id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
9,990 |
\cos\left(-c_1 + c_2\right) = \sin(c_2) \cdot \sin\left(c_1\right) + \cos(c_2) \cdot \cos\left(c_1\right)
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-5,904 |
\dfrac{1}{6 + p^2 - 5\cdot p}\cdot 5 = \frac{5}{(p + 3\cdot (-1))\cdot (p + 2\cdot (-1))}
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12,472 |
8^2 - (h + 8)^2 = (h + 16)*\left(-h\right)
|
551 |
a_i y^i + y^i d_i = y^i \cdot (a_i + d_i)
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28,851 |
3*\tan^4{z} = d/dz \tan^3{z} - \tan{z}*3 + z*3
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13,034 |
(x + 1)^2 + (-1) = x^2 + x\cdot 2
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23,630 |
50 = xx + 10 x \Rightarrow 10 x + x^2 = 50
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-3,890 |
25/5 \cdot \frac{1}{m^5} \cdot m^2 = \frac{25 \cdot m^2}{m^5 \cdot 5}
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28,831 |
\frac{4 + e}{2 \cdot \sinh(1)} = \frac{1}{e^2 - 1} \cdot (1 + 4 \cdot e) + 1
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3,721 |
2 = a\cdot 3 = a\cdot 2
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14,417 |
\dfrac{1}{z*(1 - z/2 - z^2/3 + \dfrac{z^3}{4} + \dots)} = \frac{1}{\log_e(1 + z)}
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17,000 |
b = |p|\wedge 0 \lt b \Rightarrow p = -b
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27,230 |
\tan(\alpha) = \sin(\alpha)/\cos\left(\alpha\right)
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-20,222 |
\dfrac{6p + 4}{p + 7}*\frac88 = \tfrac{p*48 + 32}{56 + p*8}
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5,254 |
2^l + 1 = x^2 \implies 2^l = (x + \left(-1\right)) \cdot (1 + x)
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-1,609 |
\pi \cdot 5/2 - 2 \cdot \pi = \pi/2
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-8,010 |
\frac{1}{-5 \cdot i + 2} \cdot \left(-12 + i\right) = \frac{i \cdot 5 + 2}{2 + i \cdot 5} \cdot \dfrac{1}{-i \cdot 5 + 2} \cdot (-12 + i)
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41,640 |
(\sqrt{-1})^3 = -\sqrt{-1}
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9,189 |
-2\cdot \int u^{-1/3}\,\mathrm{d}u = (\left(-6\right)\cdot u^{2/3})/2 = -3\cdot u^{2/3}
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23,555 |
(x + 1)^4 - (x + 1)^2 = (x + 1)^2 \cdot \left((x + 1) \cdot (x + 1) + \left(-1\right)\right) = \left(x + 1\right)^2 \cdot (x + 1 + (-1)) \cdot (x + 1 + 1)
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-192 |
\binom{4}{3} = \frac{1}{3! \left(3(-1) + 4\right)!}4!
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-2,587 |
7^{1/2}*3 - 7^{1/2} = -7^{1/2} + 7^{1/2}*9^{1/2}
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20,998 |
(-a + b) (a + b) = b \cdot b - a^2
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34,026 |
(1 + x) \cdot x! = (x + 1)!
