id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
21,289 |
4*4^j = 4^{1 + j}
|
-7,964 |
\left(38 + 50 \cdot i + 95 \cdot i + 125 \cdot \left(-1\right)\right)/29 = \frac{1}{29} \cdot (-87 + 145 \cdot i) = -3 + 5 \cdot i
|
-9,629 |
0.01*(-20) = -\dfrac{1}{100}*20 = -0.2
|
16,053 |
\frac{1}{3}\times (33\times \left(-1\right) + 333) = 100
|
14,100 |
|h_m - h_n| = |h_n - h_m|
|
-2,129 |
0 - \dfrac{19}{12}\cdot \pi = -\pi\cdot 19/12
|
-28,755 |
y^2 + y*2 + 2 (-1) + \frac{15}{y*2 + 3} = \frac{1}{2 y + 3} (9 + 2 y^3 + 7 y^2 + 2 y)
|
-20,167 |
6/6 \times \frac{q}{9 \times q + 9 \times (-1)} \times 10 = \frac{60 \times q}{54 \times q + 54 \times \left(-1\right)}
|
37,391 |
\frac{c \cdot p^5}{c \cdot p^4} = \dfrac{p^4}{p \cdot p \cdot p \cdot c} \cdot c
|
21,796 |
19 \cdot 100 \cdot 3 \cdot 3 + 20 \cdot 3 = 100 \cdot 13^2 + 13 \cdot 20
|
-10,309 |
-\frac{1}{50 \cdot x + 30} \cdot 12 = -\frac{6}{x \cdot 25 + 15} \cdot 2/2
|
7,846 |
\sqrt{\dfrac{1}{1 - \tfrac{5}{13}}\cdot 2} = \dfrac{\sqrt{13}}{2}
|
17,331 |
y^4 - 7y^2 + 1 = (y^2 + 1)^2 - 9y^2 = \left(y^2 + 1 + 3y\right) (y * y + 1 - 3y)
|
21,515 |
\mathbb{E}[(X - x) \cdot (X - x)] = \mathbb{E}[(X - \mathbb{E}[X] + \mathbb{E}[X] - x)^2] = \mathbb{E}[(X - \mathbb{E}[X])^2] + \left(\mathbb{E}[X] - x\right)^2
|
3,821 |
(-2)^2 = (-1) \cdot (-1)\cdot \left(-2\right)^2 = 4
|
7,746 |
x + 1 = y \Rightarrow y + (-1) = x
|
-20,785 |
x\cdot 5/(5\cdot x)\cdot \frac{2}{7} = x\cdot 10/\left(35\cdot x\right)
|
-2,688 |
\sqrt{3} \cdot 4 = \sqrt{3} \cdot \left(2 + 3 + (-1)\right)
|
13,510 |
(-5)\cdot 19 + 6\cdot 16 = 19 - \left(16\cdot (-1) + 19\right)\cdot 6
|
2,408 |
9/60 + \frac{36}{60^2} = 576/3600 = \tfrac{1}{25} \cdot 4
|
9,967 |
1/3 + \tfrac{1}{4} = \tfrac{4}{3 \cdot 4} + \frac{3}{3 \cdot 4} = \frac{1}{3 \cdot 4} \cdot (4 + 3)
|
-6,102 |
\frac{1}{2 \cdot (t + 4 \cdot (-1))} = \frac{1}{2 \cdot t + 8 \cdot \left(-1\right)}
|
18,809 |
7 * 7*3 - 9^2*3 = 3*((-1) + 0)*9^2 + 7^2*3*\left(0(-1) + 1\right)
|
4,597 |
\left( V\xi, z\right) = z^V V\xi = \left(z^V V\xi\right)^V = \xi^V V^V z
|
47,195 |
18 = \left(-1\right) + 19
|
4,906 |
x^2 + y^2 + z^2 + 2(zx + xy + zy) = (x + y + z)^2
|
-11,530 |
-i\cdot 12 + 6 + 0\cdot (-1) = 6 - 12\cdot i
|
-19,500 |
4/7\cdot 7/6 = \dfrac{1/6\cdot 7}{\frac{1}{4}\cdot 7}
|
8,929 |
\tfrac{1}{\tau \times Y} = \frac{1}{Y \times \tau}
|
38,773 |
