dfrac{d^2}{d \cdot d^2} \cdot 72/32 = \frac{d^2}{d^3} \cdot \dfrac{9 \cdot 8}{8 \cdot 4}
|
20,381 |
-\lim_{x \to 0} (3 + x)^2/x = -6 - \lim_{x \to 0} \dfrac1x9
|
29,952 |
5^{\frac{1}{2}}*45 = (5^3*3^4)^{1 / 2}
|
17,792 |
0.3 \frac{1}{16}7 q = q\frac{21}{160}
|
16,069 |
2\sin{X} \cos{H} = \sin(X - H) + \sin(X + H)
|
-26,468 |
5z^2 - 20 z + 20 = 5\left(z^2 - z*4 + 4\right)
|
1,824 |
(2 + l) \cdot 4^2 - l \cdot 3^2 = 32 + 7 \cdot l
|
-10,266 |
3/3*(-\dfrac{4}{x*5 + 10}) = -\frac{12}{30 + 15*x}
|
33,831 |
-x + g = g - x
|
24,482 |
\sin\left(\pi + x\right) = \cos{x} \cdot \sin{\pi} + \cos{\pi} \cdot \sin{x}
|
14,743 |
-\left(k + \left(-1\right)\right)*(1 + k) + x*k = -(1 + k)*(2*\left(-1\right) + k + 1) + x*(k + 1 + (-1))
|
9,784 |
\cos(2 \times u) = 1 - 2 \times \sin^2(u) = 2 \times \cos^2(u) + (-1)
|
5,923 |
-\frac{2}{y^2 + 1} + 2 = \frac{2 \cdot y^2}{1 + y^2}
|
13,537 |
n \cdot 4 = (-1) + 2 \cdot n + 1 + 2 \cdot n
|
-4,613 |
\frac{1}{20 + x^2 + 9\cdot x}\cdot (-x\cdot 2 + 7\cdot (-1)) = \frac{1}{4 + x} - \frac{1}{5 + x}\cdot 3
|
-6,699 |
0/10 + \frac{9}{100} = \tfrac{9}{100} + \frac{1}{100}\cdot 0
|
393 |
\operatorname{Var}[N - X] = \mathbb{E}[(N - X)^2] - \mathbb{E}[N - X] \cdot \mathbb{E}[N - X] = \mathbb{E}[N^2] - 2\cdot \mathbb{E}[N\cdot X] + \mathbb{E}[X^2] - (\mathbb{E}[N] - \mathbb{E}[X])^2
|
-20,419 |
\frac{x \cdot 9 + 90 (-1)}{10 x + 100 \left(-1\right)} = 9/10 \frac{x + 10 (-1)}{x + 10 \left(-1\right)}
|
17,583 |
\overline{y \cdot w} = \overline{y} \cdot \overline{w}
|
36,373 |
1^2 + 4 \cdot 4 = 17
|
14,876 |
g^2 - d^2 = (-d + g) (g + d)
|
7,542 |
(x \cdot a) \cdot (x \cdot a) = (a \cdot x)^2
|
48,782 |
7 \cdot 7 \cdot 19 = 931
|
13,663 |
\cos{\pi/4} = \sin{\dfrac{1}{4}\pi} = 1/\left(\sqrt{2}\right)
|
33,262 |
3^6 = 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3
|
5,376 |
\left(\sqrt{2}\right)^{(\sqrt{2})^{(\sqrt{2})^{\left(\sqrt{2}\right)^{\sqrt{2} \ldots}}}} = 2
|
-20,283 |
\frac{7}{r + 4}\cdot 9/9 = \frac{63}{36 + r\cdot 9}
|
13,346 |
t\cdot (-A\cdot B + B\cdot A)^2\cdot s = 2\cdot t\cdot \left(B\cdot A\right)^2\cdot s - 2\cdot t\cdot s\cdot A^2\cdot B \cdot B
|
35,606 |
\tan(\beta) = \sin(\beta)/\cos\left(\beta\right) rightarrow \tan\left(\beta\right)
|
-20,918 |
3/3 \cdot \frac12 \cdot (8 + 6 \cdot k) = \frac16 \cdot (k \cdot 18 + 24)
|
11,523 |
y'*4 + z*2 + 2y' y + 6(-1) = 0 \Rightarrow y' = \frac{1}{2y + 4}(6 - 2z) = \dfrac{3 - z}{y + 2}
|
2,172 |
\cos{2} < 1 - \frac{2^2}{2!} + 2^4/4! = -1/3 \lt 0
|
-19,682 |
40/5 = 4*10/(5)
|
221 |
-1/12 = 1 + 2 + 3 \cdots
|
-20,413 |
\frac{y\cdot \left(-60\right)}{100\cdot \left(-1\right) + y\cdot 10} = 10/10\cdot \frac{1}{y + 10\cdot (-1)}\cdot \left(y\cdot (-6)\right)
|
2,735 |
((-1) + n) \left(2(-1) + n\right)! = (n + \left(-1\right))!
