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ddrg
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math_formulas

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int64
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\left(z_1 + z_2\right) \cdot \left(z_1 + z_2\right) = z_2^2 + z_1^2 + z_2\cdot z_1\cdot 2
1,767
yx z = zy x
7,000
2^{k+1}=2\cdot 2^k
24,593
(x + 6\cdot (-1))\cdot (x + 3\cdot \left(-1\right)) = 18 + x \cdot x - 9\cdot x
34,921
J + x = E \Rightarrow E = x^{1 / 2} + J^{1 / 2}
26,533
(1/4)^i = (\frac{1}{2})^{i*2}
-20,342
\frac{(-1) \cdot 2 l}{-l \cdot 3 + 3(-1)} \cdot 3/3 = \tfrac{(-6) l}{-9l + 9(-1)}
-4,772
\frac{1}{4 + x^2 + 5 \cdot x} \cdot (11 \cdot (-1) - x \cdot 2) = -\frac{1}{1 + x} \cdot 3 + \dfrac{1}{4 + x}
-21,611
\sin{-2 \cdot π} = 0
21,558
(-1)^{2(-1) + l} = (-1)^l
26,928
\arcsin(\sin(π + 2 \cdot \left(-1\right))) = \arcsin(\sin(2))
29,981
3 \cdot (-1) + z_2 - z_1 = 0 \Rightarrow z_1 = 3 \cdot (-1) + z_2
30,176
\cos(y) = \sin(\dfrac{\pi}{2} - y)
22,641
\left(a + f + h\right)\cdot (-f\cdot h + a \cdot a + f^2 + h^2 - a\cdot f - a\cdot h) = -3\cdot a\cdot h\cdot f + a^3 + f^3 + h^3
20,581
e + b = -1 \implies e - b = -16
-23,081
-\frac{1}{64} \cdot 81 = \dfrac{3}{4} \cdot (-27/16)
14,629
x/y = \frac{x\cdot 2}{y\cdot 2}
-20,031
\frac{1}{-4 \cdot q + 16 \cdot (-1)} \cdot 12 = 2/2 \cdot \frac{6}{-q \cdot 2 + 8 \cdot (-1)}
20,194
y*(1 + x + \bar{z}) = xy + y\bar{z} + y
-24,829
879\cdot 6 = 5274
18,321
(c + b) \cdot (c + b) = c^2 + 2 \cdot b \cdot c + b^2
9,834
(-b + a) (b + a) = a \cdot a - b \cdot b
26,692
5! - 3!\cdot 8 = 72
-18,989
5/8 = \frac{A_x}{36 \cdot \pi} \cdot 36 \cdot \pi = A_x
39,661
y^2 = l \implies y = \sqrt{l}
1,434
\cos\left(999 z + z\right) = \cos(1000 z)
1,335
\frac{1}{y^t} = y^{-t}
14,257
\cot(3\pi/2 - y) = \cot\left(\pi - y - \pi/2\right) = -\cot(y - \pi/2) = \cot(\dfrac{\pi}{2} - y) = \tan{y}
24,374
-y*x = x*(-y)
-20,976
\dfrac{y*12}{y*(-8)}*1 = -\frac32*\dfrac{(-4)*y}{y*(-4)}
13,137
Z + V\cdot t = V\cdot Z^{-\frac12 + \frac{1}{2}}\cdot t + Z^{1/2 + \dfrac{1}{2}}
-1,952
\pi \frac{13}{12} = \pi \cdot 37/12 - \pi \cdot 2
6,595
(f + (-1))\cdot (f^2 + f + 1) = f^2 \cdot f + (-1)
29,863
\arcsin\left(\sin{y}\right) = \arcsin\left(\sin(\pi - y)\right) = \pi - y
-10,778
