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ddrg
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math_formulas

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int64
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7,894
d_x = 2*d_x
-26,441
\left(x + 2 \cdot (-1)\right) \cdot (x + 3) = 6 \cdot (-1) + x^2 + x
18,196
5 \left(-1\right) + 6 x + 4 (-1) + 2 x = x \cdot 8 + 9 (-1)
16,741
2\cdot (l\cdot 2 + 1) = 4\cdot l + 2
1,442
54 = 135\cdot 2/5
15,186
(g_1 + g_2) \cdot (g_1 + g_2) \leq 2 \cdot (g_1 \cdot g_1 + g_2^2) = 2 \cdot c \cdot c \Rightarrow g_2 + g_1 \leq c \cdot \sqrt{2}
-4,975
10^4*46.4 = 46.4*10^{3 + 1}
25,360
\dfrac{z}{1 + z} = \frac{1/(r_1)\times r_2}{\dfrac{r_2}{r_1} + 1} \Rightarrow \frac{r_2}{r_1} = z
-26,131
12 = 2^4 - 2^3 + 2^2 + 0\cdot \left(-1\right)
40,835
51 = 4 \cdot 50 + 4 \left(-20\right) + 3 (-15) + 2 (-9) + (-6)
10,934
cos(2x)=\cos^2(x)-\sin^2(x)
17,485
x^3 + 3*h*x * x + 3*x*h^2 + h^3 = (h + x)^3
11,787
\frac13\cdot (n + 1)^3 \geq 3\cdot (n + 1) + 3\cdot (-1) = \frac{1}{3}\cdot (n + 1)^3 \geq 3\cdot n
12,225
2*x + (1 - 2*x - 15*x/16 - \dfrac{1}{16})/16 = 2*x + \tfrac{15}{256} - 47*x/256 = \frac{465*x}{256} + \frac{1}{256}*15
-10,277
30 = 10 \cdot r + 16 + 50 \cdot (-1) = 10 \cdot r + 34 \cdot (-1)
-3,101
\sqrt{7}\cdot \left(4 + 1 + 3\right) = 8\cdot \sqrt{7}
4,082
\frac{1}{2}\cdot \left(1 - 1\right) = 0
29,486
(2 \cdot d + 3 \cdot a) \cdot (d - 2 \cdot a) = -6 \cdot a^2 + 2 \cdot d^2 - a \cdot d
-22,808
\dfrac{16}{40} = 8*2/(8*5)
28,060
1/3 + 4/3 \cdot 8 = 11
-23,405
\frac{6}{35} = 3/5*2/7
1,051
(x^3 + 3*(-1))*20 + 77 = 17 + x^3*20
-10,582
-\frac{1}{4\cdot q^2 \cdot q}\cdot 28 = -\frac{7}{q^3}\cdot \frac14\cdot 4
17,432
X \times Z = -(-Z + X)^2/4 + (X + Z)^2/4
24,397
z^2 + 2\cdot z - z^2 - 2\cdot z = z^2 - z \cdot z + 2\cdot z - z \cdot z + 2\cdot z = 4\cdot z
-29,183
8 = 3 \cdot 2 - -2
6,441
\tan^2\left(y\right)*3 = \sec^2(y)*3 - 3
17,457
\dfrac{1}{64}\cdot 9 = \frac{\frac14\cdot 3}{4}\cdot 3/4
-10,781
-\frac{6}{r*25 + 20 (-1)} \dfrac{2}{2} = -\frac{12}{40 (-1) + 50 r}
-3,698
\frac{11}{g} = \frac{11}{g}
12,466
1 - \tfrac{1}{1 + z_k} = \frac{z_k}{z_k + 1}
34,035
z_2*z_1*z_3 + z_3*z_2*z_1 + z_3*z_1*z_2 = 3*z_3*z_2*z_1
-29,362
(-b + a)\times (a + b) = a \times a - b^2
24,993
