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ddrg
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math_formulas

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int64
-30,985
55.9k
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27,071
(\frac{1}{2} + z)^2 = z \cdot z + z + 1/4
43,548
4! \cdot 4! \cdot 2 = 4! \cdot 4! + 4! \cdot 4!
40,845
1.5 = \frac{1}{4}\cdot 6
15,972
x - b + c - x + b = -x + b\Longrightarrow b - x = c
-3,217
9\cdot \sqrt{13} = \sqrt{13}\cdot \left(5 + 4\right)
14,578
\left(a + 4\left(-1\right)\right) * \left(a + 4\left(-1\right)\right) + b * b = a^2 - 8a + 16 + b^2 = a^2 + b^2
25,393
(k + 1)^2 - k^2 = 1 + 2*k
8,598
d^2\cdot d = d^3
-11,567
-11 - i*3 = -1 + 10 (-1) - 3i
32,126
3 \cdot s - s^2 \cdot 3 + s^2 \cdot s = s^3 + s \cdot 2 - s^2 + s - 2 \cdot s^2
-3,719
\dfrac{12 \times r}{6 \times r^2} = 12/6 \times \frac{r}{r \times r}
22,970
0 = (4 \cdot \left(-1\right) + x^2 - 3 \cdot x) \cdot 2\Longrightarrow 0 = 4 \cdot (-1) + x^2 - 3 \cdot x
-20,521
\dfrac12\cdot 1 = \frac{x + 7}{14 + 2\cdot x}
-6,139
\frac{3\cdot a}{a^2 + a + 12\cdot (-1)} = \frac{3\cdot a}{\left(a + 4\right)\cdot (3\cdot (-1) + a)}
-6,168
\dfrac{2}{(x + 4(-1))*4} = \dfrac{2}{16 (-1) + x*4}
-17,926
30 + 35 = 65
32,970
\left(0, \infty\right) = (0, 1)
18,201
{x \choose -s + x} = {x \choose s}
9,339
R < -x \implies -R \gt x
39
1 + \frac{1}{47}\cdot 24 = \dfrac{1}{47}\cdot 71
4,416
\tfrac{2\left(q + 263\right)}{2q + \left(-1\right)} = \dfrac{1}{2q + \left(-1\right)}(2q + 526) = 1 + \frac{1}{2q + (-1)}527
24,017
19/27 = 1/27 + \tfrac{12}{27} + \frac{6}{27}
-2,979
(4 + (-1) + 2*(-1))*\sqrt{7} = \sqrt{7}
6,773
\cos(6*x) = \cos\left(x + 5*x\right)
19,023
4\times 13/(52\times 52) = 1/52
-19,719
\dfrac{8 \times 5}{9 \times 1} = \dfrac{40}{9}
14,305
1 - \frac{1 - A}{1 - B} = \frac{1}{1 - B}*(1 - B - 1 - A) = \tfrac{1}{1 - B}*(A - B)
18,056
\frac32 = (l_2 - l_1 + 1)/(l_1) = \frac{1}{l_1}\cdot (l_2 + 1) + (-1)
47,150
30\times 2 + L = 60 + L
213
-w \cdot w + (w + 1)^2 = w\cdot 2 + 1
32,460
30 = (-283059965)^3 + 2220422932^3 + (-2218888517) \cdot (-2218888517) \cdot (-2218888517)
-9,242
-13\cdot 3\cdot 3 + x\cdot 3\cdot 3\cdot 5 = 117\cdot (-1) + x\cdot 45
12,319
f^{m + (-1)}\cdot f = f^m
-26
-29 = 6*(-1) - 23
-1,869
\frac{π}{12} - π \cdot 11/12 = -π \cdot 5/6
2,452
\cos(x + x) = \cos{x\cdot 2}
4,099
0.75 = 3/4 = \frac{1}{4} 3
27,040
\left(x + K\right) (x - K) = x - K^2 = (x - K) (x + K)
9,029
z_1^2 + 2*z_1*z_2 + z_2^2 = (z_2 + z_1)^2
-6,990
4/14 \cdot \frac{6}{13} = 12/91
-11,636
-5 + i \cdot 27 = i \cdot 27 - 10 + 5
-14,669
87 = \dfrac14\cdot 348
22,957
\mathbb{E}(X^2) = \mathbb{E}(X) \cdot \mathbb{E}(X) + \mathbb{Var}(X)
16,860
2 \cdot \int\limits_0^\infty \ldots\,dz = \int_{-\infty}^\infty \ldots\,dz
13
75/216 = 3/6 \cdot (\dfrac56)^2
30,239
\frac{x\cdot g}{h} = g\cdot \dfrac1h\cdot x
28,520
1 + y + y^2 + \dots*y^{n + (-1)} = \dfrac{1 - y^n}{1 - y} = \dfrac{1}{1 - y} - \frac{1}{1 - y}*y^n
-9,634
63\% = \dfrac{1}{100}*62.5 = \frac58
21,816
99*y = 13\Longrightarrow y = \frac{1}{99}*13
-7,047
2/5*3/6/4 = \frac{1}{20}
-25,072
4 \cdot y^3 \cdot \cos{y} \cdot \sin{y} + y^4 \cdot \cos^2{y} - y^4 \cdot \sin^2{y} = d/dy (\sin{y} \cdot \cos{y} \cdot y^4)
