id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
11,095 | (a + g) \cdot (a + g) = g^2 + a^2 + a\cdot g\cdot 2 |
11,686 | (X + Z) E = ZE + XE |
-160 | \frac{1}{(3*(-1) + 10)!}*10! = 10*9*8 |
-13,648 | 7 + 6\cdot 5 - 2\cdot 8 = 7 + 30 - 2\cdot 8 = 37 - 2\cdot 8 = 37 + 16\cdot (-1) = 21 |
6,915 | \frac{1}{114} = 10/1140 |
34,318 | \sqrt{3}*18 = \frac{1}{x^3} + x^3\Longrightarrow x^6 - 18*\sqrt{3}*x^3 + 1 = 0 |
36,632 | (2^{1/2} - 1) \cdot (2^{1/2} - 1) = (-2^{1/2} + 1)^2 |
-3,572 | \frac{1}{q^2} \cdot q = \frac{q}{q \cdot q} = \dfrac1q |
52,730 | \frac{1}{\sqrt{3}} = \frac{1}{\sqrt{3}} * 1 = \frac{1}{\sqrt{3}} *\frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3} |
23,087 | \sqrt{x} * x^2 = x^{1/2}*x^2=x^{2 + 1/2} = x^{5/2} |
4,647 | 0*z + 0*z^2 + z^3 + ... + z^{(-1) + k} + z^k = \frac{1}{z + \left(-1\right)}*(z^{k + 1} - z^3) |
4,157 | \sec(\pi/2 - x) = \csc(x) |
3,190 | (1 + 3 \cdot 3) \cdot (1 + 3^4) \cdot ((-1) + 3^2) = 3^{2^3} + (-1) |
33,047 | \mathbb{E}[U \cdot U \cdot U] = \mathbb{E}[-U]^3 = -\mathbb{E}[U^3] |
26,309 | z^W Az = z^W A^W z = -z^W A |
25,399 | (-p \cdot b + a \cdot q)^2 + (q \cdot b + p \cdot a)^2 = (a^2 + b^2) \cdot \left(q^2 + p^2\right) |
19,985 | \frac{1}{(1 + 0) e} = \frac{1}{e} |
13,693 | \frac{2 \cdot r \cdot \pi}{2 \cdot \pi} = r |
22,155 | 2 \cdot 3^0 + 3^1 \cdot 2 + 2 \cdot 3^2 + ... + 3^{\alpha + (-1)} \cdot 2 = 3^\alpha + (-1) |
-20,356 | \frac{-18\cdot x + 3\cdot (-1)}{5 + 30\cdot x} = -\frac{1}{5}\cdot 3\cdot \frac{x\cdot 6 + 1}{1 + 6\cdot x} |
-26,552 | 2\cdot z^2 - 40\cdot z + 200 = 2\cdot (z \cdot z - 20\cdot z + 100) = 2\cdot (z + 10\cdot \left(-1\right))^2 |
567 | (Y + x)^2 = x^2 + Y \cdot Y + Y \cdot x \cdot 2 |
8,721 | 11 = 18 + 5(-1) + 2(-1) |
26,280 | \left(x + 1\right) \cdot \left(x + 1\right) = 1 + x^2 + x\cdot 2 |
3,038 | \left(-x\right) * \left(-x\right) * \left(-x\right) = -x*(-x) * (-x) = -x*x * x = -x * x * x |
1,306 | 0 < q, 0 < 96 \cdot (-1) + q \cdot 5 \Rightarrow q > \frac15 \cdot 96 = 19.2 |
14,639 | x\cdot h = x\cdot h/x\cdot x |
-20,825 | \frac{(-28) \cdot k}{7 \cdot (-1) + 7 \cdot k} = \frac{7}{7} \cdot \frac{1}{(-1) + k} \cdot (k \cdot (-4)) |
26,239 | 24 = Z\cdot z \implies \frac{\mathrm{d}Z}{\mathrm{d}t}\cdot z + Z\cdot \frac{\mathrm{d}z}{\mathrm{d}t} = 24 |
-5,489 | \frac{3}{14 + r^2 + r \cdot 9} = \frac{3}{(2 + r) (7 + r)} |
44,802 | 1024 = 1\cdot 2^{10} |
