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ddrg
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math_formulas

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int64
-30,985
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7,554
c = c \cdot 2^0
30,173
\tfrac{8 + x}{8 - x} = 1 + \frac{x}{8 - x}\cdot 2 = 1 + \frac{1}{8/x + \left(-1\right)}\cdot 2
-208
{5 \choose 4} = \dfrac{1}{4! (5 + 4(-1))!}5!
-17,718
23 + 20*(-1) = 3
11,708
\frac{\pi*11}{12} = \frac{8*\pi}{12}*1 + \frac{3*\pi}{12}
-30,274
\dfrac12\cdot (8 - 4) = 4/2 = 2
301
d^3 - b^3 = (b^2 + d^2 + bd) (d - b)
10,577
\frac{\text{d}}{\text{d}z} (2 + z + z^2 + z \cdot z^2) = 3 \cdot z^2 + 1 + z \cdot 2
-19,496
2/7\cdot 8/3 = 1/3\cdot 8/(7\cdot \tfrac{1}{2})
26,872
E(C_t^2\cdot C_{-j + t}^2) = E(C_t^2)\cdot E(C_{t - j}^2)
22,634
D_j \cdot D_n \cdot D_i = D_i \cdot D_j \cdot D_n
8,899
p^2 + p^2 + p^2 + p^2 - p^3 - p^2 \cdot p - p^3 - p^3 + p^4 = p^2\cdot 4 - 4\cdot p^3 + p^4
6,606
2015 = 9\cdot (-1) + (((1 + 2)\cdot 3\cdot 4 + 5)\cdot 6 + 7)\cdot 8
34,580
F \cdot X = X + F = X \cdot F
15,845
a\cdot d = 1/(a\cdot d) = 1/(d\cdot a) = d\cdot a
22,746
f + \beta = \beta + f
-10,294
\dfrac44 \cdot \frac{1}{2 \cdot z + 5 \cdot \left(-1\right)} \cdot 4 = \frac{16}{20 \cdot (-1) + z \cdot 8}
21,435
KXt = KtX
36,102
x\cdot 2 + x^2 = \left(-1\right) + (1 + x) \cdot (1 + x)
39,574
2 = 5 - 3 = 5 + 3*\left(-1\right)
-5,108
10^{2(-1) + 7}*0.13 = 0.13*10^5
15,301
Q = \arccos(z) rightarrow z = \cos\left(Q\right)
6,901
\sin^2{x} = \dfrac{1}{-4} \cdot (e^{i \cdot x} - e^{-i \cdot x})^2 = -\frac14 \cdot \left(e^{2 \cdot i \cdot x} + 2 \cdot (-1) + e^{-2 \cdot i \cdot x}\right)
576
-d_2 + d_1 = \dfrac14\cdot (d_1\cdot 4 - 4\cdot d_2)
-20,641
3/3\cdot \frac{1}{-p\cdot 2 + 5\cdot (-1)}\cdot (-3\cdot p + 8\cdot (-1)) = \frac{24\cdot (-1) - 9\cdot p}{-p\cdot 6 + 15\cdot \left(-1\right)}
50,997
3^1 + 1 = 4
-14,784
\frac{1}{5}410 = 82
37,251
-\binom{32}{1}\cdot \binom{32}{1} + \binom{64}{2} = 992
20,351
l = \left(1 + \varepsilon_l\right)^l \geq 1 + l\cdot \varepsilon_l + {l \choose 2}\cdot \varepsilon_l^2
5,168
\left(5/4 + x^2 + x\right)*4 = x^2*4 + 4*x + 5
-3,342
\sqrt{11} \cdot \sqrt{9} + \sqrt{11} = 3 \cdot \sqrt{11} + \sqrt{11}
50,053
9 + 3 \cdot 17 = 60
-17,471
9 = 15 + 6\cdot (-1)
27,111
\left(x + 2 = (x + 2(-1))*2 - 1 + x + x - 3\left(x + (-1)\right) \Rightarrow 2 + x = -x + 2(-1)\right) \Rightarrow -2 = x
22,761
36 = (c + a + b)^2\Longrightarrow a \cdot a + b \cdot b + c^2 = 18
27,248
(n + (-1))\cdot (n \cdot n + n + 1) = \left(-1\right) + n^3
33,183
(b + a) \cdot \left(b^2 + a^2 - b \cdot a\right) = a^3 + b^3
40,823
64 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 4
-1,617
19/12 \cdot \pi = \pi \cdot 43/12 - 2 \cdot \pi
9,250
\frac{1}{x \cdot \dfrac{1}{y}} = \dfrac{y}{x}
3,092
(b + a)/2 = \frac{1}{2}(b + a)
25,230
2 = (1 - 2)^2 + \left(1 + 0\right)^2 - (3 - 2 + 0) \cdot 0 \cdot 2
7,536
100/p = \frac{100}{(-1) + 1 + p}
-2,408
\sqrt{24} + \sqrt{54} = \sqrt{4*6} + \sqrt{9*6}
22,267
\sin{\frac{4\cdot π}{3}} = -\sin{π/3}
17,792
\frac{7}{16} \cdot s \cdot 0.3 = \frac{1}{160} \cdot 21 \cdot s
24,225
n + 1 = n \cup n = \left\{0, n, \dots\right\}
37,755
(3 + 2*(-1))^2 = 1
23,955
\dfrac32 - -5/2 = 4
