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ddrg
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math_formulas

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int64
-30,985
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-20,228
-\frac{1}{2 + 2 \cdot y} \cdot 18 = -\frac{9}{1 + y} \cdot 2/2
20,885
1 + p + p^2 + \cdots = \dfrac{1}{-p + 1}
28,251
x^2 + 50^2 = (x + 10) * (x + 10) = x^2 + 100 + 20 x
2,519
\tfrac{1}{R\cdot x} = 1/(R\cdot x)
18,910
2^8 = 6^{-1/4 + x\cdot 0.5} rightarrow 6^{16}\cdot 2^{8\cdot 64} = 6^{32\cdot x}
4,449
\left(x_1 + x_2\right) \cdot \left(x_1 + x_2\right) = x_1^2 + x_2^2 + 2x_1 x_2 \leq x_1^2 + x_2 \cdot x_2 + x_1^2 + x_2 \cdot x_2
-30,603
(y*5 + 2)*3 = 6 + 15*y
36,124
|1/((-1)\cdot z) - z| = |z + 1/z|
6,536
x = \dfrac{x}{4} + \frac{x}{4} + x/4 + x/4
10,337
n + 1 - x + z = n + 1 - x - z
35,513
\cos(2\pi*4) + 2 = 3
20,549
250^{(-1) + z*3}*250^2 = 250^{1 + z*3}
-20,002
-7/4\cdot \frac{1}{-x\cdot 2 + 3\cdot \left(-1\right)}\cdot (-x\cdot 2 + 3\cdot \left(-1\right)) = \dfrac{1}{-8\cdot x + 12\cdot \left(-1\right)}\cdot (x\cdot 14 + 21)
13,090
z = 5\cdot \left(7\cdot z_2 + a\right) + 1 = 35\cdot z_2 + 5\cdot a + 1
8,349
3\cdot y^2 - 4\cdot y + 7 = 4 + l\cdot y \Rightarrow y^2\cdot 3 - y\cdot \left(l + 4\right) + 3 = 0
33,393
\mathbb{E}(Z_1 \cdot Z_2) = \mathbb{E}(Z_1) \cdot \mathbb{E}(Z_2)
27,955
\tan^2{x} = \tfrac{\sin^2{x}}{1 - \sin^2{x}}
33,634
2*j_2 + 1 - 2*j_1 + 1 = 2*j_2 - 2*j_1 = 2*\left(j_2 - j_1\right)
25,445
(c + d)^3 = d^3 + 3*d^2*c + 3*d*c^2 + c^3
22,748
-x^2 + x + x = 2 \cdot x - x^2
23,843
25 = \left(-1\right) \left(-25\right)
42,546
1007 + 671 + 335 \cdot (-1) = 1343
32,107
Y*v = Y*v
-22,224
20 + y^2 + y\cdot 9 = (y + 5)\cdot (y + 4)
40,600
i \times i \times i = i^{2 + 1} = i^2 \times i = -i = -i
46,751
2^3 \times 3 = 24
39,391
\lim_{v \to 2} \frac{v + 2\cdot \left(-1\right)}{v \cdot v \cdot v + 8\cdot \left(-1\right)} = \lim_{v \to 2} \frac{v + 2\cdot (-1)}{(v + 2\cdot (-1))\cdot (v^2 + 4\cdot v + 4)} = \lim_{v \to 2} \frac{1}{v^2 + 4\cdot v + 4}
-20,282
(5 + t)/4 \cdot \frac{1}{3}3 = \frac{1}{12}(15 + 3t)
19,190
\cos{-\frac{1}{2}} = \cos{\frac12}
1,490
\left(4 + z^2 - y^2 - 4z = 0 \Rightarrow (2(-1) + z) * (2(-1) + z) - y^2 = 0\right) \Rightarrow 0 = (-y + z + 2(-1)) (y + z + 2(-1))
18,393
\left(z_1 + z_2\right) (z_1 - z_2) = -z_2^2 + z_1^2
33,571
\frac{3}{2} = \frac{1}{2} 3
21,989
-g = g \Rightarrow g = 0
26,628
40320 = 8\cdot 7\cdot 6\cdot ...\cdot 3\cdot 2
25,686
-45 > -(z + z + 2) \implies -(2 \cdot z + 2) < -45
10,565
\left(y + 1\right)*(y^2 + 1)*(y + \left(-1\right)) = y^4 + \left(-1\right)
38,986
1007 = \left\lfloor{\left(2015\cdot 504\right)^{1/2}}\right\rfloor
26,444
2^n - 2^{n + (-1)} = 2^{n + (-1)} \cdot (2 + (-1)) = 2^{n + \left(-1\right)} \cdot (\cdots!)!
