Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
6,499
\frac{\pi}{6} \cdot 5 - \frac{\pi}{6} = 2 \cdot \pi/3 > 2
17,159
n*\frac{1}{100}*60 = n*3/5
30,262
0.1*z = z*\frac{10}{100}
25,371
\pi*4 + 8*\pi + \pi*8 = 20*\pi
-2,827
4\cdot \sqrt{5} + \sqrt{5}\cdot 5 = \sqrt{5}\cdot \sqrt{25} + \sqrt{16}\cdot \sqrt{5}
-27,508
12\cdot a^2 = 2\cdot a\cdot a\cdot 3\cdot 2
31,153
1 = z_1 * z_1 - j^2 z_2^2 \implies (z_1 - jz_2) \left(z_1 + jz_2\right) = 1
-9,747
0.01 (-84) = -\frac{1}{100}84 = -\frac{21}{25}
-20,055
\frac{(-9)\cdot k}{(-9)\cdot k}\cdot (-4/9) = k\cdot 36/((-81)\cdot k)
-3,067
16^{1/2}*6^{1/2} - 6^{1/2} = -6^{1/2} + 4*6^{1/2}
33,229
z^3 = z*z^2 = z*z = z^2 = z
25,516
x^4 - b \cdot x^3 + x \cdot b + (-1) = (x + 1) \cdot (x^2 - x \cdot b + 1) \cdot (x + (-1))
18,537
\frac{1}{3}\cdot (f + 2) = 2\Longrightarrow f = 4
8,779
m^4 \cdot 4 + y^4 = (y^2 - y \cdot m \cdot 2 + 2 \cdot m^2) \cdot (2 \cdot m^2 + y^2 + 2 \cdot m \cdot y)
25,367
f*h*g = \frac{1}{h}*f*g = f/h*g = \tfrac{f*g}{h}
1,693
2(\frac12 \cdot 147 \cdot 2 + 1/2 \cdot 74 \cdot 3 + \frac{1}{2} \cdot 146 \cdot 2) = 808
7,399
56 = -3*62 + 242
18,470
Z \cdot D \cdot D + Z \cdot D^2 = D \cdot D \cdot Z \cdot 2
18,632
h^{x + n} = h^n*h^x
-15,301
\frac{x^4}{\tfrac{1}{x^{15}} \times \frac{1}{y^{10}}} = \frac{x^4}{\tfrac{1}{x^{15} \times y^{10}}}
27,305
10836 = 2^2 \cdot 3 3 \cdot 7 \cdot 43
10,588
\cos\left(-\beta + x\right) = \sin{x}*\sin{\beta} + \cos{\beta}*\cos{x}
28,952
\dfrac{1}{2}*45 = 22.5
8,804
T^{n + m} = T^n \cdot T^m
9,107
\dfrac{1}{l + 4*\left(-1\right)}*7 + l + 4 = \tfrac{l^2 + 9*(-1)}{l + 4*(-1)}
-29,209
2 \cdot \left(-1\right) + 0 \cdot \left(-1\right) + 0 \cdot 2 = -2
-16,055
7\cdot 6\cdot 5\cdot 4 = \dfrac{7!}{\left(7 + 4 (-1)\right)!} = 840
21,008
Y\cdot Y^W = Y\cdot Y^W
14,084
\sin{x} = \sin((2n + 1) \pi - x) = \sin(x + 2n\pi)
1,173
4 = b*y + 4*z\Longrightarrow y = -4/b*z + 4/b
21,722
1/10 + \frac{1}{15} = \frac{1}{30}3 + 2/30 = \dfrac{5}{30}
-5,535
\frac{4}{(x + 2 \cdot (-1)) \cdot 3} = \frac{1}{3 \cdot x + 6 \cdot (-1)} \cdot 4
36,832
\int_0^k 1 \cdot 2 \cdot x\,\mathrm{d}x = 0.5 = \int\limits_k^{12} x\,\mathrm{d}x
30,906
k = (-1) + 2 \cdot k \Rightarrow 1 = k
-10,460
5/5 \cdot \frac{1}{k \cdot 10 + 10} \cdot (k \cdot 5 + 7 \cdot (-1)) = \frac{1}{k \cdot 50 + 50} \cdot (k \cdot 25 + 35 \cdot (-1))
-25,362
d/dy \cot\left(y\right) = -\dfrac{1}{\sin^2(y)}
15,132
(3 + y \cdot 5) \cdot 2 - 5 \cdot (2 y + 1) = 1 \Rightarrow ( 3 + 5 y, 1 + 2 y) = 1
36,705
133=7\cdot 19
29,270
1 + 2\cdot (2^l + \left(-1\right)) = 2^{l + 1} + (-1)
15,148
x_0 - -x_0 = 2 \cdot x_0
21,752
\frac{10}{20}\cdot 2 = 1
21,058
\frac{x^2}{4\cdot x} = x/4
-2,688
\sqrt{3}\cdot \left(3 + (-1) + 2\right) = \sqrt{3}\cdot 4
8,762
\{E,B\} \implies \{E, B\}
12,365
(n + 1)*n! + n! = n!*\left(n + 1 + 1\right) = n!*\left(n + 2\right)
-12,368
\sqrt{28} = 2 \cdot \sqrt{7}
21,470
\frac{1}{49} = \frac{1}{2 \times (-1) + 100} \times 2
-20,640
3/3 \cdot \dfrac{1}{j \cdot 6 + 8} \cdot 2 = \dfrac{6}{24 + 18 \cdot j}
24,244