|
-3,666 |
\frac19 = \frac19
|
-6,765 |
75 = 5*5*3
|
2,661 |
E + X = 180 - 180 - X - E
|
30,580 |
2! \times 4! = 2! \times 4 \times 3!
|
19,226 |
27 + k * k^2 = 3^3 + k^3 = \left(k + 3\right)*(k^2 - 3*k + 9)
|
19,409 |
|z^n| = (1 + |z| + (-1))^n \gt 1 + (|z| + (-1)) n
|
-11,747 |
(\frac25)^3 = 8/125
|
23,359 |
2^2 * 2*3*6 = 144
|
7,490 |
2450 = 2\cdot 5 \cdot 5\cdot 7^2
|
-1,165 |
\frac{5\cdot 1/9}{(-8)\cdot \frac19} = -\frac{1}{8}\cdot 9\cdot \dfrac{5}{9}
|
-3,384 |
\sqrt{10}+\sqrt{4} \cdot \sqrt{10}+\sqrt{9} \cdot \sqrt{10} = \sqrt{10}+2\sqrt{10}+3\sqrt{10}
|
22,007 |
x \times x - x\times 3 + 2 = (x + 2\times \left(-1\right))\times \left(x + (-1)\right)
|
30,204 |
x^4 + (-1) = (x + (-1))\cdot (x^2 + 1)\cdot (x + 1)
|
9,977 |
r \cdot \pi = \frac22 \cdot \pi \cdot r
|
-20,044 |
\frac{1}{8}*8*\dfrac{n + 10}{n*3 + 10} = \dfrac{80 + 8*n}{24*n + 80}
|
-6,389 |
\frac{2}{45 + m\cdot 5} = \frac{2}{(9 + m)\cdot 5}
|
11,787 |
\left(n + 1\right)^3/3 \geq 3 \cdot \left(n + 1\right) + 3 \cdot \left(-1\right) = \frac13 \cdot (n + 1)^3 \geq 3 \cdot n
|
27,400 |
n! \cdot (1 + n) \cdot (n + 2) = (n + 2)!
|
-6,681 |
40/100 + \frac{3}{100} = \frac{3}{100} + 4/10
|
26,466 |
\tfrac{6!}{3!\cdot 3!} = \frac{720}{6\cdot 6} = 20
|
24,340 |
64 \cdot (-1) + h^2 \cdot 3 - 12 \cdot h = 3 \cdot (16 \cdot (-1) + h^2 - 4 \cdot h) + 16 \cdot (-1)
|
-22,991 |
\frac{33}{44} = \frac{3}{4\cdot 11}\cdot 11
|
2,548 |
\sin{2\cdot (\pi + x)} = \sin{x\cdot 2}
|
2,311 |
x*y*4 = (x + y)^2 - (-y + x)^2
|
11,100 |
\left(0 \leq x \Rightarrow |t| = t\right) \Rightarrow xx/2 = \int_0^x t\,dt
|
8,373 |
1 + 2\cdot n\cdot s = s + 2\Longrightarrow (n\cdot 2 + (-1))\cdot s = 1
|
21,254 |
4 = 2 \times (-1) + 5 + 1
|
-29,386 |
-3/2*\frac34 = ((-3)*3)/\left(2*4\right) = -\frac{9}{8} = -\frac98
|
7,721 |
x*\frac{F}{q}*f = \frac{f*x*F}{q}
|
-7,032 |
25/182 = 5/14\cdot \dfrac{5}{13}
|
-20,411 |
\frac{1}{-9 y + 9 (-1)} ((-1) y) \frac18 8 = \frac{y*(-8)}{72 (-1) - 72 y}
|
9,336 |
\left(\left(2 = b + 1/b \implies 1 + b^2 - 2 \cdot b = 0\right) \implies (\left(-1\right) + b)^2 = 0\right) \implies b = 1
|
-3,922 |
\frac{66*d^2}{d^5*30} = \frac{d^2}{d^5}*\tfrac{66}{30}
|
20,466 |
1/(1/(\dfrac{1}{\frac{1}{25}})) = 5^{-2(-(-1) (-1))} = 5^2 = 25
|
21,428 |
\frac{1}{\frac{1}{3^x}} \cdot \sin(\frac{a}{3^x}) = 3^x \cdot \sin(\dfrac{a}{3^x})
|
