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ddrg
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math_formulas

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int64
-30,985
55.9k
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17,898
s\cdot x_1/t = x_1\cdot s/t
22,118
\frac{\text{d}}{\text{d}x} e^{3\cdot x} = e^{3\cdot x}\cdot 3
6,118
\left(-\left(-x + 1\right)^5 + 1\right)/x = 5 + x^4 - 5\times x \times x^2 + 10\times x^2 - 10\times x
-1,907
\frac{5}{6} \cdot \pi + \pi = 11/6 \cdot \pi
18,037
27.4 = 12/1 + \frac{12}{5} + \frac{12}{4} + 12/3 + 12/2
18,620
8031810175 = ((25 + \left(26\cdot ((26\cdot 25 + 25)\cdot 26 + 25) + 25\right)\cdot 26)\cdot 26 + 25)\cdot 26 + 25
14,493
1 + x + ... + x^{n + (-1)} = (-e^{\frac{\pi*2}{n}} + x) ... e^{\frac2n\pi*(\left(-1\right) + n)}
-25,818
5/40 = 5/(4\cdot 10)
-4,904
1.5*10^{(-5)*(-1) - 5} = 10^0*1.5
9,346
\mathbb{Var}[X - Y] = \mathbb{Var}[X + Y]
35,361
x \times 5 + 6 \times (-1) - 3 \times x + 2 \times \left(-1\right) = 5 \times x + 6 \times \left(-1\right) - x \times 3 + 2
11,758
(a - b)^2 = -(a + b)^2 + (b^2 + a * a)*2
5,234
2 \cdot ((-1) + 2^l) + 1 = (-1) + 2^{1 + l}
10,941
\cos(2 \xi) = (-1) + \cos^2(\xi) \cdot 2
15,604
-y' y + x = y + y' x
41,503
x + \left(-1\right) = 0 \implies x = 1
36,859
n^2 = \left(6 \cdot (-1) + n\right) \cdot (n + 6) + 36
32,389
1729 = 1^3 + 12 \times 12^2
14,212
\lim_{z \to \infty} 2 \cdot z = \lim_{z \to \infty} z
16,647
\frac{4}{6^2 \cdot 6} \cdot 2^2 \cdot 3 = 6/27
23,792
k! = 2 \cdot 3 \cdot \cdots \cdot k
1,489
3 \cdot n^2 \cdot b = 1\Longrightarrow b = \frac{1}{3 \cdot n^2}
17,035
\cos(y) = \cos(y + 2*\pi)
-5,466
\frac{1}{4*(r + 10)} = \frac{1}{4*r + 40}
-4,608
-\frac{5}{y + (-1)} + \frac{1}{y + 5} = \frac{-y\cdot 4 + 26\cdot (-1)}{5\cdot (-1) + y^2 + 4\cdot y}
-21,384
\frac{1}{4}\cdot 3 = \dfrac{1}{8}\cdot 6
11,573
(1 + x) \cdot (1 + k \cdot x) = 1 + (k + 1) \cdot x + k \cdot x^2 \geq 1 + (k + 1) \cdot x
20,018
\frac{1}{60} = \frac{1}{8}\cdot \left(1/3 - 1/5\right)
-11,759
256^{-\frac{1}{4}} = (1/256)^{\frac14} = \dfrac{1}{4}
12,117
\mathbb{Var}[A] = \mathbb{E}[A - \mathbb{E}[A]]^2 = \mathbb{E}[A^2]
35,753
\frac{b}{a^2} = \frac{1}{a^2} \cdot b
