Datasets:
ddrg
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math_formulas

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1
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int64
-30,985
55.9k
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437k
40,711
x_{i + 1} = x_{1 + i}
32,919
\dfrac1x + 1/M + 1/N = (x*M + M*N + N*x)/(x*N*M)
-18,437
\frac{r}{\left(r + 7 \cdot (-1)\right) \cdot (r + 2)} \cdot \left(7 \cdot (-1) + r\right) = \frac{1}{14 \cdot (-1) + r^2 - 5 \cdot r} \cdot \left(r^2 - 7 \cdot r\right)
11,962
0 = \overline{\sum_{k=0}^n a_k\cdot z^k} = \sum_{k=0}^n a_k\cdot \overline{z}^k
15,214
s = s/2 + \tfrac{s}{2} < \frac{s}{2} + 1
-4,114
\dfrac{1}{a^3} \cdot a \cdot a = \tfrac{a \cdot a}{a \cdot a \cdot a} = 1/a
-1,497
-2/9 \cdot \left(-5/7\right) = \frac{\dfrac19 \cdot \left(-2\right)}{1/5 \cdot (-7)}
1,663
v_1 \lambda = Bv_1 \Rightarrow B^2 v_1 = \lambda Bv_1 = \lambda * \lambda v_1
-1,247
\tfrac{30}{35} = \dfrac{1}{35*\frac{1}{5}}*6 = 6/7
9,523
\frac{10}{20}\cdot \tfrac14 = 1/8
22,346
-D \cdot 2 + D^2 = 0 \Rightarrow 0 = D,2
24,367
\int g\,\text{d}z = \lim_{m \to \infty} \int g_m\,\text{d}z = \int \lim_{m \to \infty} g_m\,\text{d}z
-18,986
\dfrac15 = \dfrac{1}{49 \cdot \pi} \cdot G_t \cdot 49 \cdot \pi = G_t
35,639
1/8 = \frac{3 * 3^2}{6 * 6^2}
17,716
12 = 2\cdot 6 + 0(-1)
7,925
5 + y^2 - 4y = 1 + (y + 2\left(-1\right))^2
3,637
((x + 1)^2 - x^2)/x = (x^2 + 2*x + 1 - x^2)/x = \frac1x*(2*x + 1)
36,075
\frac{1}{-27} = -\frac{1}{27}
-4,357
\dfrac{10}{7} \cdot q^2 = q^2 \cdot 10/7
-8,314
8 (-7) = -56
28,431
0 = \lim_{l \to \infty} |a_l|\Longrightarrow \lim_{l \to \infty} a_l = 0
14,935
u \cdot u\cdot 2 + v \cdot v = v + 4\cdot u \Rightarrow 2\cdot u^2 - u\cdot 4 + v^2 - v = 0
-7,847
\dfrac{28 + i*6}{4 - 2i} = \frac{i*6 + 28}{-i*2 + 4} \frac{1}{4 + 2i}(4 + i*2)
-23,265
1 - \frac13 = \frac{2}{3}
25,128
\gamma_x \cdot \gamma_x - 2\cdot t\cdot \gamma_x + x = 0 = (\gamma_x - t)^2
7,384
-q\cdot k = -k\cdot q
6,400
x \times (C + Y) = Y \times x + x \times C
21,286
Y\cdot A\cdot x_2 = A\cdot Y\cdot x_2
32,771
2×(2×2×2×2)=32
-16,515
\sqrt{25\cdot 11}\cdot 6 = \sqrt{275}\cdot 6
17,504
b^2 + ba = b^2 + ab
-11,973
1/3 = \frac{p}{10\cdot \pi}\cdot 10\cdot \pi = p
22,177
1 = 1/2 + \frac14 + \dfrac{1}{6} + \dfrac{1}{12}