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-18,334 |
\frac{a \cdot a + 9 \cdot a}{81 \cdot (-1) + a^2} = \frac{a \cdot (9 + a)}{\left(a + 9 \cdot (-1)\right) \cdot (a + 9)}
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14,886 |
|C - A| + |A| \geq |C| \Rightarrow |C| - |A| \leq |C - A| = |A - C|
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-11,775 |
\left(\frac{1}{4}\right)^4 = 1/256
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10,580 |
\frac{4}{2}\cdot 1 = 4/2 = 2
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28,937 |
\sin(x - \beta) = \cos(\beta)*\sin(x) - \sin(\beta)*\cos(x)
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-2,172 |
\frac{\pi}{3} = \pi - \pi \cdot \dfrac{1}{3} \cdot 2
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35,814 |
n\frac{1}{((-1) + n)!}\left(n + 2(-1)\right)! \theta = \dfrac{n}{(-1) + n} \theta
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35,940 |
(1 + 2)\cdot \left(1 + 5 + 25\right)\cdot \left(1 + 7 + 49\right) = 3\cdot 31\cdot 57 = 5301
|
7,903 |
1/\left(\frac{1}{b} a\right) = b/a
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34,979 |
x = x^{1/2}*x^{\tfrac12}
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-21,014 |
\frac{z + 6}{z + 6} \left(-1/10\right) = \frac{6(-1) - z}{z \cdot 10 + 60}
|
8,333 |
-J^2 + z \times z = (-J + z)\times (z + J)
|
9,922 |
(-c + z)\cdot (-d + z) = z^2 - z\cdot (d + c) + c\cdot d
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51,177 |
-2353*1109 + 522*4999 = 1
|
30,914 |
1 - \sin^2{y/2}\cdot 2 = \cos{y}
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-1,644 |
-\pi*2 + \tfrac{1}{12}29 \pi = \pi \frac{5}{12}
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28,192 |
a = 1/(\dfrac1a)
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9,910 |
\tan{\frac{\pi}{3}} = 3^{1/2}
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-10,478 |
36 = -30 - 36x + 12 = -36x - 18
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24,987 |
x + 0 (-1) = 0 + x + 0 (-1)
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32,707 |
z_2 \cdot l_2 + z_1 \cdot l_1 = z_2 \cdot 2 + 3 \cdot z_1 \Rightarrow (-l_2 + 2) \cdot z_2 + (3 - l_1) \cdot z_1 = 0
|
1,708 |
\frac{5*\pi}{9} - \frac{7*\pi}{18} = 3*\pi/18 = \pi/6
|
36,638 |
( x^2, x y) = ( x^2, x) \cap ( x^2, y) = x \cap \left( x^2, y\right)
|
8,072 |
(|y_2| + 1) \cdot |y_1| = (|y_1| + 1) \cdot |y_2| \implies |y_1| = |y_2|
|
6,683 |
\sqrt{x} = \dfrac{1}{2\cdot \sqrt{x}} = \frac{1}{2\cdot x^{\tfrac12}}
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-5,537 |
\frac{4}{35\cdot \left(-1\right) + n \cdot n + n\cdot 2} = \frac{4}{(n + 5\cdot (-1))\cdot (n + 7)}
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-3,644 |
\frac56 \cdot i = i \cdot 5/6
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14,527 |
4 * 4 - 2^2 = 12
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14,411 |
y \geq 3 \implies e^{y + (-1)} \gt 2^{y + \left(-1\right)} \geq 2^{y + (-1)} = (1 + 1)^{y + (-1)}
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-2,014 |
\pi*13/12 - \frac{\pi}{6} = \frac{11}{12}*\pi
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13,670 |
|1/x - \dfrac{1}{z}| = |\dfrac{x - z}{z\cdot x}|
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-8,107 |
12 = 3*4
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-21,573 |
-0.5 = \cos{-\frac23\cdot π}
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36,285 |
x = x\times 5 - 2\times x\times 2
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-18,962 |
\dfrac{1}{3} = \frac{1}{25 \pi}x_p \cdot 25 \pi = x_p
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24,308 |
Y \cdot Y^x = Y^x \cdot Y
