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ddrg
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math_formulas

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int64
-30,985
55.9k
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437k
41,077
255*257 + 1 = 256^2
11,126
(1 + \frac14)\cdot \left(1 - 1/4\right) = 1 - \dfrac{1}{16}
-6,131
\dfrac{3}{10 \cdot \left(-1\right) + 2 \cdot m} = \tfrac{3}{2 \cdot (m + 5 \cdot (-1))}
6,089
n + 3 \geq (n + (-1))\cdot 2 \Rightarrow 5 \geq n
-20,131
\frac{y\cdot (-81)}{90\cdot y} = -\frac{1}{10}\cdot 9\cdot 9\cdot y/(y\cdot 9)
10,949
2 l + (-1) = -(-l + 51) + 50 + l
11,171
\sin(x)\cdot \sin(y) = \sin\left(y\right)\cdot \sin(x)
19,048
6 \cdot (-1) + \sqrt{16} + 2 = 0
773
16 \cdot (|B \cdot D| - |C \cdot E|) = 64 \Rightarrow 4 \cdot (-1) + |B \cdot D| = |C \cdot E|
4,588
y^5 + \left(-1\right) = (y + (-1))*(y^4 + y^3 + y^2 + y + 1)
-23,229
\frac{\dfrac{5}{9}}{2}1 = 5/18
3,075
-2*x + 1 \lt -x + (-1) \implies x \gt 2
9,329
\int \frac{1}{y}\,\mathrm{d}y = (\ln(y))! = \ln(y)
-14,387
(7 + 8 \times 3) - 6 \times 8 = (7 + 24) - 6 \times 8 = 31 - 6 \times 8 = 31 - 48 = -17
-20,102
\frac{1}{4} \cdot 4 \cdot \frac{1}{(-1) \cdot 3 \cdot k} \cdot \left(-k + 9 \cdot (-1)\right) = \frac{1}{(-12) \cdot k} \cdot (36 \cdot (-1) - 4 \cdot k)
15,598
\sin\left(y\right) = \sin\left(y/2\right) \cos(\frac{y}{2})*2
-20,079
-\tfrac{1}{4}\times ((-1)\times 4\times t)/(t\times (-4)) = \dfrac{4\times t}{t\times (-16)}\times 1
30,177
-n + \frac{n}{-r + 1}*2 = n*\frac{1 + r}{-r + 1}
-11,936
\frac{8.712}{100} = 8.712\cdot 0.01
3,743
\frac{1}{4} 3 = 1^{-1}*3/4
-15,511
\frac{p^3}{\dfrac{1}{q^{20}}\cdot p^{12}} = \dfrac{1}{\frac{1}{q^{20}\cdot \frac{1}{p^{12}}}}\cdot p^3
19,257
\frac{\text{d}}{\text{d}y} (t \cdot t^{\dfrac{1}{2}}) = \frac{1}{2 \cdot t^{\frac{1}{2}}} \cdot t + t^{\frac{1}{2}} = \frac{1}{2} \cdot 3 \cdot t^{\frac{1}{2}}
-2,611
\sqrt{3}-\sqrt{27}+\sqrt{75} = \sqrt{3}-\sqrt{9 \cdot 3}+\sqrt{25 \cdot 3}
13,501
\pi*85/3 = \frac{1}{6}5 \pi*34
10,792
60 = 3!*\binom{5}{3}
33,150
\cos{\psi} \cdot \sin{Y} + \sin{\psi} \cdot \cos{Y} = \sin(Y + \psi)
7,830
-81 i = 81 \left(-i\right) = 81 (\cos(\tfrac{3\pi}{2}) + i\sin(\dfrac{3\pi}{2}1))
17,971
\left[b_1,b_2\right] = [b_1,b_2]
-20,244
\frac{1}{x + 4 \times \left(-1\right)} \times (x + 4 \times (-1)) \times (-\frac{10}{1}) = \frac{-x \times 10 + 40}{x + 4 \times (-1)}