\frac{25}{729}*9 = 25/81
|
5,223 |
(x\cdot h) \cdot (x\cdot h) = (h\cdot x)^2
|
10,222 |
0 = x_1 \cdot 2 - x_2 - z_2 + y_2\Longrightarrow -z_2 + x_1 \cdot 2 - x_2 = -y_2
|
-5,785 |
\frac{2}{4*(y + 5)} = \frac{2}{20 + 4*y}
|
-2,147 |
-\pi\cdot \frac{19}{12} + \frac76\cdot \pi = -\pi\cdot 5/12
|
7,050 |
c*\delta_n*x = x*c*\delta_n
|
36,209 |
\left(3^{x + 1} = 1 \Rightarrow 0 = 1 + x\right) \Rightarrow -1 = x
|
28,266 |
\frac{\frac{1-\cos^4 \theta}{\cos^2 \theta}}{\tan^2 \theta} = \frac{\frac{(1-\cos^2 \theta)(1+\cos^2 \theta)}{\cos^2 \theta}}{\tan^2 \theta} = \frac{\frac{(1-\cos^2 \theta)(1+\cos^2 \theta)}{\cos^2 \theta}}{\frac{\sin^2 \theta}{\cos^2 \theta}} = \frac{{(1-\cos^2 \theta)(1+\cos^2 \theta)}}{\sin^2 \theta}
|
35,512 |
{2 \choose 0} \cdot {8 \choose 3} = 56
|
10,788 |
\frac12((B + A)^2 - A^2 - B^2) = AB
|
-20,840 |
\frac{7}{7} \frac{1}{t*4}(t + 7) = \dfrac{1}{28 t}\left(t*7 + 49\right)
|
21,354 |
\lambda^7 = \bar{\lambda} = \dfrac{1}{\lambda}
|
20,827 |
X_x*X_g*f = x*g*f = g*x*f = X_g*X_x*f
|
-1,585 |
2 \cdot \pi - \frac{\pi}{12} = \frac{23}{12} \cdot \pi
|
8,067 |
p^3 + q^3 + r^3 + p\cdot q\cdot r\cdot 4 = p^3 + (q + r)^3 + 4\cdot q\cdot r\cdot p - 3\cdot (q + r)\cdot q\cdot r
|
35,839 |
\frac{15*6}{6}*1 = 15
|
-2,936 |
-3\sqrt{13} + 5\sqrt{13} = -\sqrt{13} \sqrt{9} + \sqrt{25} \sqrt{13}
|
7,968 |
-1.29129129129129...=-\frac{430}{333}
|
17,476 |
x_1 + x_2 = x_1 + x_2\Longrightarrow -x_1 + x_1 = x_2 - x_2
|
1,910 |
\frac12 \cdot (b \cdot b - a^2) = (a + b)/2 \cdot (-a + b)
|
1,888 |
y \cdot \Delta \cdot z = z \cdot y \cdot \Delta
|
-5,000 |
17.4 \cdot 10^{3 + 6} = 10^9 \cdot 17.4
|
51,030 |
18 = 2*3 3
|
-9,633 |
0.01*(-80) = -\frac{80}{100} = -\frac15*4
|
-4,487 |
x * x + 2*x + 8*(-1) = (x + 4)*\left(2*(-1) + x\right)
|
23,081 |
5 + \frac{1}{1}(5(-1) + \sqrt{29}) = \sqrt{29}
|
34,571 |
F_1\cdot F_2 = F_1\cdot F_2
|
31,301 |
378 = \frac{756}{2} \cdot 1
|
-7,931 |
\left(7 - i - 7 \cdot i + (-1)\right)/2 = \dfrac12 \cdot (6 - 8 \cdot i) = 3 - 4 \cdot i
|
7,536 |
\frac{100}{1 + t + (-1)} = 100/t
|
26,241 |
2^{2 + j} = 2^3*2^{(-1) + j}
|
15,476 |
D + G + D = G + (1 + 1)\cdot D
|
3,561 |
m + 1 + m + 2 = 2 \times m + 3 > m + 3
|
11,638 |
1^3 + 4^3 = \left(1 + 4\right) (1^2 - 4 + 4^2) = 5 \cdot 13
|
-20,202 |
7/7 \cdot (a + 6 \cdot (-1))/(-5) = (42 \cdot (-1) + 7 \cdot a)/(-35)
|
7,253 |
