id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-4,931 |
10^{0 + 5}*29.4 = 29.4*10^5
|
17,819 |
3 - 2*f = f + b + c - 2*f = -f + b + c
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26,129 |
\frac1y (-z + c) = 1 \Rightarrow y + z = c
|
15,290 |
\left(h + 6 = 25 + b\cdot 2 \Leftrightarrow 13\cdot \left(h + 6\right) = 13\cdot (2\cdot b + 25)\right) \Rightarrow 2\cdot b + 19 = h
|
9,959 |
-\frac{1}{25}\times 216 + 400/25 = \frac{1}{25}\times 184
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-11,099 |
(x + 3\left(-1\right))^2 + b = (x + 3\left(-1\right)) (x + 3(-1)) + b = x^2 - 6x + 9 + b
|
28,877 |
3^{1/2}*(c + 2^{1/2}*d) + a + 2^{1/2}*x = a + 2^{1/2}*x + 3^{1/2}*c + 6^{1/2}*d
|
1,956 |
(y + x)*(y^2 + x^2 - x*y) = y^2 * y + x^3
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-20,373 |
y*3/\left(y*24\right) = 3*y*1/(3*y)/8
|
6,717 |
1 - \cos(4\cdot z) = 2\cdot \sin^{22}(z) = 8\cdot \sin^2\left(z\right)\cdot \cos^2(z) = 8\cdot (1 - \cos\left(z\right))\cdot (1 + \cos\left(z\right))\cdot \cos^2(z)
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28,559 |
0.250 \cdot 2 = 0.50 \rightarrow 0
|
-4,933 |
3.78 \cdot 10 = \frac{10}{10^6} \cdot 3.78 = \tfrac{3.78}{10^5}
|
-22,226 |
(z + (-1))\cdot (z + 3\cdot (-1)) = z^2 - 4\cdot z + 3
|
22,812 |
-\frac12 + \frac{10}{4} + x = 0 \Rightarrow -2 = x
|
25,064 |
3!/4! = \dfrac{6}{24} = 1/4
|
-1,863 |
11/12 \cdot \pi = -\pi \cdot 0 + \frac{1}{12} \cdot 11 \cdot \pi
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-18,285 |
\dfrac{y^2 - y - 2}{y^2 + 2y - 8} = \dfrac{(y + 1)(y - 2)}{(y + 4)(y - 2)}
|
15,913 |
G\cdot i\cdot y^g = i\cdot G\cdot y^g
|
10,409 |
\dfrac{1}{2\cdot (-1) + (-1)^2\cdot 12 + \left(-1\right)}\cdot \left(\left(-1\right)^2 + 3\right) = \dfrac{4}{9}
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-1,831 |
13/4*π = 11/6*π + \tfrac{17}{12}*π
|
-22,217 |
(5 + y)*(y + 7) = 35 + y^2 + y*12
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-24,904 |
8\cdot 7\cdot 6\cdot 5\cdot 4 = \tfrac{8!}{\left(8 + 5(-1)\right)!} = 6720
|
-20,590 |
8/8*\dfrac{9*t}{t + 7}*1 = \tfrac{72}{t*8 + 56}*t
|
3,316 |
h\cdot b = h^1\cdot b^1
|
22,806 |
\sin{\frac{π}{3}} = \sin{\frac{2}{3} \cdot π}
|
4,670 |
A^B*A^B = (A*A)^B = A^B
|
24,566 |
(-1) + 2 \cdot n = n^2 - (n + (-1))^2
|
14,498 |
-\frac{1}{2} = \frac11\cdot ((-1)\cdot 2\cdot 1/4)
|
20,662 |
m \cdot 2 + 2(-1) = \left(m + (-1)\right) \cdot 2
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-1,451 |
1/5*6/(1/8*\left(-1\right)) = -\frac{8}{1}*\frac15*6
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-9,484 |
k\cdot 84 + 36\cdot (-1) = k\cdot 2\cdot 2\cdot 3\cdot 7 - 2\cdot 2\cdot 3\cdot 3
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-1,977 |
\pi\cdot \dfrac76 + 7/4\cdot \pi = 35/12\cdot \pi
|
22,363 |
(m + 1)! \cdot \left(m + 1 + 1\right) = (1 + m + 1) \cdot \left(m + 1\right)!
