id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
4,139 |
6^3 + 1^3 + 8^3 = (8 + 1)^3
|
13,791 |
-(x + 1)\cdot (x + 2\cdot (-1))\cdot 3 = -3\cdot x^2 + x\cdot 3 + 6
|
18,864 |
\sin{\pi/2} = \cos{2 \times \pi}
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47,679 |
\lim_{x \to \pi/2} \frac{\tan{5 \cdot x}}{\tan{3 \cdot x}} = \lim_{x \to \frac{\pi}{2}} \frac{\cos{3 \cdot x}}{\cos{5 \cdot x}} \cdot \lim_{x \to \pi/2} \frac{1}{\sin{3 \cdot x}} \cdot \sin{5 \cdot x} = -\lim_{x \to \frac{1}{2} \cdot \pi} \frac{\cos{3 \cdot x}}{\cos{5 \cdot x}}
|
19,545 |
g'\cdot H' = H\cdot h \implies h\cdot H/g' = H'
|
19,159 |
\left(h + 1\right)\cdot \left(h^2 - h + 1\right) = 1 + h^3
|
21,099 |
\left(2\cdot B\right)^2 = 2^2\cdot B^2 = 4\cdot B \cdot B
|
-22,216 |
(t + 10)*(t + 9) = t^2 + 19*t + 90
|
12,527 |
\dfrac{228 + 204\cdot \left(-1\right)}{6\cdot 12} = 1/3
|
25,042 |
26 * 26 = 10^2 + 24 * 24
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5,311 |
\frac26\cdot (-\sqrt{-5} + 1) = \dfrac{1}{1 + \sqrt{-5}}\cdot 2
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-1,618 |
\dfrac{23}{12} \pi + \frac{1}{12}17 \pi = 10/3 \pi
|
-8,131 |
\frac{5\cdot 6}{2} = 15
|
39,264 |
6 = 5^2 - 5 \cdot 5 + 6
|
38,985 |
-(2 (-1) + z) = -z + 2
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15,337 |
\left(-1 * 1 + 2^2\right)^{1/2} = 3^{1/2}
|
-9,298 |
12 + j\cdot 4 = 2\cdot 2\cdot 3 + 2\cdot 2 j
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-11,612 |
15 + 15 \cdot (-1) - 30 \cdot i = -30 \cdot i
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-24,762 |
\frac14\cdot (-\sqrt{6} + \sqrt{2}) = \sin{13\cdot \pi/12}
|
624 |
\left(y!\right)! \gt (y^2)^{y! - y \cdot y} = y^{2y! - 2y \cdot y} > y^{y!}
|
-5,969 |
\frac{1}{t \cdot t + t\cdot 7 + 6}\cdot 3 = \frac{1}{\left(t + 6\right)\cdot (t + 1)}\cdot 3
|
3,636 |
\dfrac{1 + n}{2 \left(n + (-1)\right)!} = \frac{1}{2 (n + 2 (-1))!} + \frac{1}{(n + (-1))!}
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20,617 |
(b \cdot b + a^2 - b \cdot a) \cdot (b + a) = b^3 + a^3
|
384 |
(q - p)^2 = p^2 - qp\cdot 2 + q^2
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-18,215 |
72 + 14 (-1) = 58
|
9,873 |
\N_{x} \coloneqq \left\{1, \ldots, x\right\}
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-4,415 |
\left(y + 1\right)*(4 + y) = 4 + y^2 + 5*y
|
25,434 |
\dfrac3x - \tfrac12\cdot x = 3/x - x/2
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-2,309 |
1/17 = \frac{1}{17}*7 - 6/17
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21,207 |
0 < (7 - x)^{1/2} - (7 - z)^{1/2} = \frac{z - x}{(7 - x)^{1/2} + (7 - z)^{1/2}} \lt (z - x)/2
|
10,278 |