\dfrac{1}{d^\psi} = d^{-\psi}
5,099
B \cdot x \cdot g = B \cdot x \cdot g
12,399
z^4 + 5 \cdot z + 1 = \left(z^2 + 1\right) \cdot (z^2 + (-1)) + 5 \cdot z + 5 \cdot (-1) = \left(z + (-1)\right) \cdot (z^3 + z^2 + z + 6)
-29,426
\frac{36}{5} = 3*12/5
16,939
\sin(Y)/\sin(Y/2) = 2 \cos(Y/2)
-1,264
-5/3*7/9 = \frac{1/9*7}{1/5 (-3)}
-15,858
8 \cdot \frac{1}{10} \cdot 7 - 9 \cdot \frac{3}{10} = \frac{29}{10}
-9,482
3(-1) + a*2*2*3 = 12 a + 3(-1)
-18,691
0.2257 = \left(-1\right) \cdot 0.5 + 0.7257
17,893
\sin\left(z\right)*2 = y \implies z = \operatorname{asin}(\frac{y}{2})
8,614
y^4 + \left(-1\right) = \left(y^2 + (-1)\right)\times (y \times y + 1)
682
\frac{1}{z^6} = (1/z)^6
17,618
(1 + x)^n\cdot (1 + x)^n = (1 + x)^{2\cdot n}
1,880
\int x * x * x*\sqrt{2^2 - x^2}\,dx = \int x * x^2*\sqrt{(x + 2)*(-x + 2)}\,dx
-19,348
\tfrac{1/6*5}{\dfrac{1}{9}*2} = \frac{9}{2}*5/6
9,407
\tfrac{5}{6}\times 1/6 + \dfrac16 = \frac{11}{36}
-2,142
\frac{7}{6}*\pi + \pi/2 = \frac53*\pi
30,725
(-24) \cdot 9 + 3 \cdot \left(-1\right) = -219
1,711
\frac{5}{5+4}\frac{6}{6+3} = \frac{30}{81} \approx 0.37
27,682
\frac12 = \cos{\frac13\times \pi}
-11,072
\left(y + a\right)^2 = (y + a) (y + a) = y^2 + 2a y + a^2
28,164
\binom{2}{1}*\binom{13}{1} = 26
-4,268
\frac{d^4}{d^2 * d} = \frac{d*d*d*d}{d*d*d} = d
19,077
-7^3 + 3042 - 12 \cdot 12^2 = 971
8,659
a + z = w \Rightarrow z = w - a
30,702
-d_1 + f + d_2 = -(d_1 - d_2) + f
6,473
\dfrac{1}{2} \cdot (\frac{1}{1 + l} \cdot (y + 1) + \frac{y}{l + 1}) = \dfrac{2 \cdot y + 1}{2 + 2 \cdot l}
4,571
x \cap ((B' \cap U) \cup (U \cap x)) = (U \cap x) \cup (U \cap \left(B' \cap x\right))
-6,102
\frac{1}{2*\left(p + 4*(-1)\right)} = \tfrac{1}{p*2 + 8*\left(-1\right)}
-15,999
\dfrac{1}{10}*5 = 6*5/10 - 5*\frac{5}{10}
27,145
(2\sqrt{x}) * (\sqrt{x}*2)^2 = x^{\frac{3}{2}}*8
14,473
z^2 \cdot 4 = \left(z \cdot 2\right) \cdot \left(z \cdot 2\right)
-5,413
10^{(-2)*\left(-1\right) - 2}*1.4 = 10^0*1.4
13,141
L + \epsilon \gt a rightarrow a - \epsilon \lt L
6,800
-c^2 + x \cdot c \cdot 2 = b \cdot b - a^2 \Rightarrow x = \tfrac{1}{c \cdot 2} \cdot \left(b^2 - a^2 + c^2\right)
-18,872
6 = \frac{1}{2} \cdot 12
17,467
-2 = 3 (-1) + 1^2
-8,016
\frac13 \cdot (12 + 6 \cdot i) = \tfrac{6}{3} \cdot i + \frac{12}{3}
2,186
p = p^2 = (-p)^2 = -p
27,464
2\times a\times b = b\times (a + a)
8,409
z\cdot (3939 - 6\cdot 606) = z\cdot 303
17,926
r = -n^3 + \frac{s}{3*n} \Rightarrow 0 = n^6 + n^3*r - \tfrac{s^3}{27}
37,539
330 + 15 \left(-1\right) = 315
43,912
771 = 3 \cdot 257
10,768
b \gt c rightarrow c^2 = c*c \lt c*b < b*b = b^2
1,192
\cos(-\beta + \alpha) = \cos{\beta}*\cos{\alpha} + \sin{\alpha}*\sin{\beta}
3,592
-z_1 + z_3 = 2 X \sin{Z} \cos{30} \Rightarrow \dfrac{1}{3^{1/2}} (-z_1 + z_3) = \sin{Z} X
14,400
\dfrac{1}{\sqrt{z^2 + 1}} = \cos(\operatorname{atan}\left(z\right))
6,514
\frac13 = \dfrac{1/36}{1/36*3} 1
18,665
(11 + \sqrt{10})*(11 - \sqrt{10}) = 3*37
33,630
r^9 = \left(r \cdot r \cdot r\right)^3 = (r + 1)^3 = r^2 \cdot r + 1 = r + 2 = r + (-1)
4,861
g*C = g*C