a \cdot 1^{-1}/1 = \frac{1}{1^{-1}} a = \frac{1}{1} a
|
20,273 |
\left(s + \alpha + (1 + \alpha^2)^{1/2}\right)*(s + \alpha - (1 + \alpha^2)^{1/2}) = (-1) + s^2 + 2*s*\alpha
|
20,769 |
3\times g + A = (g + A)\times (g + A)\times (g + A) = \left(g + A\right)^3
|
-20,389 |
\frac{1}{5}\cdot 5\cdot \frac{n}{5\cdot (-1) - n} = \frac{n\cdot 5}{-5\cdot n + 25\cdot (-1)}
|
10,955 |
1 - 2/15 = \frac{13}{15}
|
27,857 |
((6 + 4\left(-1\right))^2 + \left(5 + \left(-1\right)\right)^2 + (4 + 0(-1)) \cdot (4 + 0(-1)))^{1/2} = 6
|
19,707 |
(-x)^m = (-1)^m\times x^m = -x^m
|
-3,564 |
3 \cdot p^2/4 = p \cdot p \cdot 3/4
|
20,271 |
l \geq 1 \Rightarrow 1 + l \geq 2
|
23,775 |
\frac{1}{\left((-1) + 10^3\right)\cdot 10^4} 456 + 1.3245 = 1.3245 + \frac{456}{10000\cdot 999}
|
24,757 |
(-4)^2 = 4^2 = 16 = (\sqrt{-16}*\sqrt{-1}) * (\sqrt{-16}*\sqrt{-1})
|
6,002 |
5/6 = -6/10 \cdot 5/9 \cdot 4/8 + 1
|
9,589 |
\sin\left(D + B\right) = \cos(B)\cdot \sin\left(D\right) + \sin(B)\cdot \cos(D)
|
-19,306 |
\frac85*3/2 = 1/5*8/(2*\frac13)
|
7,603 |
3^3 + 5^3 + 19^3 + 21^3 = 1^3 + 9^3 + 15^3 + 23 * 23^2
|
19,723 |
(\frac12\cdot (2.18 + 3.64) + 2.18)/2 = 2.545
|
50,280 |
-\cos(0) = -1
|
33,663 |
(0.6 + 1)/12 = 2/15
|
1,529 |
\sin(\pi/2 + t) = \sin{\frac{\pi}{2}} \cdot \cos{t} + \cos{\pi/2} \cdot \sin{t}
|
30,916 |
\tfrac{k}{2} + 1 + k/2 + 1 = 2 + k
|
58 |
|t|\cdot |x| = |t\cdot x|
|
16,472 |
(-1) + V^s = \dfrac{V}{s}\cdot V^{(-1) + s}\cdot s + (-1)
|
-1,496 |
18/45 = \frac{18*\tfrac19}{45*\frac19} = \frac{2}{5}
|
6,523 |
\pi\cdot i\cdot 4 - 6\cdot \pi\cdot i = -\pi\cdot i\cdot 2
|
3,645 |
A \cap Y = A\Longrightarrow \{A,Y\}
|
22,600 |
L = \dfrac13\cdot \left(L + 1\right) \Rightarrow L = \frac12
|
1,940 |
l \cdot (x \cdot g_q + c \cdot g_0) = g_0 \cdot l \cdot c + x \cdot g_q \cdot l
|
265 |
\frac{1}{c b} = 1/(b c)
|
1,493 |
0 = (\lambda \cdot I - A)^2 \cdot v_2 = \left(\lambda \cdot I - A\right) \cdot (\lambda \cdot I - A) \cdot v_2
|
-9,184 |
k^3*40 = k*k*k*2*2*2*5
|
29,415 |
-\sin\left(\theta\right) = \sin(π + \theta)
|
-23,712 |
\dfrac{1/7}{2} \cdot 2 = 1/7
|
29,960 |
(-1) + t^n = t^n - 1
|
29,690 |
\left((-1) + 12\right) \cdot \left((-1) + 12\right) = 121
|
8,980 |
15 + z^2 - z*8 = \left(z + 3*(-1)\right)*(z + 5*(-1))
|
-19,273 |
\dfrac29*\frac{5}{7} = \dfrac{2*1/9}{\dfrac{1}{5}*7}
|
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