Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
-4,702
\frac{-x + 5}{x^2 - 5\cdot x + 6} = -\frac{1}{x + 2\cdot (-1)}\cdot 3 + \frac{2}{3\cdot \left(-1\right) + x}
46,505
106 = 126 + 20 \cdot (-1)
-10,294
\dfrac{4}{5*(-1) + z*2}*4/4 = \frac{16}{z*8 + 20*(-1)}
33,702
f_3\cdot f_2 = f_3\cdot f_2
872
3 + \frac13 \cdot 2 \cdot r = r \cdot 2/3 + 2 \cdot (-1) + 5
4,250
(1 + ((-1) + x)^2)\cdot (1 + (x + 1)^2) = 4^1 + x^4
-20,382
4/4 \cdot \dfrac{1}{-3} \cdot (r \cdot 7 + 1) = \left(28 \cdot r + 4\right)/\left(-12\right)
27,135
\dfrac{1}{1 + 3} \times (15 + 3 \times (-1)) = \frac14 \times 12 = 3
6,250
E[F_2]\cdot E[F_1] = E[F_1\cdot F_2]
-20,224
\frac{7 (-1) - 7 y}{2 + y*2} = -7/2 \frac{y + 1}{y + 1}
-5,019
10^5\cdot 13.8 = 13.8\cdot 10^{0 + 5}
13,445
\dfrac{1}{s^2 + 1} = \frac{\mathrm{d}}{\mathrm{d}s} \tan^{-1}{s}
4,803
f^2 + a \cdot a = \left(a + f\right) \cdot \left(a + f\right) - a\cdot f\cdot 2
15,905
C = E \setminus G \Rightarrow C \cdot E = G
25,683
6*\frac12 3 + 9 (-1) = 0
-3,263
\sqrt{2}\cdot 2 - \sqrt{2} = \sqrt{2}\cdot \sqrt{4} - \sqrt{2}
28,372
\frac{(-1)^k}{\sqrt{k-1} + (-1)^k} = \frac{(-1)^k(\sqrt{k-1} - (-1)^k)}{(\sqrt{k-1} + (-1)^k)(\sqrt{k-1} - (-1)^k)} = \frac{(-1)^k \sqrt{k-1}}{k-2} - \frac{1}{k-2}
-11,643
(0 + 9) + (-9i) = 9-9i
-19,465
\frac54\cdot 4/3 = 1/4\cdot 5/\left(\dfrac{1}{4}\cdot 3\right)
9,729
a^2 = a^1*a
3,940
\sum_{k=3}^n k^2 = \sum_{k=1}^n k^2 - 1^2 + 2^2 = \sum_{k=1}^n k^2 + 5 \times (-1)
36,639
i + 884 = 891 \Rightarrow 7 = i
12,911
(-1) + y^4 = (y + 1) \cdot ((-1) + y) \cdot \left(1 + y^2\right)
-25,501
\frac{d}{dt} \sin\left(\pi\cdot t\right) = \pi\cdot \cos\left(t\cdot \pi\right)
-2,428
(1 + 5) \sqrt{13} = \sqrt{13}*6
2,668
\mathbb{E}(Y) \cdot \mathbb{E}(Y) = \mathbb{E}(Y^2)
34,240
x_1 = 3\cdot (-1) + x_1
-14,132
4 + (3 - 5 \cdot 6) \cdot 7 = 4 + (3 + 30 \cdot (-1)) \cdot 7 = 4 - 189 = 4 + 189 \cdot (-1) = -185
66
(c\cdot x + b + I)^2 = c^2\cdot x^2 + 2\cdot c\cdot b\cdot x + b \cdot b + I = 2\cdot c\cdot b\cdot x + b^2 + 2\cdot c^2 + I
-5,852
\frac{1}{y*3 + 12}*5 = \frac{5}{(4 + y)*3}
159
\cos(x) \cdot \cos(z) - \sin(x) \cdot \sin(z) = \cos(z + x)
20,901
q^4 = ... = 2 + 3 \cdot q
13,474
ff^i = f^{i + 1}
-1,219