1 + 3 + \dotsm + 2 \cdot \left(n + 1\right) + \left(-1\right) = (n + 1)^2
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-3,656 |
\dfrac{63\cdot q}{q^4\cdot 70} = 63/70\cdot \frac{1}{q^4}\cdot q
|
1,622 |
7 = -1^2*2 + 3^2
|
9,008 |
\frac{1}{2}\cdot x = x - x/2
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14,358 |
xy = z\Longrightarrow |z|^2 = |y|^2 |x|^2
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19,366 |
1 < |y|\Longrightarrow 1 > 1/|y|
|
-6,023 |
\tfrac{1}{\left(5(-1) + l\right) (l + 10)}2 = \frac{2}{l * l + 5l + 50 (-1)}
|
13,717 |
1 - x^c - 1 - x^h = -x^c + x^h
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-1,130 |
-5/3 \cdot 6/1 = (\frac{1}{3} \cdot (-5))/\left(\dfrac{1}{6}\right)
|
14,550 |
g = \lim_{n \to \infty} \sin(n)\Longrightarrow g \in (-1, 1) = \lim_{n \to \infty} \sin(n*2)
|
31,424 |
\frac{1}{1 - x^2} = \sum_{i=0}^\infty (x^2)^i = \sum_{i=0}^\infty x^{2\cdot i}
|
21,392 |
\tan{x} = \frac{2\cdot \tan{\frac{1}{2}\cdot x}}{1 - \tan^2{\dfrac{x}{2}}} \gt 2\cdot \tan{x/2}
|
-20,671 |
\frac{1}{x\cdot 10 + 40\cdot (-1)}\cdot \left(70 + x\cdot 10\right) = \dfrac{1}{x + 4\cdot (-1)}\cdot (7 + x)\cdot \dfrac{10}{10}
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35,966 |
-\frac23 = -\frac{1}{3}\cdot 2
|
16,978 |
(S + 1)^2 = S^2 + 2S + 1 \geq S + 1
|
3,415 |
(16 \cdot S^4 \cdot r^2 + 1) \cdot 4 = 4 + S^4 \cdot r^2 \cdot 64
|
22,038 |
\frac{1}{x^{\frac{1}{2}}} = x^{-\frac12}
|
15,154 |
\cos(\alpha) = 3/(\sqrt{10}) \Rightarrow \sin(\alpha) = 1/(\sqrt{10})
|
-14,661 |
96 + 80 + 96 + 95 + 87 + 86 = 540
|
-2,446 |
50^{1/2} + 18^{1/2} = (9\cdot 2)^{1/2} + \left(25\cdot 2\right)^{1/2}
|
7,073 |
a \lt -1 \Rightarrow a^2 = |a| + (-1)
|
-446 |
(e^{\pi\cdot i\cdot 4/3})^{16} = e^{16\cdot \pi\cdot i\cdot 4/3}
|
15,807 |
\left(y + 1\right)^3 - y^3 + 1 = 3*(y + y * y)
|
-9,498 |
30 \cdot t + 5 = t \cdot 2 \cdot 3 \cdot 5 + 5
|
38,823 |
4/7\times 1/2/2\times 3/5 = \frac{3}{35}
|
13,544 |
-z + x = -(z + 1) + x + 1
|
-1,378 |
\frac{4 \cdot 1/5}{3 \cdot \frac12} = 2/3 \cdot \frac15 \cdot 4
|
14,575 |
4 + 36 + 4\cdot e + 12\cdot x + a = 0 \Rightarrow a + 4\cdot e + x\cdot 12 = -40\cdot ...\cdot 3
|
20,957 |
(2L + L)/3 = L
|
33,651 |
\frac{1}{2\cdot (1 + \frac{z^2\cdot 3}{2}\cdot 1)} = \frac{1}{3\cdot z^2 + 2}
|
26,371 |
F = -x + H \Rightarrow x + F = H
|
24,641 |
\Delta \times z = z + z \times \Delta - z
|
13,945 |
b^y = \left(\dfrac{1}{b}\right)^{-y} = \left(\frac1b\right)^{-y}
|
32,339 |
49 = (b\cdot a + h\cdot b + a\cdot h)\cdot 2 + 23 \Rightarrow 13 = h\cdot a + b\cdot a + b\cdot h
|
-6,094 |
\frac{1}{((-1) + x)*(9 + x)}*3 = \frac{1}{9*\left(-1\right) + x * x + 8*x}*3
|
11,855 |