33,691
\frac22 \cdot 1 = \frac{6}{2 \cdot 3}
2,559
6 \cdot (0.1 + 0.5) + (0.3 + 0.1) \cdot 3 = 4.8
23,557
\left(h - b\right)*(h^2 + b*h + b^2) = -b^3 + h^2 * h
-11,468
0 + 6*(-1) + i*8 = -6 + i*8
18,031
2^l = 2^{(-1) + l} + 2^{(-1) + l}
2,497
d + 1 = \left(d + 1\right)^2 = d \cdot d + 2 \cdot d + 1
43
(D\times x\times D^X)^X = (D^X)^X\times x^X\times D^X = D\times x\times D^X
3,572
z_2 = 0, z_1 \neq 0 \Rightarrow 0 = \tfrac{z_1}{z_1^2 + z_2^4} z_2^2
8,829
2 \cdot (4 \cdot x^2 - 3 \cdot x + (-1)) = 2 \cdot (x + (-1)) \cdot (x + \frac{1}{4}) = \frac{1}{2 \cdot \left(x + (-1)\right) \cdot (4 \cdot x + 1)}
3,442
7/8 + 8/8 + 6.5 \cdot \frac{3}{4} = 6.75
3,343
n^2 - -n + n^2 = n
-2,681
\sqrt{7}\cdot 11 = \sqrt{7}\cdot (5 + 4 + 2)
-7,660
\frac{1 - i \cdot 7}{-3 - 4 \cdot i} = \dfrac{-i \cdot 7 + 1}{-3 - 4 \cdot i} \cdot \dfrac{-3 + 4 \cdot i}{-3 + 4 \cdot i}
16,007
-6\cdot (a + b + c) = (a + b + c)^2\cdot 2 - 3\cdot b\cdot a - 3\cdot b\cdot c - c\cdot a\cdot 3 rightarrow 0 = a\cdot b + b\cdot c + a\cdot c
-13,640
\frac{30}{5 + 1} = \frac{30}{6} = 30/6 = 5
33,691
\dfrac13\cdot 6/2 = 6/(3\cdot 2)
12,880
m\cdot 6 + 1 + 1 = 2 + m\cdot 6
16,071
1/4 + 1/4\cdot 2 = 3/4 \lt 1
6,730
x^{b_1 + b_2} = x^{b_1}\cdot x^{b_2}
37,568
\frac{q^2 - q}{n \cdot n - n} + \frac{1}{n^2 - n}\cdot \left(q\cdot n - q^2\right) = \frac{1}{n^2 - n}\cdot (q^2 + q\cdot n - q^2 - q) = \frac{q\cdot n - q}{n \cdot n - n}
28,107
64 + 40\cdot (-1) = 24
-6,301
\frac{1}{2 \cdot \left(5 \cdot (-1) + h\right)} \cdot 5 = \dfrac{1}{10 \cdot (-1) + 2 \cdot h} \cdot 5
16,989
(x*3)^2 = 9x^2
-4,748
x \cdot x - 7\cdot x + 12 = (x + 3\cdot \left(-1\right))\cdot (4\cdot (-1) + x)
-30,853
\frac{z^3 - 9 \times z}{-3 \times z + z^2} = z + 3
13,406
3 < l \leq 4\Longrightarrow l = 4
-9,351
-z^2\cdot 121 = -11\cdot 11 z z
26,163
15 \cdot 200 = 3000
-744
(e^{\pi \cdot i \cdot 7/12})^{13} = e^{13 \cdot 7 \cdot \pi \cdot i/12}
11,415
0 + u + v + 0 = 0 + v + u + 0\Longrightarrow u + v = u + v
6,332
n = n + (-1) + 1 = n + 2*\left(-1\right) + 2 = \dots = \frac12*\left(n + 1\right) + \frac{1}{2}*(n + (-1))
7,009
-1 = (-1)^{1/2}*(-1)^{1/2} = (\left(-1\right)*(-1))^{1/2} = 1^{1/2} = 1
28,473
441 + 4(-1) = 19*23
25,412
a*b = b*a/a*a
21,722
1/10 + 1/15 = \dfrac{3}{30} + 2/30 = 5/30
