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ddrg
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math_formulas

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int64
-30,985
55.9k
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25,707
\frac73 = 2 + 1/3
43,337
|X| = |X - w + w| \leq |X - w| + |w|
-9,334
24*(-1) - p*80 = -2*2*2*2*5*p - 2*2*2*3
-23,903
\dfrac{1}{7 + 8} \cdot 15 = \dfrac{15}{15} = \frac{1}{15} \cdot 15 = 1
-22,797
90/40 = \frac{90}{4 \times 10} \times 1
2,714
\frac{\mathrm{d}}{\mathrm{d}y} \frac{1}{y^2} = -\dfrac{2}{y * y * y}
15,315
(-\alpha)^{\frac{1}{2}}\cdot i = i\cdot i\cdot \alpha^{1 / 2}\cdot \cdots
15,553
j\cdot 7 + i\cdot 14 = -7\cdot \left(-j - i\cdot 2\right)
13,339
\dfrac{6}{3} 1 = 2 (-1) + 2^2
20,898
S^2 = ((I + (I + \left(I + \dots\right)^{1/2})^{1/2})^{1/2})^2 = I + S
51,653
909 + 1 = 910
-10,695
-\tfrac{1}{100 + 100 \cdot y} \cdot 5 = \frac{5}{5} \cdot (-\frac{1}{20 + 20 \cdot y})
-29,331
-2 \cdot i + 9 = -i \cdot 2 + 1 + 8
34,787
{n + (-1) \choose r + (-1)} = {(-1) + n \choose -r + n}
-17,400
0.269 = \tfrac{1}{100}\cdot 26.9
10,281
\dfrac{dda}{d^2} = da/d
11,029
b\cdot a - a - b = \left((-1) + b\right)\cdot a + b\cdot (-1)
-26,505
b^2 + a a + 2 a b = (a + b) (a + b)
15,886
3\cdot \left(\left(-1\right) + y\cdot 2\right) + 1 = 6\cdot y + 2\cdot (-1)
11,397
\frac{1 - -1}{2.25 - 1.5} = \frac{2}{0.75} = \frac83 \approx 2.7
349
2/3 \cdot h + h = 5/3 \cdot h
-1,576
\pi = \frac{13}{12}\cdot \pi - \frac{1}{12}\cdot \pi
-19,069
\frac{17}{40} = \tfrac{C_t}{64\cdot \pi}\cdot 64\cdot \pi = C_t
17,258
171600 = r_2 \cdot r_1 - r_2 + r_1 + 1 = 172451 - r_2 + r_1 + 1
19,346
(z^{1/2})^2 = \left(z \cdot z\right)^{1/2} = z
19,040
\frac{h^2}{c + h} = -\frac{h}{c + h}c + h
19,806
\frac{3y - ny^3}{2} = y - \frac{n y^2 - 1}{2}y
10,708
Y^T\cdot Y = Y\cdot Y^T
20,881
d/dx (y^3 \times 4) = y^2 \times \frac{dy}{dx} \times 12
14,237
L = L\cdot 2 \Rightarrow L = 0
-7,008
3/8\cdot 6/7 = 9/28
15,281
\left(y + x \cdot z\right)/x = z + \frac{y}{x}
44,047
1^3 + 6\times 1^2 + 11 + 6 = 24 = 3\times 8
24,610
\dfrac{89}{55} = 1 + \frac{34}{55}
7,583
k = 1/(\dfrac{1}{k})
1,897
10 = p^4 + 35/p \geq 2 \cdot \left(35 \cdot p \cdot p \cdot p\right)^{\frac{1}{2}}
8,530
\frac{1}{x^x}*(x + \left(-1\right))^x = \left((x + (-1))/x\right)^x = (1 - \frac{1}{x})^x
3,460
126 + 5 (-1) + 15 (-1) + 0 = 106
23,477
\sin(y + h) = \sin{y} \cdot \cos{h} + \cos{y} \cdot \sin{h}
-17,440
68 + 38\cdot (-1) = 30
2,282
-3 \cdot \left(y^2 + (-1)\right) + (y \cdot y + 1) \cdot 3 = -2 \cdot (3 \cdot (-1) + 2 \cdot y) + y \cdot 4
13,000
p^2 + (-1) = (p + 1) ((-1) + p)
7,525
\sin\left((-x)^2\right) = \sin(x^2)
-1,887
\frac14 \cdot \pi = -\pi + \frac14 \cdot 5 \cdot \pi
10,004
\tan^2\left(A\right) + 1 = \frac{1}{\cos^2(A)}
-17,242
-\frac{5}{3} = -\frac13 \cdot 5
-27,629
-8 + 3*(-1) + 8 + 3*(-1) = -8 + 8 + 3*(-1) + 3*(-1) = 0 + 6*(-1) = -6
-14,725
91 = \tfrac{910}{10}
-2,852
\sqrt{24} + \sqrt{54} - \sqrt{6} = \sqrt{4\cdot 6} + \sqrt{9\cdot 6} - \sqrt{6}
30,598
\cos(\cos{90*0^{\dfrac{1}{2}}}) = \cos{1} \approx 0.54
33,413
\dfrac{f^2 + 1}{x^2 + 1} = x/f \implies f = x