2,776 |
\sin\left(\beta\right) \sin(x) + \cos(\beta) \cos(x) = \cos(x - \beta)
|
46,488 |
\dfrac{\cos{y}}{\cos{2y} + 1}2 = \dotsm \dotsm \dotsm = 1/\cos{y} = \sec{y}
|
18,053 |
\operatorname{E}\left(X_G\cdot X_B\right) = \operatorname{E}\left(X_B\right)\cdot \operatorname{E}\left(X_G\right)
|
-13,905 |
(4 + (2 - 7 \times 6)) \times 1 = (4 + (2 - 42)) \times 1 = (4 + (-40)) \times 1 = (4 - 40) \times 1 = (-36) \times 1 = -36 \times 1 = -36
|
-15,254 |
\dfrac{1}{m^6\cdot \dfrac{1}{y^6}}\cdot m^5 = \frac{m^5}{\frac{1}{\frac{1}{m^6}\cdot y^6}}
|
-29,869 |
\frac{\mathrm{d}}{\mathrm{d}z} (5\cdot z^4 - z^3\cdot 2 - z^2) = z^3\cdot 20 - z^2\cdot 6 - z\cdot 2
|
-3,514 |
\frac{1}{100}*6 = 3*2/(2*50)
|
19,623 |
-1 \lt 2 \cdot (-1) + \frac{s}{2} \implies s \gt 2
|
-6,681 |
\frac{4}{10} + 3/100 = \frac{1}{100}*3 + 40/100
|
33,709 |
\mathbb{E}[Y]\cdot \mathbb{E}[V] = \mathbb{E}[Y\cdot V]
|
11,709 |
(-1) + 2 (1 + m) = m*2 + 1
|
15,283 |
\int 1\cdot 2\cdot \pi\cdot s\,ds = 2\cdot \dfrac12\cdot s^2\cdot \pi = \pi\cdot s^2
|
10,806 |
20160 = \left(2*(-1) + 2^4\right)*(4*(-1) + 2^4)*(-2^3 + 2^4)*(2^4 + (-1))
|
-718 |
\dfrac{1}{12}*19*\pi = \pi*187/12 - 14*\pi
|
699 |
b^L*b^l = b^{l + L}
|
51,869 |
\dfrac{1}{x\cdot y} + 1/(y\cdot z) + \frac{1}{z\cdot x} = \frac{1}{(x\cdot y\cdot z)^2}\cdot (y\cdot z\cdot z\cdot x + x\cdot y\cdot z\cdot x + x\cdot y\cdot y\cdot z) = \frac{1}{x\cdot y\cdot z}\cdot \left(x + y + z\right)
|
-20,462 |
\frac{63 + 7*h}{-14*h + 14} = \frac77*\frac{1}{-h*2 + 2}*(9 + h)
|
-4,387 |
\frac{8\cdot p^5}{p^2\cdot 14} = \frac{8}{14}\cdot \frac{p^5}{p^2}
|
-20,620 |
\frac{8z}{z*(-14)} = \left((-1)*2 z\right)/(z*(-2)) (-\dfrac47)
|
32,313 |
k + (-1) = {k \choose 1} + (-1)
|
-18,481 |
5\cdot k = 2\cdot (3\cdot k + (-1)) = 6\cdot k + 2\cdot (-1)
|
17,007 |
1 = \frac33 = 3 \cdot 0.333 \cdot ... = 0.999 \cdot ...
|
-7,785 |
\dfrac{-2\cdot i + 8}{i - 4}\cdot \frac{-i - 4}{-4 - i} = \tfrac{8 - 2\cdot i}{-4 + i}
|
-20,498 |
-3/2*9/9 = -\dfrac{27}{18}
|
38,290 |
2/8 + 10/16 = \frac{1}{8} \cdot 7 \leq 1
|
-8,060 |
(-52 - 14 \cdot i + 130 \cdot i + 35 \cdot (-1))/29 = \left(-87 + 116 \cdot i\right)/29 = -3 + 4 \cdot i
|
5,910 |
\frac{1}{100} \cdot 3 = 3\%
|
-23,291 |
0.28^8 = ((-1)\cdot 0.72 + 1)^8
|
25,517 |
X_j \cdot X_x = X_j \cdot X_x
|
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