Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
31,451
0 = c_1 + c_2\cdot |1| \Rightarrow c_1 = -c_2
34,310
1 + 2015 + 1007*\left(-1\right) = 1009
20,084
1 = 5^{x/2} - 2^x = 5^{\frac12 \cdot x} - 4^{x/2}
26,917
\int \sin(x)/\cos(x)\,\mathrm{d}x = \int \tan(x)\,\mathrm{d}x
2,773
j \cdot 4 + 1 + k \cdot 4 + 1 = 2 + (j + k) \cdot 4
26,887
det\left(E*Z\right) = det\left(Z*E\right) = det\left(E\right)*det\left(Z\right)
12,007
i^2 + i \cdot x \cdot 2 = y^2 \Rightarrow (i \cdot x \cdot 2 + i^2)^{\tfrac{1}{2}} = y
-3,832
144/72 \frac{\eta^5}{\eta} = \eta^5/\eta \frac{144}{72} 1
11,557
y^2 - 2\cdot y + 5 = 4 + (y + (-1))^2
35,138
\frac{P^3}{\left(P^2 + 1\right)^{5/2}} = -\frac{P}{\left(1 + P^2\right)^{5/2}} + \dfrac{P}{(P^2 + 1)^{\frac{1}{2}\cdot 3}}
8,197
\dfrac{\sin\left(\alpha\right)}{\cos\left(\alpha\right)} = \tan(\alpha)
-26,173
\frac{8}{2} + 3\cdot 7 + 18\cdot \left(-1\right) = 4 + 21 + 18\cdot (-1) = 7
34,243
T^\complement^k = T^1 \dots T^k
-20,226
-\frac{1}{-21} \cdot 9 = -3/(-3) \cdot 3/7
30,284
( x_1 + (-1), z') = \varnothing \Rightarrow \left[x_1, z'\right] = \varnothing
31,349
x \cdot x + 3\cdot x + 10\cdot \left(-1\right) = (x + 2\cdot (-1))^2 + 7\cdot x + 14\cdot (-1) = \left(x + 2\cdot (-1)\right)^2 + 7\cdot x + 14\cdot (-1) = (x + 2\cdot (-1))^2 + 7\cdot (x + 2\cdot (-1))
21,327
\sum_{i=1}^l x_i = \sum_{i=1}^l x_i
11,569
x\cdot f = \frac{1}{\tfrac1x\cdot \frac1f} = 1/\left(1/f\cdot 1/x\right) = f\cdot x
33,443
T\Longrightarrow T
5,645
\sin(\frac12π - x) = \cos{x}
17,200
x = \lambda = \dfrac{x^2}{\lambda}
28,088
\binom{10}{3} = \dfrac{10!}{3! \cdot 7!}
19,213
\frac{1}{1 + \tanh^2\left(y\right)}\frac{\mathrm{d}}{\mathrm{d}y} \tanh(y) = \frac{\mathrm{d}}{\mathrm{d}y} \tan^{-1}(\tanh(y))
48,342
2 * 2*127 = 508
15,348
\mathbb{E}[x - 2\cdot (x + (-1))^2] = \mathbb{E}[x - 2\cdot (x^2 - 2\cdot x + 1)] = \mathbb{E}[-2\cdot x^2 + 5\cdot x + 2\cdot (-1)] = -2\cdot \mathbb{E}[x^2] + 5\cdot \mathbb{E}[x] + 2\cdot (-1)
22,242
2=1\times 2
-10,538
-6/(s\times 8)\times \frac22 = -\dfrac{12}{16\times s}
11,098
\tfrac{x*y*\dfrac{1}{y*x}}{x*y} = 1/\left(x*y\right)
664
\left(-1\right) + r = \frac{r + (-1)}{\left( r + (-1), f \cdot x\right)} \implies ( \left(-1\right) + r, x \cdot f) = 1
8,985
\frac{1}{V*U} = 1/\left(V*U\right)
42,488