1,916
x^6 + (-1) = (x^3 + 1) (x^3 + (-1))
48,009
(5 \cdot 5)^{1/2} = 5 = |5|
31,103
a^{1 + l} = a^{l + 1}
8,496
4 < y^2\Longrightarrow (y + 2 \cdot \left(-1\right)) \cdot (2 + y) \gt 0
27,765
8\cdot x = 90 \Rightarrow x = \frac{45}{4} = 11.25
10,468
det\left(Z\right) = det\left(Z_{k + \left(-1\right)}\right) = 1 \implies Z_{k + \left(-1\right)}
36,368
49*8 = 392
11,783
(x + b)^2 - x^2 - x*b + b^2 = x*b*3
-1,326
((-8)\cdot \frac{1}{3})/(1/7\cdot (-4)) = -7/4\cdot \left(-\frac83\right)
28,913
h + g \geq 2 \implies g \geq -h + 2
6,165
-C + E(T) = E(T - C)
-7,563
\frac{9 - i \cdot 9}{3 + i \cdot 3} = \frac{1}{-3 \cdot i + 3} \cdot (3 - 3 \cdot i) \cdot \dfrac{-i \cdot 9 + 9}{3 + i \cdot 3}
21,363
2 \cdot x + \left(-1\right) + 3 \cdot (-1) + 1 = 3 \cdot (-1) + 2 \cdot x
-3,122
125^{1/2} + 20^{1/2} = \left(25 \cdot 5\right)^{1/2} + (4 \cdot 5)^{1/2}
17,782
7578/24541 + 2 = \frac{1}{24541}*56660
2,595
k + 2*(-1) = k + 3*(-1) + 1
36,025
z^6 = z^3 z z^2 = z^2 z z z^2
-24,544
\dfrac{1}{3 + 5}\cdot 32 = 32/8 = 32/8 = 4
8,749
h/g*\frac1x*c = c/x*\frac1g*h
-2,807
2^{\dfrac{1}{2}}*25^{\dfrac{1}{2}} - 16^{\frac{1}{2}}*2^{1 / 2} = 2^{\frac{1}{2}}*5 - 4*2^{1 / 2}
-2,664
(3 + 4 + 5)\cdot \sqrt{3} = 12\cdot \sqrt{3}
-448
(e^{\pi i/4})^{12} = e^{12 \pi i/4}
13,121
{3 \choose 2} {6 \choose 3} = 60
23,422
\sin{z} = \sin(1 + z + (-1)) = \sin{1} \cos(z + (-1)) + \sin(z + (-1)) \cos{1}
32,521
10 = \sqrt{0^2 + D_x^2} \Rightarrow 10 = |D_x|
2,861
\frac{1}{44} = -\frac{1}{11} + 1/33 + 1/12
26,227
Y \cdot J = J \cdot Y
28,046
\frac{(2 + f)^3 + 8 (-1)}{2 + f + 2 (-1)} = (12 f + 6 f^2 + f^3)/f = 12 + 6 f + f^2
21,262
yN xN/\left(yN\right) = yN xN N/y = yx/y N
29,506
-n + n^2 \cdot n = n \cdot (n + (-1)) \cdot \left(1 + n\right)
18,948
1 = (z + y)^2 \leq 2*(z^2 + y * y)
-2,827
\sqrt{25} \cdot \sqrt{5} + \sqrt{16} \cdot \sqrt{5} = 5 \cdot \sqrt{5} + 4 \cdot \sqrt{5}
6,952
\frac{3 + 4\cdot \left(-1\right)}{5 + 2\cdot (-1)} = -\dfrac13
1,358
\left(84 - 2\times M + 15 = M \Rightarrow 99 = M\times 3\right) \Rightarrow 33 = M
24,816
\frac{1}{n^2 \cdot n \cdot 3} = \frac{1/n}{3 \cdot n \cdot n}
1,774
33600 = \binom{6}{3} \times \binom{6}{3} \times \binom{9}{3}
27,450
\left(2 - x = n\times x \implies 2 = (n + 1)\times x\right) \implies x = \tfrac{2}{1 + n}
-29,567
\left(2 + z^5 + z\cdot 6\right)/z = z^5/z + z\cdot 6/z + \dfrac{2}{z}
23,766
z^{\frac1e} = z^{\dfrac1e}