33,608
\dfrac{1}{12}\cdot ((-1) + 6 \cdot 6) = \frac{1}{12}\cdot 35
48,352
0 = b \frac{-c^3}{b^2} + c \frac{-c}{b} = \frac{ -c^3-c^2b } { b^2} = - \frac{ c^2 (c+b) } {b^2}
15,562
\frac{\dfrac1y \cdot y}{y \cdot x} = \dfrac{1}{y \cdot x}
-2,575
\sqrt{5}\cdot (3 + 2\cdot (-1)) = \sqrt{5}
4,045
\frac1n \cdot k = \frac{k}{n}
-16,427
2(16*11)^{\frac{1}{2}} = 176^{\frac{1}{2}}*2
-2,886
\sqrt{2}*7 = \sqrt{2}*(5 + 4 + 2*(-1))
-20,506
\dfrac{n \cdot (-10)}{(-1) \cdot 10 \cdot n} \cdot (-\tfrac{1}{5}) = \dfrac{n \cdot 10}{(-1) \cdot 50 \cdot n}
-5,127
10^5 \cdot 0.79 = 0.79 \cdot 10^{2 - -3}
-21,039
\frac18\cdot (g + 5\cdot (-1))\cdot 7/7 = \frac{1}{56}\cdot (35\cdot \left(-1\right) + 7\cdot g)
-11,590
0 + 12\times (-1) - i\times 9 = -12 - i\times 9
32,955
495 = \tfrac{12!}{8!\cdot 4!}
-25,245
-\dfrac{4}{2^5} = -\dfrac{4}{32} = -1/8
8,215
0 = -2*z_1 * z_1 + 8*z_2 \implies 4*z_2 = z_1^2
-26,924
\sum_{m=1}^\infty \frac{3\times \left(3 + 1\right)^m}{m\times 4^m} = \sum_{m=1}^\infty \frac{3\times 4^m}{m\times 4^m} = \sum_{m=1}^\infty \frac{3}{m} = 3\times \sum_{m=1}^\infty 1/m
11,571
x^4 + 10 x^2 + 25 = (x^2 + 5)^2 = \left(2*3^{1 / 2} x\right)^2 = 12 x^2
9,543
\left(8 \cdot 8 + 16^2\right)^{1/2} = 8\cdot 5^{1/2}
10,598
10^2 = \frac{2}{2} \cdot 10^2 = \frac33 \cdot 10^2 = \cdots
-20,133
-1/10 \cdot \frac{(-8) \cdot z}{(-8) \cdot z} = \frac{8 \cdot z}{z \cdot \left(-80\right)}
27,088
\left(-4\right)^2 + 3 * 3 = (-4 + 1)^2 + (1 + 3)^2
16,799
\tan^{-1}(\infty) = \dfrac{1}{2}*\pi
7,649
b/x = \frac1x\cdot b
-1,653
\frac{1}{3} 5 \pi + \pi*3/4 = \pi*29/12
-5,940
\dfrac{5}{2\cdot h + 4} = \frac{1}{(2 + h)\cdot 2}\cdot 5
16,813
-x_3 + x_2 = 4 \Rightarrow 8 = 2 \cdot x_2 - 2 \cdot x_3
2,337
\frac{1}{1/T*M*T} = \frac{1}{T}*\frac{1}{M}*T
13,499
\left(1 + p^2\right) (1 + p^4 - p^2) = 1 + p^6
-20,809
\frac{-6 \cdot k + 10 \cdot (-1)}{-k \cdot 6 + 10 \cdot (-1)} \cdot (-\frac19 \cdot 4) = \frac{1}{90 \cdot \left(-1\right) - 54 \cdot k} \cdot (40 + k \cdot 24)
-26,213
(6 - 14\cdot y)\cdot e^{6\cdot y - y^2\cdot 7} = \frac{\text{d}}{\text{d}y} e^{y\cdot 6 - y^2\cdot 7}
3,260
c \cdot c^2 - f \cdot f \cdot f = \left(-f + c\right) (f^2 + c \cdot c + fc)
-29,026
y^8 = y^5 \cdot y^3
28,268
\frac{1}{\sqrt{2}} = \sin\left(3*π/4\right)