v^T*A^T*A*v = \|A*v\| * \|A*v\| \leq \|A\|^2*v^T*v
31,304
\dfrac32 = \dfrac18\cdot (2 + 1 + 1 + 2 + 2 + 1 + 1 + 2)
1,493
0 = (x \times I - C)^2 \times v_2 = \left(x \times I - C\right) \times (x \times I - C) \times v_2
22,685
1/(\sqrt{2}) = \frac{1}{2}\cdot \sqrt{2}
-5,402
\frac{10.6}{10^5} = \dfrac{10.6}{10^5}
14,072
\dfrac12 \cdot (\left(-1\right) \cdot \pi) = -\pi/2
-1,586
\frac{\pi}{3} + \dfrac{23}{12} \pi = \dfrac149 \pi
6,949
\dfrac{1}{AD} = 1/(AD)
-20,436
\frac{1}{n + 10\cdot \left(-1\right)}\cdot \left(n + 10\cdot (-1)\right)/9 = \dfrac{n + 10\cdot (-1)}{90\cdot (-1) + 9\cdot n}
4,948
k*m = \left(m + (-1)\right)*k + k
12,107
-(17^{1/2} - 1)/4 = \frac{1}{4} - 17^{1/2}/4
-27,592
4 \cdot \frac{1}{9}/4 = 1/9
-5,666
\dfrac{1}{6 + 2\cdot x} = \dfrac{1}{2\cdot (x + 3)}
-5,538
\frac{1}{k \cdot k + k + 72 \cdot (-1)} \cdot 2 = \tfrac{2}{\left(k + 9\right) \cdot (8 \cdot \left(-1\right) + k)}
14,700
\frac{1 + 3\cdot x^2}{x \cdot x + 3\cdot (-1)} + 3\cdot (-1) = \frac{10}{3\cdot \left(-1\right) + x \cdot x}
38,086
(1 + 6 + 15 + 12)^x = 34^x
34,766
1/2016 = \dfrac{1}{63 \cdot 32}
39,494
\tfrac{1}{36}\cdot 3 = 3\cdot 1/6/6
3,142
x^2/x! = \frac{x}{(x + (-1))!}
22,025
\frac{1}{y + 4 \cdot (-1) + 4 + (-1)} = \frac{1}{3 \cdot ((y + 4 \cdot \left(-1\right))/3 + 1)}
14,592
1/2*1/2*\frac12 = \frac{1}{8}
9,211
(3 (-1) + t) (1 + t) = t^2 - 2 t + 3 \left(-1\right)
-22,720
\dfrac{90}{81} = \frac{10\times 9}{9\times 9}
329
((-1) + n) \cdot \left(n + 1\right) = (-1) + n^2
-1,354
-\frac19*7/3 = (\left(-1\right)*7)/(9*3) = -\dfrac{1}{27}*7
2,551
\frac{X}{x - X\cdot W} = \dfrac{X}{-W\cdot X + x}
15,221
G*\mathbb{E}(\Delta) = \mathbb{E}(\Delta)*G
17,013
x^3 + 3x^2 + 2x = x \cdot (1 + x) (2 + x)
7,848
4^{m + 1} = 4^m \cdot 4 > 4 \cdot m
-16,407
6\times \sqrt{99} = \sqrt{9\times 11}\times 6
32,628
5/9 = \frac{1}{3} + 2 \cdot 1/3/3
10,135
K + \dfrac{n\cdot K}{p + 1} = \left(1 + \dfrac{1}{1 + p}\cdot n\right)\cdot K
-18,358
\dfrac{-x \cdot 6 + x^2}{6 \cdot (-1) + x^2 - x \cdot 5} = \frac{(x + 6 \cdot \left(-1\right)) \cdot x}{(x + 1) \cdot \left(6 \cdot (-1) + x\right)}
6,350
\frac{1}{y^2} - y^2 = 1 \implies 1 - y^4 = y^2 \implies y^4 + y^2 - 1 =0
10,990
(1 + 4*n)*\pi/2 = \frac{\pi}{2} + 2*n*\pi
14,146
0.1 = 0.0111111 \cdot \dotsm
21,531