50,967 | 24 = 3\cdot 4\cdot 2 |
23,006 | 76923 = \frac{1}{13}\times (-1 + 10^6) |
32,162 | m + (-1) = 0\Longrightarrow 1 = m |
-270 | \tfrac{7!}{(7 + 6(-1))! \cdot 6!} = {7 \choose 6} |
19,698 | \sin{\dfrac{π*4}{3}1} = \sin{-\frac13π} |
8,359 | \binom{l}{y} = \dfrac{l!}{y! \cdot (-y + l)!} |
37,068 | AA^C = A^C A |
4,221 | \dfrac{3\pi}{4} = \pi*9/12 |
-10,748 | -\frac{1}{40\cdot r^3}\cdot 60 = 10/10\cdot (-\frac{6}{4\cdot r^3}) |
33,671 | \left\lceil{\dfrac{1}{3\cdot (-1) + \pi}}\right\rceil = 8 |
-7,967 | \tfrac{1}{25} \cdot (-21 + 72 \cdot i + 28 \cdot i + 96) = \tfrac{1}{25} \cdot (75 + 100 \cdot i) = 3 + 4 \cdot i |
34,924 | \frac{\delta_{a_i}}{2} = \delta_{a_i} |
20,468 | (-y + z)\cdot (y + z) = z^2 - y^2 |
13,654 | \tan^{-1}(1)=\frac{\pi}{4} |
-11,959 | \frac{1}{15}*14 = \frac{1}{4*\pi}*s*4*\pi = s |
19,804 | 2^3 + 2^3 + 2^3 = 2^4 + 2^2 + 2 \cdot 2 |
33,160 | F = (F \cap W) \cup (F \cap Y') = F \cap (W \cup Y') |
6,031 | x^3 + v \cdot v^2 = (v^2 + x^2 - x\cdot v)\cdot (x + v) |
10,876 | \sin{a}\cdot \cos{b} = (\sin(a + b) + \sin(-b + a))/2 |
14,218 | \sin{x} = \cos(\pi/2 - x) = \cos{2 (\pi/4 - x/2)} |
26,921 | 25 (-1) + 25 = 25 \left(-1\right) + 25 |
-98 | -28 + 5*\left(-1\right) = -33 |
-30,747 | (y^2 + 2\cdot \left(-1\right))\cdot 9 = 18\cdot (-1) + 9\cdot y^2 |
3,292 | a^2 + b^2 = \left(a + b + (a\cdot b\cdot 2)^{1/2}\right)\cdot (-(a\cdot b\cdot 2)^{1/2} + a + b) |
20,262 | 2 \cdot \cos^2{\dfrac{1}{2} \cdot x} + (-1) = \cos{x} |
-1,990 | -\pi/4 + 3/2 \times \pi = \dfrac{5}{4} \times \pi |
11,894 | -(z + 10 \cdot (-1)) \cdot \left(z + 4 \cdot (-1)\right) = -40 + 14 \cdot z - z^2 |
-17,282 | 0.767 = \frac{1}{100}\cdot 76.7 |
30,192 | 20683 = 10^3 + 27 27 27 = 19^3 + 24^3 |
22,156 | \frac{3 - 1 + 2 + 4}{1\times 2 - 3\times 4} = 4/\left(-10\right) \neq 0 |
-26,658 | (3 + y) \cdot (1 + 2 \cdot y) = 2 \cdot y \cdot y + 7 \cdot y + 3 |
27,403 | 1 - \frac{6}{20} = \frac{1}{10}*7 |
-5,781 | \tfrac{2}{z\cdot 5 + 40\cdot (-1)} = \dfrac{1}{5\cdot (8\cdot (-1) + z)}\cdot 2 |
-19,424 | 9*\frac{1}{8}/(7*1/6) = \dfrac{6}{7}*\frac98 |
4,658 | \int\limits_{-1}^1 (a + h)^2\,\mathrm{d}z = \int \left(a^2 + \int (h^2 + 2\times \int a\times h\,\mathrm{d}z)\,\mathrm{d}z\right)\,\mathrm{d}z = \int (a^2 + \int h \times h\,\mathrm{d}z)\,\mathrm{d}z |
25,761 | \frac{1/4 \cdot 3}{2 \cdot \frac13} = \frac{9}{8} |