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-22,272 |
15\cdot (-1) + a^2 + 2\cdot a = (a + 5)\cdot \left(a + 3\cdot (-1)\right)
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-2,298 |
2/11 = -1/11 + 3/11
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-20,971 |
\dfrac{-t\times 7 + 4}{-7\times t + 4}\times (-5/6) = \frac{1}{24 - 42\times t}\times (35\times t + 20\times (-1))
|
-3,041 |
52^{\frac{1}{2}} + 117^{1 / 2} = \left(4*13\right)^{\frac{1}{2}} + (9*13)^{\frac{1}{2}}
|
13,732 |
1/5 = k \cdot k \cdot k \Rightarrow k = \dfrac{1}{5^{\dfrac13}}
|
26,069 |
x + (-1) \geq x^2 + x + 1 \Rightarrow -2 \geq x^2
|
11,832 |
(z + 1) \cdot (z + 2) \cdot (z^2 - z \cdot 4 + 13) = 26 + z^4 - z^3 + 3 \cdot z \cdot z + 31 \cdot z
|
2,301 |
k * k*32 = (k*8)^2/2
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-25,021 |
4x-\frac{{64}}{3}x^3+\frac{1024}{5}x^5-\frac{16384}{7}x^7+...=\arctan(4x)
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-19,208 |
\frac15 = \frac{A_t}{16 \pi}\cdot 16 \pi = A_t
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-15,779 |
5/10 \cdot 5 - 6 \cdot \frac{5}{10} = -\frac{5}{10}
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11,904 |
aa^T x = xa^T a
|
29,431 |
(2 \cdot c)^n = 2^n \cdot c^n
|
21,111 |
2^{k + 2(-1)} = 2^{-k} \left(2^{k + (-1)}\right)^2
|
41,191 |
30 = 4 \cdot 7 + 2
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32,454 |
1 + y \cdot y \cdot y + y = y \cdot (y \cdot y + 1) + 1
|
18,827 |
k \cdot x \cdot e = x \cdot e \cdot k
|
529 |
\sin(f + z) = \sin{f}*\cos{z} + \sin{z}*\cos{f}
|
3,773 |
4*\dfrac{5}{8} = \dfrac{5}{2}
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25,325 |
-5\cdot 8\cdot 7 + 5\cdot 8\cdot 7\cdot 9 = 2240
|
9,538 |
x + y \times y' = -y + y' \times x
|
13,840 |
x^4 + \left(-1\right) = (x^2 + 1)\cdot \left(x^2 + (-1)\right) = (x + i)\cdot (x - i)\cdot (x + 1)\cdot (x + (-1))
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46,163 |
45 = 5 * 5 + 4*5 + 0 = 140
|
-15,210 |
\dfrac{1}{\frac{1}{s^{20}}*\frac{1}{\frac1q s^2}} = \dfrac{s^{20}}{\frac{1}{s^2} q}
|
-2,490 |
\sqrt{28}-\sqrt{63}+\sqrt{112} = \sqrt{4 \cdot 7}-\sqrt{9 \cdot 7}+\sqrt{16 \cdot 7}
|
11,267 |
2*\sqrt{x*y} \lt x^2 + 2*x*y + y * y - x - y = (x + y)^2 - x + y = (x + y)*\left(x + y + (-1)\right)
|
24,985 |
E(A^2) = E(A \cdot A) = E(A) \cdot E(A) = E(A)^2
|
20,901 |
q^4 = \ldots = 2 + 3 \cdot q
|
39,848 |
\sin\alpha = \sin((\alpha+\beta)-\beta) = \sin(\alpha+\beta)\cos\beta-\sin\beta\cos(\alpha+\beta)
|
6,384 |
1/(m m!) = \dfrac{1}{m! (m + 1 + (-1))}
|
7,283 |
\cos(\pi/4) = \cos(\frac{1}{4} \cdot ((-1) \cdot \pi))
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-6,059 |
\dfrac{1}{z^2 - 15 \times z + 54} \times z = \dfrac{z}{\left(z + 6 \times (-1)\right) \times (z + 9 \times (-1))}
|
-22,288 |
r^2 + r\cdot 10 + 9 = (1 + r)\cdot (r + 9)
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38,506 |
-30 = 6 \cdot \left(-5\right)
|
4,479 |
1 + (1 + z)^2 = z^2 + z \cdot 2 + 2
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-20,805 |
\dfrac{-24\times \eta + 20\times \left(-1\right)}{5 + 6\times \eta} = -\frac{4}{1}\times \tfrac{6\times \eta + 5}{5 + 6\times \eta}
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1,268 |
(l_2^2 + l_1 \cdot l_1)^2 - (l_2^2 - l_1^2)^2 = (2l_2 l_1)^2 = 2 \cdot 2l_2^2 l_1^2
|
17,409 |
2\cdot z = \arccos(x) \Rightarrow x = \cos(z\cdot 2),0 \leq 2\cdot z \leq \pi
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-20,116 |
\frac{q \cdot 14}{q \cdot 2} = 7/1 \frac{q}{2q}2
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10,387 |
t \cdot s \cdot x - x = x \cdot s \cdot t - x \cdot s + s \cdot x - x
|
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