40/7 = (4\times 7 + 12)/7 = 4 + 12/7
|
24,224 |
(H_1*H_2*\cdots*H_l*H_{(-1) + l})^R = H_l^R*H_{(-1) + l}^R*\cdots*H_2^R*H_1^R
|
23,295 |
\sin(z) = \sum_{m=0}^\infty a_m \cdot z^m = z + \sum_{m=2}^\infty a_m \cdot z^m
|
28,834 |
\cos\left(B\right) = 2 \cdot \cos^2(B/2) + \left(-1\right) = 1 - 2 \cdot \sin^2(\dfrac{B}{2})
|
13,468 |
(3\cdot a + 2007) \cdot (3\cdot a + 2007) = (3\cdot (a + 669))^2 = 9\cdot (a + 669)^2
|
10,371 |
a*g = -a*\left(-g\right)
|
-7,682 |
\dfrac{4 - 18i - 2i - 9}{5} = \dfrac{-5 - 20i}{5} = -1-4i
|
15,159 |
n/n! = \frac{1}{((-1) + n)!}
|
27,420 |
(9 a + 80 \varepsilon)^2 - 80 (a + 9 \varepsilon) (a + 9 \varepsilon) = -80 \varepsilon^2 + a^2
|
222 |
4\cdot \left(-1\right) + 3\cdot x = 0\Longrightarrow 4/3 = x
|
18,115 |
-l + x - j = x - l + j
|
1,598 |
\binom{l_1}{l_1 - l_2} = \dfrac{1}{(l_1 - l_2)!\cdot (l_1 - l_1 - l_2)!}\cdot l_1! = \frac{l_1!}{(l_1 - l_2)!\cdot l_2!} = \binom{l_1}{l_2}
|
-14,051 |
(8 + 1 - 3\cdot 8)\cdot 4 = \left(8 + 1 + 24\cdot \left(-1\right)\right)\cdot 4 = (8 - 23)\cdot 4 = (8 + 23\cdot (-1))\cdot 4 = \left(-15\right)\cdot 4 = (-15)\cdot 4 = -60
|
-3,567 |
\frac{x^5 \cdot 96}{x \cdot 64} 1 = x^5/x \cdot 96/64
|
10,645 |
(e^{-i*t}/2 + e^{i*t}/2)^k = \cosh^k{i*t} = \cos^k{t}
|
-20,998 |
-\dfrac{6}{7} \cdot (-3/(-3)) = 18/(-21)
|
2,265 |
x_I/g = x_C/a rightarrow x_C \cdot g/a = x_I
|
50,902 |
\frac{1}{\gamma^2\cdot (1 - u/\gamma) \cdot (1 - u/\gamma)} - \frac{1}{\gamma \cdot \gamma} = \frac{1}{\gamma^2}\cdot \sum_{k=1}^\infty \left(k + 1\right)\cdot (u/\gamma)^k = \sum_{k=1}^\infty (k + 1)\cdot \frac{u^k}{\gamma^{k + 2}}
|
6,978 |
(-(-g + h)^2 + (h + g)^2)/4 = gh
|
15,679 |
-z^2 + 1 = \tfrac{-z^4 + 1}{1 + z \cdot z}
|
12,885 |
\binom{m}{\left(-1\right) + k} + \binom{m}{k} = \binom{m + 1}{k}
|
30,570 |
360 = {5 \choose 2} \cdot {9 \choose 2}
|
6,066 |
\sin\left(\beta\right) = \frac{15}{17} \implies \cos(\beta) = \frac{1}{17}\cdot 8
|
27,510 |
\sqrt{2 + x} = x \implies x = 2
|
2,181 |
B_2\cdot a = a\cdot B_2
|
3,664 |
\frac{1}{z + (-1)} - \frac{1}{3 + z} = \tfrac{1}{(\left(-1\right) + z) (3 + z)}4
|
-151 |
\binom{5}{3} = \frac{5!}{\left(5 + 3 \cdot (-1)\right)! \cdot 3!}
|
15,073 |
1 = \frac{2 + 2}{2 + 2} = \dfrac22 + 2/2 = 2
|
14,108 |
s/R = \frac{1}{R}\cdot s
|
30,014 |
d^{2 \cdot n} \cdot d^{2 \cdot m} = d^{2 \cdot \left(m + n\right)}
|
29,193 |
-\left(b\times 2\right) \times \left(b\times 2\right)\times m + \left(2\times a\right)^2 = (a^2 - m\times b^2)\times 4
|
12,040 |
a^2 + ag*2 + g^2 = (a + g)^2
|
30,079 |
(BA)^2 = A^2 B^2
|
2,497 |
a + 1 = (a + 1)^2 = a * a + 2a + 1
|
36,263 |
2 \cdot 2 - 3\cdot 1^2 = 1
|
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