id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
37,488 |
|x - g| = -(x - g) = g - x
|
12,304 |
(t - s) (t - s) = (-s + t) * (-s + t)
|
5,419 |
50 (11 + 60)/2 = 1775
|
30,623 |
1 + n\cdot z + z = 1 + (n + 1)\cdot z \leq (1 + z)^n
|
-155 |
9*8*7 = \frac{9!}{(9 + 3(-1))!}
|
10,902 |
((3/4)^f + 1)*4^f = 3^f + 4^f
|
15,257 |
1/15 = \frac{1}{3 \times 5} = 19 \times 16 = 16 \times 3 \times 6 + 16 = 6 + 16 = 22
|
33,911 |
\frac{145}{3} = -7/3 + \frac13\cdot 152
|
10,644 |
\dfrac{1}{c}(c + a + b) + (-1) = (b + a)/c
|
32,587 |
675 = 3^3 \cdot 5 \cdot 5
|
23,778 |
16/9 = \tfrac{1920}{1080}
|
-19,305 |
5/3\cdot 5/4 = \dfrac{5\cdot \dfrac14}{\dfrac15\cdot 3}
|
8,448 |
(1/2 + z)^2 = \left(1 + z \cdot 2\right) \cdot \left(1 + z \cdot 2\right)/4
|
12,219 |
1/4 = \frac{1}{H_1}*(x_1 - H_1) \Rightarrow H_1*5/4 = x_1
|
-9,758 |
-1/5\cdot 9/20 = \left((-1)\cdot 9\right)/(5\cdot 20) = -\tfrac{1}{100}9
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22,437 |
(-1) + n = 2 + n + 3*(-1)
|
19,510 |
\frac{\mathrm{d}x}{\mathrm{d}s} = 1 + \left(s - x\right) \cdot \left(s - x\right) = 1 + (x - s)^2
|
24,346 |
\overline{y_1} \cdot \overline{y_2} = \overline{y_1 \cdot y_2}
|
-2,406 |
\sqrt{6} \sqrt{4} + \sqrt{9} \sqrt{6} = 3\sqrt{6} + \sqrt{6} \cdot 2
|
19,988 |
24 - 7\cdot x = -2 \Rightarrow 26/7 = x
|
-10,486 |
-\dfrac{1}{q^2\cdot 60}\cdot (48\cdot q + 72) = 12/12\cdot (-\frac{1}{q \cdot q\cdot 5}\cdot (6 + 4\cdot q))
|
9,152 |
Cov[W, Y] = \mathbb{E}[WY] - \mathbb{E}[W] \mathbb{E}[Y] = \mathbb{E}[WY]
|
9,108 |
xz - z\xi = z*(x - \xi)
|
22,293 |
X*x^{1/2} = X*x^{\frac{1}{2}}
|
31,199 |
120 = 1 + 2 + 3\cdot \dots + 15
|
1,723 |
(2\left(-1\right) + n) (1 + n) = n^2 - n + 2\left(-1\right)
|
25,893 |
n - 2*k = 2 \Rightarrow k = (n + 2*(-1))/2
|
-20,527 |
\frac{56}{-48} = -7/6 \cdot (-8/(-8))
|
-16,700 |
-3 = -3 \cdot \left(-2 \cdot y\right) - 21 = 6 \cdot y - 21 = 6 \cdot y + 21 \cdot (-1)
|
19,803 |
g - x = -(-g + x)
|
-1,797 |
-\pi \cdot \frac{7}{4} + \frac{1}{4} \cdot \pi = -\pi \cdot 3/2
|
-4,335 |
\tfrac{y}{y^3}\cdot 60/50 = \frac{60\cdot y}{50\cdot y \cdot y \cdot y}\cdot 1
|
24,743 |
(\xi + 1)\cdot n = \xi\cdot n + n
|
3,743 |
\frac{3}{4} \cdot 1 = \frac14 \cdot 3
|
32,809 |
\min{\frac{1}{20}\cdot 120,\frac{1}{8}\cdot 80} = \min{6,10} = 6