6\cdot7\cdot49=2058
1,769
1/2 = \frac12 \cdot (3 + 2 \cdot \left(-1\right))
18,398
\dfrac{\sqrt{2}}{8}\cdot 3 = \frac{3}{\sqrt{32}}
38,823
3/35 = \frac{4/7\times 1/2}{2}\times 3/5
24,011
1 + u^2 = \frac{1}{\cos^2(x)}\Longrightarrow \cos^2(x) = \dfrac{1}{u^2 + 1}
-7,263
6/14\cdot \frac{4}{13} = \dfrac{12}{91}
31,827
4(-1) + 35 + 60 (-1) + 20 = -9
12,445
p = 1/6 + 5/6 \cdot (-p + 1) \Rightarrow \frac{6}{11} = p
28,524
\dfrac{\frac{1}{6}}{3}\cdot 2\cdot 2/3 = 2/27
-26,134
-9 \cdot 1^{-3} - 3 - -9/(-1) - 3 \cdot (-1) = -12 + 12 \cdot (-1) = -24
-11,739
\left(\dfrac{5}{2}\right)^3 = 125/8
538
\frac{db}{dy} = \frac{db}{dx}*i
8,095
-\frac{1}{-8}\cdot 4^3 + 15 = -\dfrac{1}{-8}\cdot 64 + 15
-141
-32 = 6\cdot (-1) - 26
25,068
1/2 = 0 + \frac14 + \frac{1}{8} + \ldots
13,853
n^2 \cdot 4 + n \cdot 4 + 1 = 1 + \left(n + n^2\right) \cdot 4
30,893
(3 - \sqrt{2})(3 + \sqrt{2}) = 3^2 - 2 \times 1^2 = 7
7,555
((98 \times 100 + 2) \times (2 + 100 \times 102) + (100 \times 2)^2)^{1 / 2} = 10002
30,416
134 = 11^2 + 3^2 + 2^2 = 10^2 + 5^2 + 3^2 = 9^2 + 7^2 + 2 * 2 = 7^2 + 7^2 + 6^2
15,579
19^2*4 = 36^2 + 2^2 + 12^2
10,568
k\cdot s + r = k\cdot s - k + k + r = (s + \left(-1\right))\cdot k + k + r
5,819
5/12\cdot \frac{25}{25} = \dfrac{125}{300}
12,698
x^T\times y = (x^T\times y)^T = y^T\times x
1,826
2*π/8 = \tfrac{2*π}{8} = \frac{π}{4}
39,119
120 = 15\cdot 8
9,196
y \cdot 2 \cdot \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\mathrm{d}}{\mathrm{d}x} y^2
-20,451
\frac{1}{10 + p}\times (9\times (-1) + 9\times p)\times \frac{6}{6} = \dfrac{1}{60 + 6\times p}\times \left(54\times (-1) + p\times 54\right)
-5,196
0.43\cdot 10^{(-3)\cdot \left(-1\right) + 0} = 10^3\cdot 0.43
15,315
i\cdot i\cdot \sqrt{x}\cdot \cdots = i\cdot \sqrt{-x}
14,932
\left(a + x\right)^2 = a^2 + x^2 + 2*x*a
18,583
\frac{1}{2} - \frac{1}{3 \cdot 4} = \frac{5}{12}
28,192
\dfrac{1}{\dfrac1a} = a
20,909
8\cdot (\cos{-\pi} + i\cdot \sin{-\pi}) = -8
1,529
\cos(\pi/2) \sin(r) + \cos(r) \sin(\dfrac{\pi}{2}) = \sin\left(\frac12 \pi + r\right)
31,457
2 + \nu \geq 1 + 2x \Rightarrow x \cdot 2 \leq \nu + 1
-3,971
\frac{n}{n^4} = \frac{n}{nn n n} = \frac{1}{n^3}
-6,352
\frac{3}{4 \cdot (t + 2 \cdot (-1))} = \frac{1}{4 \cdot t + 8 \cdot \left(-1\right)} \cdot 3
11,112
-2*5 + 5*3 = (3 + 2(-1))*5
14,766
