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ddrg
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math_formulas

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int64
-30,985
55.9k
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-11,518
-20 + 3*(-1) + 11*i = -23 + i*11
-22,557
-7/9 \cdot 8/9 = \dfrac{(-7) \cdot 8}{9 \cdot 9} = -56/81 = -56/81
16,491
-\frac{20}{3} \cdot u \cdot u + 6 + (24 \cdot (-1) + 3 \cdot u^2 - 17 \cdot u) \cdot -\frac13 \cdot u = 6 - u^3 - u^2 + u \cdot 8
19,066
\mathbb{E}[W_x/\left(A_x\right)] = \mathbb{E}[\frac{1}{A_x}] \cdot \mathbb{E}[W_x]
34,721
\frac{1}{6} \cdot (π \cdot (-1)) = \operatorname{asin}(-1/2)
387
57\cdot 6 + 1 = 343 = 7^2 \cdot 7
13,731
{(-1) + n + r \choose (-1) + r} = {(-1) + n + r \choose n}
3,628
\frac{2^2}{2 + 9} = \frac{4}{11}
20,208
-\tfrac15 = 2\cdot \pi - 9/5 - 2\cdot \pi - \frac85
-5,051
\dfrac{10.8}{1000} = \dfrac{10.8}{1000}
-1,605
\pi*\frac23 = 7/6*\pi - \frac{1}{2}*\pi
16,168
x\times 3/4 = x\times 3/4
-26,389
(-3)*(-3)*(-3)*\left(-3\right) = 81
18,724
10/4323 = \frac{1}{4323} \times 10
30,516
24/45 = \frac{1}{10!}(8!*2*7 + 9!*2 + 8!*2*8)
5,737
\dfrac34 + (-\frac12 + w)^2 = w^2 - w + 1
-26,213
\frac{\mathrm{d}}{\mathrm{d}x} e^{x \cdot 6 - x^2 \cdot 7} = e^{x \cdot 6 - 7 \cdot x^2} \cdot (-x \cdot 14 + 6)
-2,621
\sqrt{7} \cdot 2 = \sqrt{7} \cdot ((-1) + 3)
-1,652
\pi/4 = \frac{23}{12} \cdot \pi - \pi \cdot 5/3
10,905
32 (-1) + y^3 - 12 y^2 + 36 y = (y + 2 (-1))^2 (8 (-1) + y)
50,750
(-1)*9 = -9
30,171
\tan(y + π) = \tan(y)
31,873
\cos{x} + \sin{x} = A \sin(x + x_0) = A \sin{x} \cos{x_0} + A \cos{x} \sin{x_0}
11,901
\frac{x + (-1) + 2}{(x + (-1)) \cdot (1 + x)} = \tfrac{1}{(-1) + x}
30,788
e^y = 1 + y + y^2/2 + \dots
35,845
\cos{x*2} = \cos^2{x}*2 + \left(-1\right)
-2,735
\sqrt{11}\cdot 6 = \sqrt{11}\cdot (4 + 3\cdot \left(-1\right) + 5)
-407
(e^{\pi*i*3/2})^{17} = e^{17*i*\pi*3/2}
3,657
k \cdot 4 = k \cdot 3 + x \cdot 3 \implies k = 3 \cdot x
11,411
e^1 = z\Longrightarrow z = \cos(1) + i \sin(1)
-28,941
16^{\tfrac{1}{2}} = 4
-23,596
12/49 = 3/7\cdot \dfrac{4}{7}
24,401
(3\cdot (-1) + y^2 - y\cdot 2)\cdot (2\cdot \left(-1\right) + y) = 6 + y^3 - 4\cdot y^2 + y
29,856
-(-\frac{1}{2} + R) + X - 1/2 = -R + X
21,457
\left(m = x^{1/2} \implies x^{\frac{1}{2}} \times x^{\frac{1}{2}} = m^2\right) \implies x = m^2
31,498
b^2\cdot 3 + (b + 2\cdot a) \cdot (b + 2\cdot a) = (a \cdot a + b\cdot a + b \cdot b)\cdot 4
-20,944
9/9 \cdot (-4/9) = -36/81
23,735
-(4 + 3 \cdot k) + 0 = 0 \implies -\dfrac43 = k
22,256
1/(\sqrt{2}) = \frac{1}{2 \cdot \sqrt{2}} + \dfrac{1}{2 \cdot \sqrt{2}}
6,570
\tan\left(h\right) = \frac{2}{6} rightarrow h = 22
-8,782
54\cdot \pi + 9\cdot \pi + 9\cdot \pi = 72\cdot \pi
24,363
1 + \left(x + 1\right) (x^3 + x^5 - x^4) = x^6 + x \cdot x^2 + 1
-29,164
-0 - 4 = -4
24,427
k \cdot p = p \cdot k
2,953
z^2 + 5\cdot z + 4 = \left(1 + z\right)\cdot (4 + z)
-8,491
-4 = -\frac{16}{4}
30,928
F = e^{\log_e\left(F\right)}
-20,416
\frac{1}{5 \cdot z + 2} \cdot (2 + z \cdot 5) \cdot \frac{2}{7} = \tfrac{1}{14 + 35 \cdot z} \cdot (z \cdot 10 + 4)