|
-22,971 |
9\times 10/(10\times 5) = 90/50
|
10,650 |
x = t^3 \Rightarrow t = x^{\frac{1}{3}}
|
16,060 |
(a + b)^3 = a * a * a + 3*a^2*b + 3*a*b^2 + b^3 = a * a^2 + 0*a^2*b + 0*a*b^2 + b^3 = a * a^2 + b^3
|
-27,485 |
22 \times x^3 = 11 \times 2 \times x \times x \times x
|
-4,330 |
q\cdot 5 = q\cdot 5
|
11,296 |
u^2 + v \cdot v\cdot 3 = (u + v)^2 + \left(u + v\right)\cdot (-u + v) + (v - u)^2
|
28,368 |
y^2 - 2 y + 1 \geq 0 \implies y^2 + 1 \geq y*2
|
17,497 |
1/2 = \frac{1}{100} + \frac{1}{99}*49*99/100
|
8,224 |
\frac{1}{6^3}*(1 + 5/6 + 5/6) = \frac{1}{81}
|
9,158 |
0 = a^4 \cdot t^2 \cdot 4 - 4 \cdot t^3 \cdot a^2 + 1 \Rightarrow \frac{1}{t \cdot 2} \cdot (t^2 \pm \sqrt{t^4 + (-1)}) = a^2
|
23,456 |
\cos(\frac12\cdot \pi - z) = \sin{z}
|
29,943 |
\tan{x} = \frac{1}{\cos{x}} \times \sin{x}
|
22,877 |
\sin(y + x) = \sin{y} \cdot \cos{x} + \cos{y} \cdot \sin{x}
|
2,111 |
\dfrac{144}{2^{15}} = \frac{1}{2048} \cdot 9 \approx 0.0043945
|
42,268 |
\frac{1}{2}\cdot \left(214\cdot \left(-1\right) + 360\right) = 73
|
18,161 |
(d + g)/x = (g + x + d)/x + (-1)
|
6,837 |
\tanh{J} = \frac{1}{e^{2J} + 1}(e^{2J} + (-1)) = 1 - \frac{1}{e^{2J} + 1}2
|
42,354 |
32 \times 35 \times 36 = 40320 = 8!
|
28,472 |
|\varphi_1| = |\varphi_2| = p \implies |\varphi_2 \varphi_1| = p
|
22,944 |
(-1) + x^l = ((-1) + x) \cdot (-e^{\pi \cdot 2/l} + x) \cdot ... \cdot e^{2 \cdot ((-1) + l) \cdot \pi/l}
|
36,477 |
47\cdot 257 - 66\cdot 183 = 12079 + 12078 (-1) = 1
|
26,716 |
16 z = z + 15 z
|
-23,703 |
5/24 = \frac{1}{6}*5/4
|
27,717 |
\left(6x + y \cdot 5 = 1 + x \cdot 7 + y \cdot 3\Longrightarrow 0 = x - 2y + 1\right)\Longrightarrow (-1) + y \cdot 2 = x
|
19,150 |
\left(k + z\right)\cdot (-k + z) = z^2 - k^2
|
-21,910 |
-\frac{1}{12} \cdot 8 + 4/8 = -\tfrac{16}{12 \cdot 2} \cdot 1 + \frac{1}{8 \cdot 3} \cdot 12 = -16/24 + 12/24 = -\dfrac{1}{24} \cdot (16 + 12) = -\frac{4}{24}
|
17,849 |
z^{\frac{2}{6}} = z^{\frac13}
|
31,442 |
\dfrac14 (9 + 9 + 10 + 11) = 9.75
|
17,837 |
(-\tfrac{1}{x^2 + x + 1}(x + 2) + \frac{1}{(-1) + x})/3 = \frac{1}{x^3 + \left(-1\right)}
|
-30,253 |
\tfrac{1}{x + 7}(x^2 + 49 (-1)) = \dfrac{1}{x + 7}(x + 7) (x + 7(-1)) = x + 7(-1)
|
41,004 |
2*50 + 16*\left(-1\right) = 84
|
6,572 |
(x - \beta)^2 = -x \cdot \beta \cdot 2 + x^2 + \beta^2