32,531 | 2^{m + 1} - 2^m = 2^m \cdot (2 + (-1)) = 2^m |
-20,671 | \dfrac{1}{m + 4\cdot (-1)}\cdot (7 + m)\cdot 10/10 = \frac{1}{10\cdot m + 40\cdot (-1)}\cdot (m\cdot 10 + 70) |
520 | 20 + 6*(-1) + 8*(-1) = 6 |
23,437 | ((-1) + x \cdot 2) \cdot (2 \cdot x + 3 \cdot (-1)) \cdot (5 \cdot (-1) + 2 \cdot x) \cdot \cdots = (((-1) + 2 \cdot x)!)! |
-4,641 | \frac{13 + 2 \cdot z}{20 + z^2 + 9 \cdot z} = -\tfrac{3}{z + 5} + \frac{5}{z + 4} |
22,451 | 162 ((-1) + k) + 126 = (2 (-1) + k)*180 \Rightarrow 18 = k |
19,775 | \frac{mx}{m * m}1 = \dfrac{x}{m} |
21,333 | (5*(-1) + x)*(x + 1) * (x + 1) = (x^2 - 4*x + 5*\left(-1\right))*(1 + x) |
6,023 | 6/2 \times \left(2 + 1\right) = 9 |
21,511 | \cos^3\left(π\right) = (-1)^3 = -1 |
44,032 | {6\choose 1} = 6 |
-2,454 | ( 5 + 1 )\sqrt{10} = 6\sqrt{10} |
-1,073 | -8/1 \cdot \frac{8}{9} = \frac{1/9 \cdot 8}{(-1) \cdot 1/8} |
6,682 | 0 = x^2 + 4 \times x + 5 \times (-1)\Longrightarrow 0 = (x + 5) \times ((-1) + x) |
-21,052 | \frac18 \cdot 4 = 2/4 \cdot 2/2 |
29,441 | \frac{1}{3} + \frac13 = \frac{2}{3} |
505 | (g^2 + b^2)^3 = 8^2 = 64 rightarrow g * g + b * b = 4 |
12,267 | \frac1n \leq 1\Longrightarrow 1 + \dfrac1n \leq 2 |
9,601 | \frac{x^i}{g} \cdot g = (x/g \cdot g)^i |
12,438 | 1 = -397 \cdot 42094239791738433660^2 + 838721786045180184649^2 |
16,266 | 5\cdot \tan^2{\frac{π}{10}} + 10\cdot (-1) + \cot^2{\frac{π}{10}} = 0 |
3,567 | b' x + 1 = 2(b' + x) |
13,785 | \dfrac{3*8}{6} = 4 |
16,167 | \binom{l}{k} = \frac{l!}{k!\cdot (l - k)!} = \binom{l}{l - k} |
-19,069 | 17/40 = \frac{1}{64 \cdot \pi} \cdot X_r \cdot 64 \cdot \pi = X_r |
-20,610 | \frac{1}{28 - 20 r} (63 (-1) + 45 r) = \dfrac{-r\cdot 5 + 7}{7 - 5 r} (-\frac94) |
-1,078 | -\dfrac{10}{6} = \left(\left(-10\right) \dfrac12\right)/(6\cdot \frac12) = -\dfrac13 5 |
21,554 | 1 + \dotsm + p^{m + 1} = \frac{1}{1 - p}\cdot \left((1 - p)\cdot p^{m + 1} + 1 - p^{m + 1}\right) |
25,205 | \left(x + b\right)\cdot \sqrt{2} + a + a' = a' + x\cdot \sqrt{2} + a + \sqrt{2}\cdot b |
28,030 | \frac{\mathrm{d}}{\mathrm{d}x} \tan(x) = 1 + \tan^2(x) = \sec^2(x) |
10,499 | 6 - \tan^2\left(\frac{\pi}{10}\right)*2 = \cot^2(\pi/10) + 4 (-1) + \tan^2(\pi/10)*3 |
30,416 | 134 = 11^2 + 3 * 3 + 2^2 = 10^2 + 5 * 5 + 3^2 = 9^2 + 7^2 + 2^2 = 7^2 + 7^2 + 6^2 |
7,434 | x^3 = (x + (-1) + 1)^3 = (x + (-1))^3 + 3 \cdot \left(x + (-1)\right)^2 + 3 \cdot \left(x + (-1)\right) + 1 |
Subsets and Splits