15,295
\sin(u - v) + \sin(v + u) = \cos{v}\cdot \sin{u}\cdot 2
23,875
x_n = x_{n + (-1)} + g_n \implies g_n = -x_{\left(-1\right) + n} + x_n
-30,855
\frac{7}{z + 3 \cdot (-1)} = \frac{28 + 7 \cdot z}{z^2 + z + 12 \cdot (-1)}
-13,103
-10.6 \div 20 = -0.53
-28,935
\dfrac{285}{5} = 57 = 3 \cdot 19
14,521
9*37 = 333
8,397
\left(3 + (-1)\right)/2 = 1
25,520
f*(3*W + 2) = 80 \Rightarrow 80/\left(3*f\right) - 2/3 = W
10,944
l!/m! = ((3 + l)*(l + 1)*(l + 2)*\dotsm*(m + 2*(-1))*((-1) + m)*m)^{-1}
18,796
(aH)(bH) = (ab)H = (ba)H = (bH)(aH)
14,898
\frac23\cdot 5/7 = \frac{15}{21}\cdot 2/3
-27,919
\frac{\mathrm{d}}{\mathrm{d}z} \sec(z) = \sec(z) \tan\left(z\right)
14,223
0 = (-1) + t\cos{\theta}*2 \Rightarrow t\cos{\theta} = 1/2
-20,785
10*x/\left(x*35\right) = \frac27*5*x/(5*x)
-20,008
\frac{1}{-4\cdot f + 2}\cdot (-4\cdot f + 2) = \dfrac{1}{-f\cdot 4 + 2}\cdot \left(-f\cdot 4 + 2\right)/1
6,091
1 = \left[a, b\right] \Rightarrow ( b a, b + a) = 1
32,393
24 - 24 \times (-1) + 47 = 24 \times 2 + 47 \times \left(-1\right)
30,016
\tfrac12 \cdot (1 - \cos(t \cdot 2)) = \sin^2\left(t\right)
12,122
\dfrac{1}{x^n y^n}(x^n + y^n) = \tfrac{1}{x^n} + \dfrac{1}{y^n}
26,480
A^2*B^2 = (A*B) * (A*B)
7,394
\frac{1 / 50}{1000} \cdot 1 = \frac{1}{50000}
-1,367
1/9 \cdot 7/9 = \frac{1}{9 \cdot 9/7}
22,373
\left(10*b\right)^2*n*0.09 = n*b^2*9
18,098
\frac{\partial}{\partial x} x^a = a \cdot x^{a + \left(-1\right)}
4,591
15 j = 3j \cdot 5
24,208
B'\cdot C + D'\cdot A + A'\cdot B + x\cdot D = (D + A + B + C)\cdot (D' + A' + B' + x)
-16,531
5\cdot \sqrt{9}\cdot \sqrt{7} = 5\cdot 3\cdot \sqrt{7} = 15\cdot \sqrt{7}
-3,858
\dfrac{z^5 \cdot 63}{z^5 \cdot 54} = \frac{z^5}{z^5} \cdot \frac{63}{54}
5,748
\dfrac{1}{x \cdot x + (-1)}x = \frac{1}{1 + x}1/2 + \frac{\dfrac12}{\left(-1\right) + x}
23,832
50 \cdot x + 20 \cdot y = 1020 \implies 102 = 2 \cdot y + x \cdot 5
9,007
p = \frac1p*\left(p^2 + 1\right) = p + 1/p
-23,496
\frac{1}{3} = 5/9\cdot \tfrac{3}{5}
25,120
42/132 + \dfrac{20}{132} = \frac{1}{132}\cdot 62 = 31/66
5,506
544320 = \binom{7}{2} \cdot \binom{9}{2} \cdot 6!
12,273
\frac{1}{x + 2 \cdot (-1)} = -\frac{1}{2 \cdot (1 - x/2)}
7,181
\dfrac{x + 1}{2 + x} = \frac{1}{x + 2}*(x + 1)
-12,142
\frac{1}{30} = \frac{q}{20\cdot \pi}\cdot 20\cdot \pi = q
-25,791
\dfrac{10}{28} = \dfrac{10}{7 \times 4}
37,774
8/17 = \sin(\alpha) \Rightarrow \frac{1}{17}\cdot 15 = \cos(\alpha)
4,427
6 + x^2 - 5\cdot x = \left(x + 3\cdot \left(-1\right)\right)\cdot (x + 2\cdot \left(-1\right))
-20,126
\dfrac{1}{6 + 3 \cdot m} \cdot (27 \cdot (-1) + m \cdot 24) = \frac13 \cdot 3 \cdot \frac{1}{m + 2} \cdot (m \cdot 8 + 9 \cdot (-1))
28,463
\tan(a) = \tan(2 \cdot a/2) = \frac{2 \cdot \tan(a/2)}{1 - \tan^2(\frac{a}{2})} \cdot 1
24,499
k = r \cdot n + d \Rightarrow n \cdot r = k - d
1,777
(a\cdot x + b)\cdot x = b\cdot x + a\cdot x^2
19,683
\int \sum_{k=1}^\infty x_k\,d\mu = \sum_{k=1}^\infty \int x_k\,d\mu
25,578
A\cdot Y = I_m rightarrow Y\cdot A = I_m
-26,061
\dfrac{1}{5}(-2 - 16 i + i + 8(-1)) = (-10 - 15 i)/5 = -2 - 3i
14,834
{n \choose k} = \frac{n!}{(-k + n)! k!}
13,834
x^{\left(-1\right) + K} x = x^K