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-26,516 |
(5 x)^2 = 25 x^2
|
27,409 |
b_1\times s_1 + ... + b_q\times s_q = s_1\times b_1 + ... + b_q\times s_q
|
7,078 |
\sin(y) = \cos(-y + \tfrac12 \cdot \pi)
|
17,409 |
z \cdot 2 = \operatorname{acos}(x) \implies x = \cos{2 \cdot z},0 \leq 2 \cdot z \leq \pi
|
21,298 |
b^z*b^y = b^{z + y}
|
9,498 |
\left|{A \times A^T}\right| = \left|{A^T \times A}\right|
|
1,991 |
x \cdot a = a^T \cdot x = x^T \cdot a
|
-1,650 |
\pi \cdot 4/3 + \pi \frac{11}{12} = \pi \frac{9}{4}
|
-22,179 |
\dfrac{24}{32} = \frac{3}{4}
|
1,445 |
1 + i^2 + i = 0 \implies 1 + i^2 = -i
|
16,860 |
\int\limits_{-\infty}^\infty ...\,\text{d}x = 2 \int_0^\infty ...\,\text{d}x
|
38,236 |
\left\{z, g\right\} = \left\{z, g\right\}
|
32,955 |
\frac{1}{8!\cdot 4!}\cdot 12! = 495
|
6,054 |
(x + 0)\times (2 + x^2 + x) = x^3 + x^2 + 2\times x + 0
|
25,121 |
2 - 9\cdot z^7 + 7\cdot z^9 = (1 - z)^2\cdot \left(2 + 4\cdot z + 6\cdot z \cdot z + 8\cdot z^3 + 10\cdot z^4 + 12\cdot z^5 + 14\cdot z^6 + 7\cdot z^7\right) \approx 63\cdot \left(1 - z\right) \cdot \left(1 - z\right)
|
23,193 |
\cos^2\left(x\right) - \sin^2(x) = 2 \cdot \cos^2\left(x\right) + (-1)
|
12,041 |
2/27 = \frac{\frac{1}{3}}{3}\cdot 2\cdot \frac13
|
-16,891 |
5 = 5 \cdot 4 \cdot x + 5 \cdot \left(-5\right) = 20 \cdot x - 25 = 20 \cdot x + 25 \cdot (-1)
|
-6,024 |
\frac{3*q}{q * q + q*6 + 40*(-1)} = \frac{3}{(10 + q)*(4*(-1) + q)}*q
|
22,611 |
2\times ((-1) + 2\times 7)^2 + 5\times (2 + (-1)) \times (2 + (-1)) = 7\times (2\times 4 + (-1)) \times (2\times 4 + (-1))
|
5,700 |
x \cdot \alpha \lt \alpha \cdot x \Rightarrow x^2 \cdot \alpha \cdot \alpha < \alpha^2 \cdot x \cdot x
|
23,929 |
h d = \dfrac{1}{h d} = 1/(d h) = d h
|
11,645 |
(y^Z \cdot \theta^Z \cdot z)^Z = \left(\theta^Z \cdot z\right)^Z \cdot y = z^Z \cdot \theta \cdot y
|
36,037 |
\frac{2}{3}\cdot \pi = \frac{1}{3}\cdot 2\cdot \pi
|
12,750 |
|\overline{h_j}| = |h_j|
|
28,184 |
(\dfrac{1}{4})^4\cdot 3/4 = \frac{3}{1024}
|
28,091 |
\cos{B} \sin{C} + \sin{B} \cos{C} = \sin\left(B + C\right)
|
35,214 |
-\frac18\cdot \pi = \tfrac{(-1)\cdot \pi}{8}
|
8,200 |
a/(c\cdot b) = a/(c\cdot b)
|
15,985 |
-2^n + 2^x = 2^n\cdot (2^{x - n} + (-1))
|
6,473 |
\frac{1 + 2 \cdot z}{2 + 2 \cdot n} = \dfrac12 \cdot (\tfrac{z + 1}{n + 1} + \frac{z}{n + 1})
|
-4,113 |
\dfrac{1}{r \cdot 4} = \tfrac{1}{4 \cdot r}
|
9,747 |
Z^R*Z = Z*Z^R
|
12,402 |
\tfrac12(2 + 0) = 1
|
1,040 |