5,766
Z_1 \cap Z_1 \cap Z_2^\complement = Z_1 \cap (Z_1^\complement \cup Z_2^\complement) = (Z_1 \cap Z_1^\complement) \cup (Z_1 \cap Z_2^\complement)
22,205
\frac{\partial}{\partial t} d_2*d_1 + \frac{\partial}{\partial t} d_1*d_2 = \frac{\partial}{\partial t} (d_2*d_1)
23,293
(-y)^k = (-y)^k = (-1)^k \cdot y^k
-15,682
\frac{z^4}{\tfrac{1}{z^4 \frac{1}{r^2}}} = \frac{1}{r^2 \frac{1}{z^4}}z^4
-18,425
\frac{k\times (5\times (-1) + k)}{(k + 5\times (-1))\times (k + 6\times \left(-1\right))} = \frac{k^2 - 5\times k}{30 + k^2 - k\times 11}
16,311
\tfrac{1}{k^2} \cdot k \cdot c = c/k
-5,487
\frac{1}{5(y + 2\left(-1\right))}4 = \dfrac{1}{10 (-1) + 5y}4
24,838
\mathbb{E}(V) \cdot \mathbb{E}(W) = \mathbb{E}(V \cdot W)
-1,333
\frac{(-2)\cdot 1/9}{3\cdot 1/2} = 2/3\cdot (-2/9)
-20,879
\frac{(-30) \cdot z}{z \cdot 18 + 36 \cdot (-1)} = \dfrac{(-1) \cdot 5 \cdot z}{3 \cdot z + 6 \cdot (-1)} \cdot 6/6
25,547
-5^{\frac13}/2 + 1 = -\dfrac{1}{\left(\frac{8}{5}\right)^{\frac{1}{3}}} + 1
19,511
\dfrac{\frac{1}{2}}{2}*1 = 1/(2*2) = \frac{1}{4}
24,959
3/4 = \frac{\frac{\sqrt{3}}{2}\cdot \sqrt{3}}{2}
-8,717
270^{\frac13} = (3\cdot 3\cdot 3)^{\frac{1}{3}}\cdot (2\cdot 5)^{\dfrac{1}{3}} = 3\cdot (2\cdot 5)^{1/3} = 3\cdot 10^{1/3}
16,724
x\cdot h\cdot x = \frac{1}{\frac{1}{x - 1/h} - 1/x} + x
32,427
\frac{0}{1} = \tfrac12 0
-16,990
-8 = -8\times (-q) - -48 = 8\times q + 48 = 8\times q + 48
27,625
π/4 = y \implies \cos^5\left(y\right) - \sin^5(y) = 0 \neq \cos(5 \cdot π/4)
5,706
g^3 + (-1) = (g + (-1))\cdot (g^2 + 2\cdot g + 1 - g) = (g + \left(-1\right))\cdot (g^2 + g + 1)
-6,098
\dfrac{1}{(z + 9)\cdot 4}\cdot 5 = \frac{5}{4\cdot z + 36}
42,288
43 = 50 + 7 (-1)
8,277
x + b'' + c = c + x + b''
26,117
12\cdot \left(-1\right) + 243 = 231
2,122
XDZ/Z = DZX/Z
20,785
z/4 = z^2 + y * y = -y \implies -y*4 = z
23,519
x = \sec{\theta} \cdot 3 \implies \sec{\theta} = x/3
-22,369
35 (-1) + m^2 - 2m = (m + 7(-1)) (m + 5)
33,127
(-1)^{i + 1} = \left(-1\right)^{i + (-1) + 2} = (-1)^{i + \left(-1\right)}\cdot (-1)^2 = \left(-1\right)^{i + \left(-1\right)}
10,762
\frac{1}{2}\times (-\frac{1}{3 + 2\times x} + 1) = \tfrac{x + 1}{3 + x\times 2}
9,926
\sin^4{y}*\cos^2{y} = \sin^4{y}*\left(1 - \sin^2{y}\right) = \sin^4{y} - \sin^6{y}
5,551
\lambda = \lambda + 0*\left(-1\right)
-6,099
\frac{2}{k^2 + k\cdot 4 + 60\cdot (-1)} = \dfrac{2}{\left(k + 6\cdot (-1)\right)\cdot (10 + k)}