\frac{y \cdot y}{y \cdot y + 1} = \dfrac{1}{y^2 + 1}\cdot (y^2 + 1 + (-1)) = 1 - \frac{1}{y^2 + 1}
26,518
p \cdot e^{z \cdot p} = \frac{\partial}{\partial z} e^{p \cdot z}
-18,334
\frac{9 \cdot a + a^2}{a^2 + 81 \cdot (-1)} = \frac{a}{\left(a + 9\right) \cdot (a + 9 \cdot (-1))} \cdot (a + 9)
2,107
U \cdot N = U \cdot N
5,066
\frac{1}{17}*2 + 1/16 = 1/16 + 1/17 + \dfrac{1}{17}
-23,475
1/7 \cdot 5/2 = 5/14
47,608
1523 = 1 + 79 \left(-1\right) + 1601
-9,547
64 = 8\cdot 8
9,360
1/x \cdot a = a/x
19,382
((-1) + z^4) \left(1 + z^4\right) = (-1) + z^8
5,026
0 = 1 + \tan^4{\pi/10} \cdot 5 - 10 \cdot \tan^2{\frac{1}{10} \cdot \pi}
17,594
1/12 = 7/x \Rightarrow x = 84
5,210
5x^2-2x-10=(ax+b)(cx+d)=acx^2+(ad+bc)x+bd
19,479
x = p^2 \Rightarrow \sqrt{x} = p
-20,744
\dfrac22 \cdot \tfrac{1}{\left(-2\right) \cdot x} \cdot (x + 3 \cdot (-1)) = \frac{1}{(-1) \cdot 4 \cdot x} \cdot (6 \cdot (-1) + x \cdot 2)
19,612
|D/A| = |D|/|A|
38,281
\sum_{k=0}^\infty M^k/k! = \sum_{k=0}^{n + (-1)} M^k/k! + \sum_{k=n}^\infty M^k/k! = \sum_{k=0}^{n + (-1)} M^k/k!
14,980
\frac{\partial}{\partial z} (g/z) = g \cdot d/dz \frac{1}{z}
14,490
det\left(A + B\right)\times det\left(A - B\right) = det\left(A + B\right)\times det\left(A^T - B^T\right) = det\left(\left(A + B\right)\times (A^T - B^T)\right)
23,906
(a^3 - c^3) (a^2 + a c + c c) = (a - c) (a^2 + a c + c^2) \left(a^2 + a c + c^2\right) = (a - c) (a^2 + a c + c^2) (a^2 + a c + c^2)
8,373
2 + q = 1 + j\cdot q\cdot 2 \Rightarrow q\cdot (2\cdot j + (-1)) = 1
13,791
-x^2\cdot 3 + 3\cdot x + 6 = -3\cdot (x + 1)\cdot (2\cdot (-1) + x)
8,770
h * h + x * x \geq h^2 = h^g h^{2 - g} \geq h^g x^{2 - g}
-483
e^{\frac{i\pi}{12}19} \cdot (e^{\frac{1}{12}19 \pi i})^2 = e^{3\frac{1}{12}\pi i \cdot 19}
46,106
\binom{20}{3} - \binom{4}{3} = 1140 + 4\left(-1\right) = 1136
-27,686
\frac{\text{d}}{\text{d}y} (18*\sin{y}) = \cos{y}*18
26,543
a^n\cdot y = a\cdot ...\cdot a\cdot a\cdot y = a\cdot ...\cdot a\cdot y\cdot a = a\cdot ...\cdot y\cdot a\cdot a = ... = y\cdot a^n
21,701
\frac{1}{x^n}e^x = x^{-n} e^x \gt \frac{x}{(n + 1)!}
9,072
5*\tan(z) = 2*\tan(2*z) = 2*\dfrac{2}{1 - \tan^2(z)}*\tan(z)
-603
e^{11\cdot i\cdot π/2} = (e^{i\cdot π/2})^{11}
18,086
\rho^2 + (-1)^n \rho - \frac{1}{4} = 0 \implies (\sqrt{2} + \left(-1\right)^{1 + n})/2 = \rho