z^7 = z^4\cdot z \cdot z^2
|
-7,618 |
\dfrac{i*2 - 1}{-1 + 2*i}*\frac{-6 + i*8}{-1 - 2*i} = \frac{8*i - 6}{-1 - 2*i}
|
-3,818 |
\frac{144 \cdot a^5}{72 \cdot a} = \frac{a^5}{a} \cdot 144/72
|
13,670 |
|\left(x - y\right)/(y\cdot x)| = |1/x - 1/y|
|
11,259 |
\left(0 > z + 5 \cdot (-1) \Rightarrow 1 = 5 - z\right) \Rightarrow 4 = z
|
29,333 |
\left(11 + 1\right) \cdot (22 + 1) \cdot (10 + 1) = 12 \cdot 23 \cdot 11 = 3036
|
31,459 |
\int\limits_c^b \cot{x}\,\mathrm{d}x = \int\limits_c^b \cot{x}\,\mathrm{d}x
|
2,813 |
(10 + y) \cdot (10 + y) = x^2 + y^2 = (x + 27 \cdot (-1))^2 + (y + 9)^2
|
7,469 |
4/36 = \frac46 \cdot 1/6
|
54,616 |
62 - 56 = 6
|
-8,061 |
\dfrac{-2 + i\times 5}{-2 + i\times 5}\times \dfrac{26 + 7\times i}{-5\times i - 2} = \frac{26 + i\times 7}{-5\times i - 2}
|
25,456 |
2^{n + 1} = 1 + 2^0 + 2^1 + 2 \cdot 2\cdot \dots\cdot 2^n
|
7,695 |
(3 + 2)^2 = 2 \cdot 2 + 2\cdot 2\cdot 3 + 3^2
|
19,964 |
x^2 + x \cdot x + 1 = x\cdot x + x + x + x\cdot x = x \cdot x + x + x + x \cdot x + 1
|
-30,249 |
\frac{1}{z + 4 \cdot (-1)} \cdot (z^2 - 8 \cdot z + 16) = \tfrac{1}{z + 4 \cdot \left(-1\right)} \cdot (z + 4 \cdot \left(-1\right))^2 = z + 4 \cdot (-1)
|
1,429 |
\|f-g\|_p=\|f-f_n+f_n-g\|_p\le\|f-f_n\|_p+\|f_n-g\|_p<\tfrac\varepsilon2+\tfrac\varepsilon2=\varepsilon
|
71 |
\{A, H\} \implies A \cup H = H
|
3,285 |
(\frac{1}{2})^{-2/3} + (-1) = 2^{\tfrac23} + (-1) = 4^{\frac13} + (-1)
|
18,357 |
(12*\sqrt{2} + 19)*(19 - 12*\sqrt{2}) = 73
|
17,278 |
3 = 1^3 + 1 \cdot 1 + 1^2
|
1,390 |
a = b^3 \frac{a}{b^3} = b^2 ba\cdots ba\frac{1}{bb^2}/b
|
28,274 |
\binom{j + i}{i} = \frac{\left(i + j\right)!}{j!\times i!}
|
18,326 |
999 = 10 10^2 + (-1)
|
30,882 |
(-1) + 2^n = 2*2^{n + (-1)} + 2*\left(-1\right) + 1
|
42,362 |
6/60 = 1/10
|
-7,150 |
\frac{1}{28} \cdot 3 = \frac18 \cdot 3 \cdot \frac27
|
16,341 |
\frac{d}{dD} \left(\frac{\sin{D}}{1 + \cos{D}}\right) = \frac{1}{1 + \cos{D}}
|
19,857 |
x^2\times \alpha^2 = x \times x\times \alpha \times \alpha
|
6,802 |
\frac{\pi}{10} = \operatorname{asin}(\frac14 \cdot (\left(-1\right) + \sqrt{5}))
|
32,256 |
2^n - 2^{n-1} = 2^{n-1}(2 -1) = 2^{n-1}
|
9,922 |
\left(-\lambda + x\right)\cdot \left(-c + x\right) = x \cdot x - (\lambda + c)\cdot x + c\cdot \lambda
|
23,056 |
4/k = b^2 - c^2 = (b - c)*\left(b + c\right) \Rightarrow \dfrac{1}{k*(-c + b)}*4 = b + c
|
24,602 |
\left(1/2\right)^2 + (\frac12) * (\frac12) = \frac12
|
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