2,849
20 \cdot \dfrac34 = 15
23,319
9 \cdot 9 - 5 \cdot 4^2 = 81 + 80 \cdot (-1) = 1
3,298
7^{340} = ((((\left(\left((7^2)^2 \cdot 7\right)^2\right)^2 \cdot 7)^2)^2 \cdot 7)^2)^2
-3,354
(3 + 2 + 4) \cdot 13^{1/2} = 13^{1/2} \cdot 9
38,531
y - z = y - z
-20,415
\frac{5}{5} \cdot (-\frac{1}{s + 7} \cdot 9) = -\frac{1}{5 \cdot s + 35} \cdot 45
32,415
87 = 9 + 78
-11,755
100^{-1/2} = (1/100)^{1/2} = 10^{-1}
5,516
z \cdot z = 1 + (z + \left(-1\right))\cdot (z + 1)
34,261
-\frac{\pi}{3} = \sin^{-1}(\sin\left(\frac{4\pi}{3}1\right))
-20,383
-\dfrac{1}{9} \cdot 4 \cdot \frac{9 \cdot \left(-1\right) + k}{9 \cdot (-1) + k} = \frac{1}{k \cdot 9 + 81 \cdot (-1)} \cdot (-k \cdot 4 + 36)
10,336
\int \sec^2(y)\,dy = \tan(2\cdot y/2) + H = \tan\left(y\right) + H
-23,334
1/5*3/7 = \frac{3}{35}
1,402
-2*(x^2*4 + 3*x^2 * x) + 3*(1 + 2*x^2 + 3*x^3) = 3 - 2*x^2 + x^2 * x*3
9,229
\frac{1}{\left(1 - x\right)^3}(x^2 + 1 + x) (1 - x) = \frac{1}{(1 - x)^2}(x^2 + 1 + x)
-15,658
\frac{k^4}{(\dfrac{1}{k^3\cdot q^5})^2} = \dfrac{k^4}{\frac{1}{k^6}\cdot \dfrac{1}{q^{10}}}
4,118
\tfrac{1}{2} \times 1 = 1/2
-30,256
\frac{y^2 + 36\cdot \left(-1\right)}{y + 6\cdot (-1)} = \frac{(y + 6)\cdot (y + 6\cdot (-1))}{y + 6\cdot (-1)} = y + 6
-4,995
3.95\cdot 10 = 3.95\cdot 10\cdot 10 \cdot 10 = 3.95\cdot 10 \cdot 10 \cdot 10
23,879
d c = c d
22,248
(n + \left(-1\right))\cdot (n + 1) = (-1) + n^2
9,764
z^3 + (-1) = \left(z + (-1)\right)*(z^2 + z + 1)
4,513
( s' + \gamma, m + x) = ( s', x) + ( \gamma, m)
303
\frac{x^2 + 1}{x^2 + 3} = \frac{1}{x^2 + 3} \cdot (x^2 + 3 + 2 \cdot (-1)) = 1 - \frac{2}{x^2 + 3}
-24,890
\dfrac{1}{6} = \frac{q}{6 \cdot \pi} \cdot 6 \cdot \pi = q
758
\frac{1}{y^q} = y^{-q}
-608
e^{11*5*π*i/3} = \left(e^{5*π*i/3}\right)^{11}
-28,869
\frac{0.2}{60\cdot 0.01}\cdot 1 = 1/3
-20,458
\dfrac{1}{-2\cdot k + 2}\cdot (9\cdot (-1) + 9\cdot k) = -9/2\cdot \frac{1}{1 - k}\cdot (-k + 1)
-6,597
\dfrac{1}{2 (3 + r)} = \frac{1}{6 + 2 r}
13,553
3 + \sqrt{9} - 3*\sqrt{1} - \sqrt{9}*\sqrt{1} = 0
26,776
1728 = (3 \cdot x + 3 \cdot y) \cdot (2 \cdot x + 2 \cdot z) \cdot \left(2 \cdot y + 2 \cdot z\right) \leq ((5 \cdot x + 5 \cdot y + 4 \cdot z)/3)^2 \cdot ((5 \cdot x + 5 \cdot y + 4 \cdot z)/3)