|
11,682 |
y z - z_0 y + z_0 y - z_0 y_0 = -y_0 z_0 + y z
|
17,079 |
\overline{cd} = \bar{c} \bar{d} = -c \cdot (-d) = cd
|
11,401 |
2/31 = \frac{1}{31} + \frac{30}{30} \cdot 1/31
|
-5,864 |
\dfrac{s*2}{s^2 - 11*s + 18}*1 = \frac{s*2}{(s + 2*\left(-1\right))*(s + 9*(-1))}
|
-7,873 |
\frac{1}{-3 - i}\cdot (2 - i\cdot 16) = \frac{1}{-3 - i}\cdot (-16\cdot i + 2)\cdot \frac{i - 3}{i - 3}
|
34,663 |
\frac15*1 = 1/5 = \tfrac{1}{5}
|
22,868 |
\cos{x} = \left(-1\right) + \cos^2{\dfrac{x}{2}}*2
|
-12,015 |
4/5 = t/(8*\pi)*8*\pi = t
|
35,459 |
A_n/(Y_n) = A_n/(Y_n)
|
39,283 |
18 = (6 \cdot (-1) + 12) \cdot 3
|
24,573 |
2z^2 = z \cdot z + z^2
|
20,185 |
2 U = U + U
|
39,307 |
B_0 = 0 \cup B_0
|
15,718 |
\dfrac{1}{2!*2!}*5! = \frac{120}{4} = 30
|
20,363 |
\|-(-e + f) + g - b\| = \|-(b - e) + g - f\|
|
18,135 |
(180 + y^2 + 20 \cdot y) \cdot \left(y^2 - 2 \cdot y + 18 \cdot \left(-1\right)\right) = y^4 + 18 \cdot y^3 + 122 \cdot y^2 - y \cdot 720 + 3240 \cdot (-1)
|
32,863 |
\binom{m}{i} = \frac{1}{i!\cdot (m - i)!}\cdot m!
|
26,858 |
y \cdot x = \frac12 \cdot (x \cdot y + x \cdot y)
|
-26,426 |
\frac{1}{3125\cdot 5^8} = 5^{-5 + 8\cdot (-1)} = \frac{1}{1220703125}
|
17,305 |
f^\gamma = d^y = (fd)^{\gamma y}
|
-20,045 |
\tfrac77 \cdot \dfrac{3 \cdot (-1) - x \cdot 9}{4 \cdot (-1) - x \cdot 5} = \frac{21 \cdot (-1) - x \cdot 63}{28 \cdot (-1) - 35 \cdot x}
|
29,831 |
c + z = y \cdot e^{-z^2} \Rightarrow e^{-z^2} \cdot c + e^{-z^2} \cdot z = y
|
9,201 |
z^{r_1 + r_2} = z^{r_2} z^{r_1}
|
53,537 |
\tfrac{x}{10 \cdot k + 3} = g \Rightarrow x = 10 \cdot k \cdot g + 3 \cdot g
|
4,280 |
\cos(f)*\cos\left(h\right) = \tfrac12*(\cos(h - f) + \cos(f + h))
|
27,499 |
\dfrac{1601}{1138} = 1 + \frac{463}{1138}
|
-23,155 |
((-3) \times \frac12)/2 = -3/4
|
-26,419 |
\dfrac{1}{390625 \cdot 9765625} = 5^{-8 - 10} = 5^{-8 + 10 \cdot \left(-1\right)} = 1/3814697265625
|
27,688 |
d/dz y^3 + \frac{\partial}{\partial z} (z^2*y) = -\frac{dy}{dz} + \frac{dz}{dz}
|
9,942 |
((-1) + z) (z^2 + z + 1) = (-1) + z^3
|
-23,000 |
26/39 = \dfrac{1}{3*13}26
|
10,166 |
10^3*4 + 10^2*5 + 10^1*7 + 6*10^0 = 4576
|
11,181 |
\frac{d}{dz} (z\cdot |z|) = |z| + \tfrac{z}{|z|}\cdot z = \frac{2\cdot z^2}{|z|}
|
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