5/5*\dfrac{1}{p + 4*(-1)}*7 = \tfrac{35}{20*(-1) + p*5}
20,044
(3!)! = \left(3! + (-1)\right)\cdot 3!\cdot \ldots\cdot 2
40,963
{6 \choose 4} = {2 + 5 + (-1) \choose 5 + (-1)}
-22,366
\left(k + 6*(-1)\right)*(k + 3) = k * k - 3*k + 18*(-1)
8,691
3 \cdot 8^3 + 8^2 \cdot 7 + 3 \cdot 8^1 + 8 \cdot 8^0 = 2016
-1,504
\frac{36}{72} = \frac{1}{72 \times \frac{1}{36}} \times 1 = 1/2
25,998
\left(x + (-1)\right)^4 + 3\cdot (x + (-1))^2 + 2 = (\left(-1\right) + x)^4 + 3\cdot x^2 - x\cdot 6 + 5
-11,910
1.575\cdot 0.1 = \tfrac{1.575}{10}
17,431
0\cdot x = \left(-1 + 1\right)\cdot x
35,124
\frac{1 \cdot 2 \cdot 2 \cdot \ldots \cdot 2}{2 \cdot 4 \cdot 6 \cdot \ldots \cdot n \cdot 2} < \frac{3 \cdot 5 \cdot \ldots \cdot (2 \cdot n + (-1))}{2 \cdot 4 \cdot 6 \cdot \ldots \cdot n \cdot 2}
40,568
-\sqrt{1 - \cos^2{x}} = -\sqrt{\sin^2{x}} = -|\sin{x}|
22,776
\varphi\cdot y\cdot z = \varphi\cdot y\cdot z
9,811
\frac{1}{4 \cdot 5} = -\frac{1}{5} + \frac{1}{4}
-17,206
\frac{1}{\sec^2\left(\theta\right)}\cdot \sec^2(\theta) = \frac{1}{\sec^2(\theta)}\cdot (\tan^2(\theta) + 1)
-6,528
\frac{3}{\left(a + 7\right)*2} = \frac{3}{2*a + 14}
-4,904
1.5 \cdot 10^{\left(-5\right) \cdot (-1) - 5} = 1.5 \cdot 10^0
6,381
\sum_{i=1}^\infty \int |f_i| \cdot a \cdot m\,dx \leq \int \sum_{i=1}^\infty |f_i| \cdot m \cdot a\,dx
18,982
42 = M + S \implies S = 42 - M
11,406
g \cdot b + e \cdot g = (e + b) \cdot g
46,243
10^6\times 4.5 = 4500000
-18,318
\tfrac{(t + 7) \cdot (t + 8 \cdot (-1))}{(t + (-1)) \cdot (t + 8 \cdot (-1))} = \dfrac{56 \cdot (-1) + t^2 - t}{t^2 - 9 \cdot t + 8}
51,691
\left(d = \frac{1}{\sqrt{x}} + \sqrt{x} \Rightarrow 1 + x = \sqrt{x}\times d\right) \Rightarrow (1 + x)^2 = d^2\times x
-22,381
(x + 6)\cdot (4\cdot (-1) + x) = 24\cdot \left(-1\right) + x \cdot x + 2\cdot x
32,967
169/1326 = \frac{1}{102} \cdot 13
-10,442
\frac{36}{24 + x\cdot 60} = 4/4\cdot \frac{1}{6 + 15\cdot x}\cdot 9
12,244
\tfrac{1}{2} = \frac{\frac13}{1 - \frac{1}{3}}
-3,183
(1 + 2)\cdot 6^{1 / 2} = 6^{\frac{1}{2}}\cdot 3
-29,331
-2i + 1 + 8 = 9 - 2i
12,645
\frac{6}{5} = 1 + 1/5
17,181
6 \cdot q + 1 = 1 + 2 \cdot q \cdot 3
22,284
18 + y \cdot y - 9y = \left(3(-1) + y\right) (y + 6\left(-1\right))
31,951
d*h = \frac{1}{2}*(-d^2 + (d + h)^2 - h^2)
45,983
452 = 364\cdot (-1) + 816
-20,521