5,510
\frac{1}{2^{l + (-1)}} = \frac{1}{2^l} \left(0 (-1) + 2\right)
29,325
15 + 3\cdot (-5) = 0
10,347
\tfrac{1}{2} \cdot \left(3 + 6\right) + (1 + 2) \cdot \frac12/2 = 21/4
-7,385
1/11 = \frac{2}{12}*\dfrac{6}{11}
18,671
x^2\cdot 0.2/l = \frac{1 / 5\cdot x \cdot x}{l}\cdot 1
2,710
f \cdot h \cdot g = h \cdot g \cdot f
-18,444
5 \cdot t + 4 \cdot (-1) = 8 \cdot \left(t + 8\right) = 8 \cdot t + 64
6,028
\binom{8}{2} \cdot 8 = 9\binom{8}{2} + 28 (-1)
-3,220
-4^{\dfrac{1}{2}} \cdot 6^{\dfrac{1}{2}} + 6^{\frac{1}{2}} \cdot 16^{\tfrac{1}{2}} = 4 \cdot 6^{\frac{1}{2}} - 2 \cdot 6^{\frac{1}{2}}
6,236
( 0, 1) + ( b_1, b_2) = ( 0 + b_1, b_2) = [b_1, b_2]
16,742
4^{\tfrac14} = 2^{\frac12}
-10,420
-\frac{12}{20 \cdot a + 12 \cdot \left(-1\right)} = 2/2 \cdot (-\dfrac{6}{10 \cdot a + 6 \cdot (-1)})
25,746
-(x + w) = \dots = -x - w
27,548
3^{n + 1} = 3\times 3^n = 3^n + 2\times 3^n > 3^n + 2
41,732
\frac{2^{\frac{1}{2}}}{2} = \frac{1}{2^{\frac{1}{2}}}
-20,662
\frac{1}{r + 5}\cdot (r + 5)\cdot (-10/7) = \frac{-r\cdot 10 + 50\cdot \left(-1\right)}{7\cdot r + 35}
45,513
10 = 2 + 6 + 2
3,056
y \cdot z \cdot c^2 = z \cdot c \cdot c \cdot y
18,817
0 = j^3 + (-1) = \left(j + (-1)\right)\cdot (j \cdot j + j + 1)
26,596
\left(y + (-1)\right) \times (y + 2 \times (-1)) = 2 + y^2 - y \times 3
-19,674
24/7 = \frac{4*6}{7}
39,438
-z - v = -(v + z)
27,290
\|x\| \times x/\|x\| = x
19,249
(-y) * (-y) = -y*(-y) = y^2
-1,993
\pi\cdot \dfrac{3}{2} = -\frac{\pi}{12} + 19/12\cdot \pi
12,416
r = r*\left(e^{\pi}\right)^0
12,304
(q - p)*(q - p) = (-p + q)^2
-5,818
\frac{3}{4 \cdot m + 8} = \frac{3}{4 \cdot (2 + m)}
32,429
a \cdot H \cdot \frac{n}{a \cdot H} \cdot H = n \cdot H = a \cdot \frac{n}{a} \cdot H
11,044
\arcsin(\dfrac12) = \pi/6
-527
\left(e^{\pi*i}\right)^{19} = e^{i*\pi*19}
16,697
2\cdot 10^2 - 16\cdot 10 + 40 = 80
-23,814
\frac{1}{5 + 7} \times 84 = \tfrac{1}{12} \times 84 = \frac{84}{12} = 7
15,943
25 - 2\cdot (4 - -\frac13\cdot 2\cdot 3\cdot 2) = 9
-20,917
\frac{1}{8 + x*6}(8 + 6x) \frac{1}{3}8 = \dfrac{64 + 48 x}{24 + 18 x}
25,431
2^l + 2^l + 2^l = 3 \cdot 2^l
43,754
(\sum_{k=1}^l \frac{(2^{\dfrac{2}{l}})^k}{2})\times \frac2l = \frac{\sum_{k=1}^l (2^{2/l})^k}{l}