3,570
3^n - 3^{2 \cdot (-1) + n} = 3^{n + 2 \cdot (-1)} \cdot \left(\left(-1\right) + 9\right)
9,041
\frac{h}{d}\cdot d = \tfrac{h\cdot d}{d}
21,700
\cos(3*x) = -\cos(x)*3 + 4*\cos^3\left(x\right)
-20,329
-10/1 \times \frac{z}{6 \times z} \times 6 = \frac{z \times (-60)}{6 \times z}
27,327
exe = eex = ex
833
L^2 + L \cdot x - x \cdot L - x \cdot x = (L + x) \cdot (L - x)
25,291
A^n = (-3)^{n + \left(-1\right)}\cdot A = -\frac{\left(-3\right)^n}{3}\cdot A
-3,178
\sqrt{7} \cdot 4 - \sqrt{7} \cdot 3 = \sqrt{7} \cdot \sqrt{16} - \sqrt{9} \cdot \sqrt{7}
22,161
0 = (1 - \frac{1}{a \times b}) \times (b - a) = \frac{1}{a \times b} \times \left(b - a\right) \times (a \times b + \left(-1\right))
27,297
8 = 2 \cdot 4!/3!
17,807
V_1 = \frac{1}{2} \cdot (V_1 + V_2) + W \cdot V_2 = \dfrac{1}{2} \cdot (V_1 + V_2) - W
19,040
\frac{b^2}{h + b} = -\tfrac{h \cdot b}{b + h} + b
-1,783
\dfrac34 \pi + \pi\cdot 11/6 = \pi\cdot 31/12
18,395
81 = 4*3^3 + 27 (-1)
-26,583
-10 \cdot y^2 + 640 = (-y^2 + 64) \cdot 10
-20,159
\frac{1}{24 \cdot (-1) + 3 \cdot y} \cdot (-y + 8) = -1/3 \cdot \frac{1}{y + 8 \cdot (-1)} \cdot (y + 8 \cdot (-1))
-10,422
-16 = -14 + 5 \cdot x + 2 = 5 \cdot x + 12 \cdot (-1)
17,830
\cos(\dfrac{π}{4}) = \frac{1}{2^{\tfrac{1}{2}}} = \frac{1}{2}2^{1 / 2}
11,219
g \approx a\Longrightarrow a \approx g
16,573
2^l\cdot 2 + (-1) = -2^l + 2^l\cdot 3 + (-1)
13,565
10^3 \cdot 2.0 \cdot 5.0 \cdot 10^{13} = 10^{17} \cdot 1
25,943
1 + \frac{1}{2} 3 + 3 = \frac{1}{2} 11
3,482
{6 \choose 4}*\frac{1}{6^6} 5^2 = \tfrac{1}{46656} 375
-3,144
208^{1/2} - 13^{1/2} = (16 \cdot 13)^{1/2} - 13^{1/2}
-20,701
-7/1 \cdot \frac{1}{8 \cdot (-1) + n} \cdot (n + 8 \cdot (-1)) = \frac{1}{8 \cdot (-1) + n} \cdot (-7 \cdot n + 56)
32,887
151657 \cdot 27099 = \left(58^2 - 41^2\right) \cdot x = 99 \cdot 17 \cdot x
28,490
\sin(90 - x) = -\sin(x + 90*\left(-1\right)) = \sin(x + 90*\left(-1\right) + 180) = \sin(90 + x)
8,585
b\cdot h = 1/(b\cdot h) = 1/\left(h\cdot b\right) = h\cdot b
-11,964