-19,412
\frac29\times \tfrac29 = 2\times 2/(9\times 9) = 4/81
6,470
\tan{x*3} = \tan{3*x}
15,349
\dfrac{1}{s} \cdot l \cdot l^2 = l^3/s
3,927
x \cdot B = B \cdot x^2 rightarrow x \in B
20,856
FFF^T F^T FF^T = FFF^T FF^T F^T
3,181
n^9 - n^3 = \left((-1) + n^3\right)\times n \times n \times n\times (n^3 + 1)
29,368
\cos(-\arccos{x} + \pi) = -\cos(\arccos{x})
22,950
C - B = 0 \Rightarrow C = B
2,033
-\cos{\alpha} = \sin(3*\pi/2 - \alpha)
40,002
\frac{20}{4} = 5 = \left\lfloor{\dfrac{20}{4}}\right\rfloor
-18,320
\dfrac{(p + 2 \cdot (-1)) \cdot p}{(2 \cdot (-1) + p) \cdot (p + 4 \cdot (-1))} = \frac{-2 \cdot p + p^2}{p^2 - 6 \cdot p + 8}
-20,685
-54/12 = 6/6*(-\frac92)
10,576
\frac{1}{35}*20 = \frac17*4
-26,538
-(5*z)^2 + 3^2 = 9 - 25*z^2
5,342
\frac{1}{(x + 4\cdot (-1))\cdot (x + (-1))}\cdot (x + 2) = \frac{2}{x + 4\cdot (-1)} - \frac{1}{(-1) + x}
-16,355
6*16^{1 / 2}*5^{1 / 2} = 6*4*5^{\frac{1}{2}} = 24*5^{1 / 2}
-18,614
-\frac{2}{10} = -\dfrac15
21,788
(h + x) \cdot (h^2 + x^2 - x \cdot h) = h^3 + x^3
5,230
W - y - z = z + W - y
-17,598
23\cdot \left(-1\right) + 43 = 20
30,014
a^{2 \cdot l} \cdot a^{n \cdot 2} = a^{2 \cdot (l + n)}
26,309
z^R Z z = z^R Z^R z = -z^R Z
-19,226
1/45 = \tfrac{A_s}{36*\pi}*36*\pi = A_s
4,032
8 = \dfrac{1}{1 - a/2}a\Longrightarrow -a*4 + 8 = a
-26,601
5 \cdot x^2 + 320 \cdot (-1) = 5 \cdot \left(x^2 + 64 \cdot (-1)\right) = 5 \cdot (x + 8) \cdot (x + 8 \cdot (-1))
10,763
1 = (1 - z) \cdot (z^8 + z^7 + \dots + 1) = (z^8 + z^7 + \dots + 1) \cdot (z + (-1))
-5,617
\dfrac{1}{4\cdot p + 32}\cdot 5 = \frac{1}{4\cdot (8 + p)}\cdot 5
43,472
0 = 3 + 4 + 7\cdot (-1)
23,818
\alpha^3 + \alpha = (1 + \alpha^2) \alpha
27,005
\left(-x_1 + x\right) \cdot (x_2 - v) = x_2 \cdot x - v \cdot x - x_1 \cdot x_2 + x_1 \cdot v
-4,145
\dfrac{1}{x^4}x = \frac{x}{xx x x} = \frac{1}{x^3}
10,590
z^3 + \dfrac{1}{z^3} = -(1/z + z)\cdot 3 + (z + \frac1z) \cdot (z + \frac{1}{z})^2
8,445
d*f*y = f*y*d
28,492
d_{l + 1}^2 = 2 + d_l^2 + \frac{1}{d_l d_l} \Rightarrow d_{1 + l}^2 > d_l^2 + 2
10,348
-\dfrac{1}{\left(-1\right)\cdot 1/2} = 2
38,985
-(2\cdot \left(-1\right) + x) = 2 - x
16,328
(1 + l)! = l! \cdot (l + 1)
19,259
\dfrac{16}{105}\cdot 2\cdot \tfrac{1}{4}\cdot \pi = \dfrac{8}{105}\cdot \pi
26,645
\cos(z*2) = \cos(-2*z)
4,562
4 = 0^2 + 0^2 + 0^2 + 2^2
-6,062
\frac{3}{k\cdot 2 + 6\cdot \left(-1\right)} = \frac{3}{\left(3\cdot (-1) + k\right)\cdot 2}
-22,344
k k - 3 k + 18 (-1) = \left(k + 6 \left(-1\right)\right) (k + 3)
-9,242
q \cdot 45 + 117 (-1) = q \cdot 3 \cdot 3 \cdot 5 - 3 \cdot 3 \cdot 13
24,290
\frac{X''}{C} = -m_y^2\Longrightarrow Cm_y^2 + X'' = 0
28,551
(\sqrt{A}\cdot \sqrt{B}) \cdot (\sqrt{A}\cdot \sqrt{B}) = \sqrt{A}\cdot \sqrt{B}\cdot \sqrt{A}\cdot \sqrt{B}
-25,866
6^4/6 = \frac{1}{6^1} \cdot 6^4 = 6^{4 + \left(-1\right)} = 6^3
39,520
32 = 81 + 49\cdot \left(-1\right)
30,551
{-\frac{1}{2} \choose 2} = \tfrac{1}{8} \cdot 3
28,510
e*d = d = d*e
2,062
-c^2 + x \cdot x = (-c + x) \cdot (c + x)
28,362
x \cdot (a + b) = a \cdot x + x \cdot b
-3,057
\sqrt{7}\cdot 9 = \sqrt{7}\cdot (4 + 5)