\dfrac132\cdot \frac{3}{5} = \frac{3\cdot \frac{1}{5}}{3\cdot \dfrac{1}{2}}
35,910
\dfrac{91}{24} + 2 \cdot \left(-1\right) - 1^{-1} - 1/2 = \frac{1}{24} \cdot 7
4,964
\cos\left(5y\right) = \cos\left(y\cdot 2 + y\cdot 3\right)
23,642
(x^2 + 2x + 2) (x^2 - 2x + 2) = x^4 + 4
-18,417
\dfrac{n^2 - 4}{n^2 - 7n + 10} = \dfrac{(n + 2)(n - 2)}{(n - 5)(n - 2)}
17,901
4\cdot \left(-1\right) + x \cdot x = x \implies \left(2 + x\right)\cdot (x + 2\cdot (-1)) = x
21,312
(10^{410})^{7*x + 10*(-1)} = 10^{7*x + 10*\left(-1\right) + 4} = 10^{7*x + 6*(-1)}
38,591
(y^{1/2})^2 = y
28,644
5 + (n + 1)^2 = n^2 + 2*n + 6
5,712
\left(y = -3 \cdot x + 4 \Rightarrow -x \cdot 3 = y + 4 \cdot (-1)\right) \Rightarrow x = \frac{1}{-3} \cdot \left(y + 4 \cdot \left(-1\right)\right)
-2,103
\pi\times 5/12 = -\pi/12 + \pi/2
15,727
|\frac{1}{2+x} - \frac{1}{2+y}| = \frac{|x-y|}{(2+x)(2+y)} \le \frac14|x-y|
-7,710
\frac{1}{20}(8 - 4i - 16 i + 8(-1)) = \frac{1}{20}(0 - 20 i) = -i
41,888
\dfrac{1}{4!} \cdot (5 + 1)! = 30
-18,324
\frac{1}{(2\cdot (-1) + f)\cdot (f + 5\cdot \left(-1\right))}\cdot (f + 5\cdot (-1))\cdot (f + 5) = \frac{f^2 + 25\cdot \left(-1\right)}{f^2 - 7\cdot f + 10}
35,631
0 = \sin{π \cdot 4}
-30,280
\dfrac{4 + P^2}{P + 3\cdot (-1)} = \dfrac{1}{3\cdot (-1) + P}\cdot 13 + P + 3
18,759
20!/2 = 18!*19*20/2
11,723
\frac{1}{y + (-1)}(y + 1) (y + (-1)) = \dfrac{y + (-1)}{y + \left(-1\right)} (y + 1) = y + 1
43
\left(A_2 \times A_1 \times A_2^T\right)^T = (A_2^T)^T \times A_1^T \times A_2^T = A_2 \times A_1 \times A_2^T
-17,482
56 = 43*\left(-1\right) + 99
8,574
(\omega + z) \cdot (\omega + z) - z^2 = \omega^2 + z \cdot \omega \cdot 2
32,611
p^{-n} = \frac{1}{p^n}
-13,941
\frac{35}{1 + 6} = \frac{1}{7}\cdot 35 = \frac17\cdot 35 = 5
-1,387
\frac{1}{9*\frac17}((-1) \tfrac19) = -1/9*7/9
8,082
4*y*z = (y + z)^2 - (-y + z)^2
28,706
y^6 + \left(-1\right) = (y^3 + (-1))*(y * y * y + 1) = (y^2 + \left(-1\right))*(y^2 + y + 1)*(y^2 - y + 1)
-699
(e^{7 \cdot \pi \cdot i/6})^6 = e^{7 \cdot i \cdot \pi/6 \cdot 6}
-30,157
\frac{\mathrm{d}}{\mathrm{d}y} y^k = ky^{(-1) + k}
-20,557
\frac{-x \cdot 18 + 2 (-1)}{x \cdot \left(-10\right)} = 2/2 \frac{1}{(-5) x} ((-1) - 9 x)
11,041