16,193
E(Y)*E(X) = E(Y*X)
-4,280
\frac{1}{3}\cdot f = \frac{f}{3}
28,771
z^2 - 6\cdot z + 38 = 29 + (3\cdot \left(-1\right) + z) \cdot (3\cdot \left(-1\right) + z)
-10,287
\frac{10}{2 \cdot y + 5 \cdot (-1)} \cdot \tfrac44 = \frac{1}{20 \cdot (-1) + y \cdot 8} \cdot 40
19,203
\nu + x - c_{n+1}*2 = -(c_{n+1} - \nu) + x - c_{n+1}
-2,517
\sqrt{11} \cdot \left(5 + 1\right) = 6 \cdot \sqrt{11}
17,923
\frac{1}{m + 1} + \frac{1}{\left(m + 1\right) \cdot \left(m + 2\right)} = \dots = \frac{1}{m + 1 + 1}
-1,376
\frac{5\cdot 1/7}{4\cdot \frac{1}{9}} = \frac57\cdot \frac94
31,956
x^6 + 1 = (x^2 + 1)\cdot \left(1 + 3^{\frac12}\cdot x + x^2\right)\cdot \left(1 - 3^{1/2}\cdot x + x^2\right)
10,347
\frac{21}{4} = (1 + 2) \cdot 1/2/2 + (3 + 6)/2
18,503
\dfrac{1}{13} = 76923/999999 = \dfrac{1}{10^6 + (-1)}*76923
21,067
r' + x + r + x = r + r' + x
8,694
(z^{2^n})^2 = z^{2^{n + 1}}
15,553
-(-j - 2 \cdot i) \cdot 7 = 7 \cdot j + i \cdot 14
39,538
\sin(2 \cdot y) = 2 \cdot \cos(y) \cdot \sin(y)
30,902
\frac{2 \cdot p}{2 \cdot p + 2 \cdot (-1)} = \dfrac{p}{p + (-1)}
8,658
y^\varphi*y^b = y^{\varphi + b}
21,530
l^2 = {l \choose 1} + 2{l \choose 2}
-6,048
\dfrac{1}{80 (-1) + g^2 - 2 g} g = \frac{g}{\left(g + 8\right) (10 (-1) + g)}
32,359
\frac14 \cdot \left(20 + 30 + 10 + 5\right) \cdot \left(5 + 6 + 100 + 4\right)/4 = 16.25 \cdot 28.75 = 467.18
10,980
2 \cdot \frac{4}{6} \cdot 6/6 \cdot 5 \cdot 1/6/6 = \frac{5}{27}
29,199
2^{\frac{1}{3}} = \frac{2}{(2^{\frac13})^2}
-3,076
2 \sqrt{2} = \sqrt{2}*(4 + 2 (-1))
22,324
\frac{1}{w + (-1)} \times w = \frac{w + (-1)}{w + (-1)} + \frac{1}{w + (-1)} = 1 + \frac{1}{w + \left(-1\right)}
4,333
5 \cdot (-1) \cdot (-5) \cdot (-25) \cdot (-110) = 68750
27,645
(1/2 - i)^2 + 2*i = i*2 + \left(\frac{1}{2}\right)^2 - \frac{i}{2}*2 + i * i
-4,305
n^3/4 = n^3/4
27,464
2\cdot c\cdot d = c\cdot (d + d)
-8,954
119.2\% = \frac{119.2}{100}
-22,362
(z + (-1))\cdot (z + 4\cdot \left(-1\right)) = z^2 - 5\cdot z + 4
21,895
1 + d \cdot 2 = 4 d \Rightarrow \frac{1}{2} = d
10,235
1/4 = \frac{10}{40}
17,550
a' ax + a' b + b' = a' x a + b' a + b
-20,569
8/8 \times \frac{1}{9 \times z} \times (-z \times 7 + 5 \times \left(-1\right)) = \frac{1}{72 \times z} \times \left(40 \times (-1) - z \times 56\right)
11,666
(c_2 + c_1)^2 = c_2^2 + c_1^2 + c_1*c_2*2
522
5 - 0*3 + \frac{9}{3} = 5 + 0(-1) + \frac{9}{3} = 5 + 0(-1) + 3 = 5 + 3 = 8
29,390
15 = 3\times 10/2
7,327
(-3*2 + 2*3) + 1*(2*(-1) + 3) - 1*\left(3 + 2*(-1)\right) = 0
30,838
e^{-y} = \dfrac{1}{e^y} \neq e^{\dfrac{1}{y}}
16,440
h^2 - d^2 = (h + d)\cdot (h - d)
14,624
x = k + 2 \cdot \left(-1\right)\Longrightarrow \left\lfloor{(x + 1) \cdot (x + 1)/k}\right\rfloor = k + 2 \cdot (-1)
28,986
\cot\left(-x + \frac{\pi}{2}\right) = \tan{x}
12,806
\frac{(n!)!}{\left(n! + (-1)\right)!} = \frac{n!}{1!}
22,462
y - \frac{y^3}{3} + y^5/5 + y^7/7 - \dotsm = \arctan{y}
-21,009
-\frac{1}{4}*7*\frac{r + 6}{r + 6} = \frac{-r*7 + 42*(-1)}{4*r + 24}
24,743
n*(m + 1) = n + n*m
6,823
A_{1 + n}^2 + \left(-1\right) + x_n^2 - n + 2x_n A_{n + 1} = (x_n + A_{n + 1})^2 - n + 1
-9,138
-80*x^2 + 130*x = -x*2*2*2*2*5*x + 2*5*13*x
-6,753
8/100 + \dfrac{60}{100} = 6/10 + 8/100
298
2/7 = \dfrac23 \cdot \dfrac{3}{7}
25,243
\frac{π}{2} \cdot 2 = π