\dfrac{4}{15} = \dfrac{r}{20 \pi} \cdot 20 \pi = r
27,123
y^{1/4}\cdot y^4 = y^{\tfrac14 + 4} = y^{17/4}
27,225
2 \cdot 16 + 3 \cdot (-1) = 29
10,650
V = x^3 \Rightarrow V^{\frac13} = x
-7,290
1/2 = 3/4*2/3
-11,542
-12 + i \cdot 20 = 4 + 16 \cdot (-1) + 20 \cdot i
-10,948
\frac{85}{5} = 17
-27,348
0 = z^2 - 29\cdot z + 198 = (z + 11\cdot (-1))\cdot (z + 18\cdot (-1))
28,178
(z^2 + 1) \cdot z \cdot 3 - z^2 \cdot 2 - z \cdot 2 + 5 \cdot (-1) = 5 \cdot (-1) + z \cdot z \cdot z \cdot 3 - z^2 \cdot 2 + z
-3,761
\frac{m^4}{m^4}\cdot 35/15 = \frac{m^4\cdot 35}{15 m^4}
5,418
\frac{\mathrm{d}}{\mathrm{d}z} \left(\ln(z)\cdot z\right) = \ln(z) + 1
-20,231
\frac{1}{-18}*(2 + a*2) = \frac{1}{-9}*(1 + a)*\dfrac{2}{2}
23,751
\binom{r + (-1)}{k + (-1)} = \binom{\left(-1\right) + r - k + k}{(-1) + k}
10,008
546 = -(-1109*4 + 4999) + 1109
1,156
1.6^{m + 2\cdot (-1)} + 1.6^{2\cdot (-1) + m} = 1.6^{m + 2\cdot (-1)}\cdot 2
115
16/49 = \dfrac{1}{49}34 - \frac{18}{49}
29,217
(7*x^2 + 1)*(x^2 + x + 1) = 7*x^4 + 7*x^3 + 7*x^2 + x * x + x + 1 = 7*x^4 + 7*x^3 + 8*x^2 + 1
22,792
\cos^3{z} = (1 - \sin^2{z}) \cdot \cos{z}
-10,420
-\frac{6}{a \cdot 10 + 6 \cdot \left(-1\right)} \cdot 2/2 = -\dfrac{1}{20 \cdot a + 12 \cdot \left(-1\right)} \cdot 12
-12,705
42 = \dfrac{84}{2}
16,232
a = a + b + (-1) > a + b + 2*(-1)
-27,662
d/dz e^{-z} = -\dfrac{1}{e^z}
9,610
\left(a + b\cdot i\right)\cdot (a - b\cdot i) = a^2 - b \cdot b\cdot i^2 = a^2 + b^2
24,053
(3 - 5^{1/2})^{1/2} = \left(10^{1/2} - 2^{1/2}\right)/2
-18,298
\frac{q \cdot q + q\cdot 5 + 6}{q \cdot q + 2\cdot q} = \frac{1}{q\cdot \left(q + 2\right)}\cdot \left(2 + q\right)\cdot (3 + q)
-1,619
11/6 \pi + \frac{23}{12} \pi = 15/4 \pi
6,187
9 \cdot (g + 1) = 9 \cdot g + g + b + c = 10 \cdot g + b + c
3,763
2/7 = 4/6\cdot \frac17\cdot 3
9,906
125/5 \cdot (5 + 1 + 2 + 3 + 4) \cdot 111 = 41625
4,298
h + a = 0 \Rightarrow h = -a
-4,867
0.65/1000 = \dfrac{1}{1000}\cdot 0.65
39,134
q = q/3 \cdot 3
-6,293
\frac{1}{(9 + n)\cdot 5} = \frac{1}{45 + n\cdot 5}
32,288
x - (-1) + M = x - M + 1