\frac{1}{b^x \cdot h} \cdot f = f \cdot b^{-x}/h
-3,033
(1 + 2) \sqrt{11} = 3 \sqrt{11}
40,215
2568 = 2 \cdot 2^2 \cdot 3 \cdot 107
-20,779
\frac{10}{n*5 + 15 (-1)} = \frac{1}{n + 3(-1)}2*\frac55
16,941
0 = 6 - \frac{42}{7} 1
9,907
\frac{1}{7} + 1/21 + 1/28 + 1/42 = \frac14
39,061
\frac14 + \frac{1}{6} = (3 + 2)/12 = \dfrac{5}{12}
7,574
d^2*d * d = d^4 = d^3*d = d
27,924
2^2*2013^3 = 61 * 61 * 61*2 * 2*3^3*11^3
25,776
\binom{3}{1}\binom{2}{1}\binom{5}{3} = 60
16,266
5\cdot \tan^2{\frac{\pi}{10}} + 10\cdot \left(-1\right) + \cot^2{\dfrac{1}{10}\cdot \pi} = 0
7,904
|E*C| = |E|*|C|
28,771
z^2 - z \cdot 6 + 38 = (3 \cdot (-1) + z) \cdot (3 \cdot (-1) + z) + 29
19,516
\dfrac{1}{2550} \cdot 288 = \frac{48}{51} \cdot \dfrac{1}{50} \cdot 6
9,480
y^{1/2} \cdot y^{\frac{1}{2}} = y^1 = y
9,823
0 = -4\cdot 3^{1/8} x + 1 + x\cdot 3^{9/8}\cdot 4 \Rightarrow 8\cdot 3^{1/8} x = -1
19,311
\operatorname{atan}(y) = a + z \Rightarrow y = \tan(a + z)
967
x \cdot x = -\dfrac{1}{3} + \frac{1}{3} \cdot (x^3 - (x + (-1))^3) + x
17,435
e^{t\cdot y}\cdot e^y = e^{t\cdot y + y} = e^{(t + 1)\cdot y}
9,326
(a^{x + g} - a^x)/g = \tfrac{1}{g}\cdot (a^x\cdot a^g - a^x) = a^x\cdot \frac1g\cdot (a^g + (-1))
32,193
-16 = a + b \implies -b + a = -1
15,901
2 \cdot \left(2 + k \cdot 3\right) = 6 \cdot k + 4
2,370
z^{2 \cdot (-1) + \tfrac{1}{3} \cdot 4} = z^{-\dfrac{2}{3}}
-9,469
3*3*3*3 - 2*3*3*3*x = -54*x + 81
28,773
\cos(90 - \theta) = \cos(\theta) \cdot \cos(90) + \sin(90) \cdot \sin(\theta)
-11,552
-i*17 - 6 + 5 = -17 i - 1
15,441
z^{50} = z^{32} z \cdot z z^{16}
-18,652
-\frac{90}{20} = -9/2
-11,505
-8 - 20 \cdot i = -8 + 0 \cdot (-1) - 20 \cdot i
-20,175
\frac{1}{8 - 24\times p}\times (14\times (-1) + p\times 42) = \frac{-p\times 6 + 2}{-6\times p + 2}\times (-7/4)
-11,604
15 + 2 - i\cdot 7 = -7\cdot i + 17
45,125
7\cdot (\dfrac{1}{5^4}\cdot 7^2 \cdot 7)^{18} \lt 7\cdot (\frac12)^9 = 7/512 < 1
38,423
(x + 1) \cdot (x + 3) = (x + 1) \cdot x + (x + 3) \cdot 3 = x \cdot x + x + 3 \cdot x + 9 = x^2 + 4 \cdot x + 9
29,054
a^{0 + 1} = a^1 \cdot a^0
15,174
\frac{1}{3} = \frac{0}{3}*1/2 + 2*1/3/2
-21,122
\frac{6}{9} = \tfrac{1}{3} \cdot 2 \cdot 3/3
-6,009
\frac{4}{2x + 8} = \frac{4}{2(x + 4)}