|\varepsilon\cdot x|\cdot |\varepsilon \cap x| = |\varepsilon\cdot x| = |\varepsilon|\cdot |x|
24,663
\left(m\cdot h\right)!/m! = (m + 1)\cdot (m + 2)\cdot \cdots\cdot m\cdot h
10,988
3 = 2\cdot (-1) + x\Longrightarrow x = 5
25,896
\binom{n}{x} = \binom{n}{n - x} = \left(-1\right)^{n - x} \binom{-x + (-1)}{n - x}
-20,023
\tfrac{1}{14} \left(7 - a*56\right) = \frac{1}{7} 7 (-8 a + 1)/2
-20,309
\frac{-k\cdot 35 + 14\cdot (-1)}{12\cdot (-1) - 30\cdot k} = 7/6\cdot \frac{1}{2\cdot (-1) - 5\cdot k}\cdot (2\cdot \left(-1\right) - 5\cdot k)
24,729
204 = 224 + 20\cdot (-1)
1,870
\left(1 - t\right) \cdot (1 + s) = -t \cdot s + 1 + s - t
-6,691
1/100 + \frac{50}{100} = \frac{1}{100} + 5/10
3,135
(1 + y)^{k + l} = \left(y + 1\right)^k\cdot (1 + y)^l
-9,153
-80 \cdot t = -t \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5
15,562
\frac{1}{z_2} z_2/\left(z_1 z_2\right) = 1/(z_1 z_2)
5,548
2\sin\left(A\right) \cos(A) = \sin(2A)
22,205
\frac{\partial}{\partial t} (gf) = g\frac{df}{dt} + \frac{dg}{dt} f
8,814
(x + y)^3 = \left(x + y\right) \cdot (x + y) \cdot (x + y) = x \cdot x \cdot x + x \cdot x \cdot y + x \cdot y \cdot x + x \cdot y \cdot y + y \cdot x \cdot x + y \cdot x \cdot y + y \cdot y \cdot x + y \cdot y \cdot y
-29,059
0.19 \cdot 7 = 1.33
20,203
3 = 5 + 2 \left(-1\right)
-9,198
z \cdot z \cdot z \cdot 12 - z^2 \cdot 96 = z \cdot 2 \cdot 2 \cdot 3 \cdot z \cdot z - z \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot z
-7,005
\frac37 \cdot 2/6 = 1/7
-1,463
5\cdot 1/4/(\dfrac{1}{7}\cdot (-6)) = -7/6\cdot 5/4
10,137
(-1) + l^2 = (l + (-1))*(1 + l)
43,036
\frac{\partial}{\partial x} d^x = d^x
14,808
\frac{1}{1 + y} \cdot ((-1) + y) = 1 - \frac{2}{1 + y}
8,213
2^d \cdot 5^d = 10^d
16,314
\left(b + g\right)^2 = b^2 + g^2 + 2\cdot b\cdot g \Rightarrow g^2 + b^2 = \left(g + b\right)^2 - 2\cdot g\cdot b
3,211
\left(7 = 8 + (-1) \Rightarrow (-1) + 8M = 7^{1 + 2n}\right) \Rightarrow M*8 = 1 + 7^{n*2 + 1}
16,203
\sin(\alpha) \cdot \cos(\alpha) \cdot 2 = \sin\left(2 \cdot \alpha\right)
2,540
F^T \cdot F = F^T \cdot F
18,283
\arctan\left(-y\right) = -\arctan\left(y\right)
16,088
2^{1024}\cdot 2^{64}\cdot 2^4\cdot 2^1 = 2^{1093}
-1,255
\frac{5 / 8}{9\times \dfrac{1}{7}}\times 1 = \dfrac58\times \frac{1}{9}\times 7
32,087
180 = 3 \cdot 6 \cdot 10