423
\frac{t - b}{-b + Y} + (-1) = \frac{t - Y}{Y - b}
-2,965
10 \cdot \sqrt{7} = (3 + 2 + 5) \cdot \sqrt{7}
10,589
2 \cdot x + (-1) = -\cos(2 \cdot \sin^{-1}{\sqrt{x}}) = 2 \cdot \sin^2\left(\sin^{-1}{\sqrt{x}}\right) + (-1) = 2 \cdot x + (-1)
25,058
\frac{1}{3}5 = \frac53
2,465
1 + \ln(a) \cdot x + \dfrac12 \cdot x^2 \cdot \ln(a)^2 + x^3 \cdot \ln(a)^3 \cdot \dots/6 = a^x
38,169
10 = \dfrac{40}{4}
2,356
\lim_{n \to \infty} a_n*n = 0 \Rightarrow \infty \gt \sum_{n=1}^\infty a_n
-1,614
23/12 \cdot \pi - 19/12 \cdot \pi = \pi/3
28,660
\dfrac{1}{2 + \sqrt{z}} = -\frac{\sqrt{z}}{-z + 4} + \frac{2}{-z + 4}
47,173
5\cdot 13\cdot 29 = 1885
23,155
0 = -z + 3 rightarrow z = 3
-20,302
\dfrac11\cdot 1 = \frac{-s\cdot 4 + 4}{-4\cdot s + 4}
5,969
r \cdot r = 1 + \left(r + 1\right) ((-1) + r)
36,566
(1 + y)\cdot (1 + y^2 - y) = y^3 + 1
-20,460
\frac{18\cdot (-1) + 18\cdot f}{-f\cdot 14 + 14} = \frac{1}{2 - f\cdot 2}\cdot \left(-2\cdot f + 2\right)\cdot (-\frac{9}{7})
9,146
\tfrac{c}{f}\cdot f\cdot x = \dfrac{c}{f}\cdot f\cdot f\cdot x/f
37,563
2^{a \cdot b} = 2^{b \cdot a} = \left(2^a\right)^b
-27,473
\frac{21}{3} = 7
15,679
1 - x \cdot x = \frac{1 - x^4}{x^2 + 1}
-19,088
\frac{44}{45} = \frac{1}{81 \cdot \pi} \cdot A_s \cdot 81 \cdot \pi = A_s
-18,350
\frac{-y\cdot 7 + y^2}{y^2 - y\cdot 11 + 28} = \frac{(y + 7\left(-1\right)) y}{(y + 4\left(-1\right)) \left(y + 7(-1)\right)}
19,031
\frac{1}{E \cdot D} = \frac{1}{D \cdot E}
39,417
x^3 - y^3 = \left(-y + x\right) (x^2 + yx + y \cdot y)
27,620
\dfrac32 \cdot \frac14 = \frac38
-1,618
\pi \cdot 17/12 + 23/12 \cdot \pi = \frac{1}{3} \cdot 10 \cdot \pi
40,172
32 \cdot 28 = 896
1,231
\frac{1/15*8}{3} = \frac{1}{45}*8
-25,229
-\tfrac{6}{1^7} = -\frac{6}{1} = -6
-11,534
-6 + 4*(-1) - 2*i = -10 - i*2
-4,589
\frac{1}{x^2 - x \cdot 5 + 6} \cdot \left(19 \cdot (-1) + 8 \cdot x\right) = \dfrac{3}{x + 2 \cdot (-1)} + \frac{1}{3 \cdot (-1) + x} \cdot 5
24,033
\tfrac{1}{70}*83 = \frac{2}{7} + \frac{1}{5}*2 + \frac{1}{2}
25,686
-(x + x + 2) \lt -45 \Rightarrow -45 > -(2\cdot x + 2)
31,816
\frac14\cdot 0 + 3\cdot \tfrac{1}{4}/32 = \frac{3}{128}
30,893
(3 - \sqrt{2}) (3 + \sqrt{2}) = 3^2 - 2\cdot 1^2 = 7
33,787
u^5 = -\bar{u} = -1/u
-4,096
\frac{144*r}{72*r^3} = \frac{r}{r^3}*\frac{144}{72}
9,715
-y \cdot y \cdot 2 + 12 \geq -y \cdot 8 + 16 + y^2 \Rightarrow 4 + y \cdot y \cdot 3 - y \cdot 8 \leq 0
27,581
-\tan(\theta) = \tan(-\theta + π)
-25,256
\frac{3}{4 \cdot 1^{1/4}} = 3/(4) = \tfrac34
11,057
\frac{b^3 + a^3}{a^2 - b \cdot a + b^2} = a + b
23,700
d^{16}*d^8*d^2*d^{64} = d^{90}
-2,224
3/18 = -\frac{1}{18}\cdot 2 + 5/18
34,887
43\cdot 6! = 30960
-10,700
\tfrac{1}{30*y + 18}*27 = \frac{9}{10*y + 6}*\frac33
8,895
\phi \cdot (-m + l) + h + j + (d - \phi) \cdot k = p \implies -h + p - \phi \cdot \left(-m + l\right) - k \cdot \left(-\phi + d\right) = j
14,337
16 - \sin{x}*32 + (\sin^2{x} + \cos^2{x})*16 = 32*(-\sin{x} + 1)
13,648
x^{\frac{1}{4}} = x^{1/4} = e^{\log_e(x^{1/4})} = e^{\log_e(x)/4}
29,583
k = 0 + k = 1 + k + (-1) = 2 + k + 2\cdot \left(-1\right) = \cdots = k + (-1) + 1 = k + 0
41,721
{7 \choose 3}*4! = 7!/\left(3!*4!\right)*4! = \tfrac{7!}{3!}