\frac{n + 7}{14 + n \cdot 2} = \frac{1}{2} \cdot 1
34,536
\sum_{n=0}^\infty \frac{\left(-1\right)^n}{3^n} = \sum_{n=0}^\infty \frac{1}{9^n} - \left(\sum_{n=0}^\infty \frac{1}{9^n}\right)/3 = \frac23*\sum_{n=0}^\infty \frac{1}{9^n}
-10,684
-\frac{1}{4x^2}8 = -\frac{1}{x * x*2}4*2/2
7,174
\frac{1}{2}(10 + 2(-1)) + (-1) = 3
12,013
(c + h)*(c + h) = c + c*h + h*c + h = c + h
-20,148
\frac{28 - k\cdot 42}{-21\cdot k + 49} = \frac{1}{-3\cdot k + 7}\cdot \left(-6\cdot k + 4\right)\cdot \frac77
14,234
b c = \frac{b}{c} = c^2 b
22,117
(n + 1) \cdot (n + 1) + (2 + n) \cdot n = 1 + n^2 \cdot 2 + 4 \cdot n
9,333
6 = \tfrac{1}{\frac{2}{3}*\frac14}
37,874
|-e^{π} + 1 + 4| = |-e^{π} + 5|
12,984
\frac12(3^{(-1) + n} + 1) = \frac16(3^n + 3\left(-1\right)) + 1
-15,788
-47/10 = -6\cdot \frac{9}{10} + \frac{1}{10}\cdot 7
3,356
\left(3 \cdot (-1) + k^2 - k \cdot 6 = q^2 \Rightarrow 12 \cdot (-1) + (3 \cdot \left(-1\right) + k)^2 = q \cdot q\right) \Rightarrow (3 \cdot \left(-1\right) + k + q) \cdot (k - q + 3 \cdot (-1)) = 12
33,297
\left((p + p)^2 = p + p \Rightarrow p + p = p + p + p + p\right) \Rightarrow p + p = 0
-21,606
\cos{4/3\cdot \pi} = -0.5
-26,159
-9 \cdot \cos(6 \cdot π) - -9 \cdot \cos(11 \cdot π/2) = -9 + 0 \cdot \left(-1\right) = -9
-10,590
-4/(q\cdot 60) = -\frac{1}{15\cdot q}\cdot 4/4
12,590
\sin^5{z} = \sin^4(z\cdot \sin{z}) = (1 - \cos^2{z})^2\cdot \sin{z}
12,837
\dfrac{2 \cdot z_j}{z_d \cdot 2} = \frac{z_j}{z_d}
-10,708
\frac{1}{s*4}*(32*\left(-1\right) + s*4) = 4/4*(s + 8*(-1))/s
13,743
\frac{z}{z + 4 \times (-1)} = \frac{1}{z + 4 \times (-1)} \times (z + 4 \times (-1) + 4) = 1 + \frac{4}{z + 4 \times (-1)}
17,256
e + b + c + d = e + b + c + d
-1,781
π\dfrac56 = \frac12π + π/3
8,412
0 = x^{\dfrac13} + 1 rightarrow x = -1
24,881
\frac12 = 0.0111 \cdot ... = 0.1
1,031
-y \cdot 3 + 15 \cdot y = 12 \cdot y
9,823
0 = 1 + 4\times 3^{9/8}\times x - 4\times x\times 3^{\dfrac18} \implies 3^{\frac{1}{8}}\times x\times 8 = -1
4,064
\mathbb{Var}(x - Y) + \mathbb{E}(x - Y) \cdot \mathbb{E}(x - Y) = \mathbb{E}((-Y + x)^2)
-2,575
(2\cdot (-1) + 3)\cdot \sqrt{5} = \sqrt{5}
15,668
\dfrac14*4/4/4*\frac14/4 = \frac{4}{4^5}
40,934
4! = \dfrac{5!}{5}
20,875
-l \cdot 13 + 95 = 4 - 13 \cdot (l + 7 \cdot \left(-1\right))
29,094
z^3 + (-1) = (z + (-1))*(z^2 + z + 2*(-1)) + z*3 + 3*(-1)