id
int64 -30,985
55.9k
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stringlengths 5
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|---|---|
-10,118 |
63\% = \tfrac{63}{100} = 0.625
|
-10,565 |
-\tfrac{6}{8 + 4*x}*\frac{1}{5}*5 = -\frac{1}{x*20 + 40}*30
|
34,275 |
z^4 + 16 (-1) = \left(z \cdot z + 4(-1)\right) (z^2 + 4) = (z + 2(-1)) (z + 2) (z - 2i) (z + 2i)
|
-20,891 |
-\frac{9}{4}*\frac{1}{-8*x + 7*\left(-1\right)}*(-8*x + 7*\left(-1\right)) = \frac{1}{28*(-1) - x*32}*(72*x + 63)
|
19,630 |
(X^2 + X*2 + (-1))*(X^2 - 2*X + \left(-1\right)) = X^4 - X^2*6 + 1
|
9,602 |
\frac{1}{2}(N + 1) (2 + N) = 1 + 2 + \dotsm + N + N + 1
|
-6,999 |
\frac{7}{12} = \dfrac{1}{8}6*7/9
|
-12,042 |
17/40 = \frac{1}{10 \pi}p \cdot 10 \pi = p
|
8,281 |
p + 1 = d^2 \Rightarrow p = d^2 + \left(-1\right) = (d + 1)*(d + (-1))
|
-22,710 |
28/49 = \dfrac{7 \cdot 4}{7 \cdot 7}
|
30,910 |
-x^2 \cdot 20 + 4 + 3 = 4 \cdot (-5 \cdot x^2 + 1) + 3
|
-4,570 |
\frac{2}{z + 3} + \frac{1}{z + 2} = \frac{1}{6 + z^2 + z \cdot 5} \cdot \left(7 + 3 \cdot z\right)
|
11,548 |
x + x = (x + x)^2 = \left(x + x\right)\cdot (x + x) = x^2 + x^2 + x^2 + x^2 = x + x + x + x
|
-20,951 |
\frac{1}{14 \cdot k} \cdot (8 \cdot \left(-1\right) + 2 \cdot k) = \tfrac{1}{k \cdot 7} \cdot \left(k + 4 \cdot (-1)\right) \cdot \frac{1}{2} \cdot 2
|
7,638 |
\tfrac{4}{s \times 4} = \dfrac{1}{s}
|
19,000 |
(x + 2\cdot h\cdot \cos{u})^2 = x^2 + 4\cdot x\cdot h\cdot \cos{u} + 4\cdot h^2\cdot \cos^2{u} = (x + h\cdot \cos{u})\cdot 4\cdot h\cdot \cos{u} + x^2
|
23,436 |
\left(x + 2 \cdot (-1)\right) \cdot \left(x + 2 \cdot (-1)\right) + 16 = 20 + x^2 - 4 \cdot x
|
-23,063 |
\frac{40}{27} = 2/3\cdot \frac{20}{9}
|
-15,737 |
\frac{1}{s^{12} \cdot s^{15} \cdot t^{20}} = \frac{\frac{1}{s^{15}}}{t^{20}} \cdot \frac{1}{s^{12}} = \frac{1}{s^{27} \cdot t^{20}} = \frac{1}{s^{27} \cdot t^{20}}
|
5,493 |
71 = \frac17 \cdot (64 + 433)
|
26,013 |
5^2 = \frac12\cdot \left(1^2 + 7^2\right)
|
45,976 |
z^3 = z * z * z
|
-30,241 |
\frac{x^2 + 9*(-1)}{x + 3*(-1)} = \dfrac{(x + 3)*\left(x + 3*(-1)\right)}{x + 3*(-1)} = x + 3
|
-1,287 |
\frac{1/3 \cdot 8}{\left(-7\right) \cdot 1/2} = \frac83 \cdot (-\frac17 \cdot 2)
|
18,075 |
\sqrt{13}\cdot (\dfrac{1}{\sqrt{13}}\cdot 2 + -\frac{3}{\sqrt{13}}\cdot i) = 2 - i\cdot 3
|
9,770 |
(y + x) \cdot (x \cdot x - x \cdot y + y^2) = y \cdot y \cdot y + x^3
|
29,847 |
16^{\frac{1}{4}\cdot 3} = (16^3)^{1/4} = (2^{4^3})^{1/4} = 2^3
|
34,379 |
\left(f + h\right)^4 = f^4 + 4\times f^2 \times f\times h + 6\times f \times f\times h^2 + 4\times f\times h^3 + h^4 = f^4 + h^4 + 4\times f\times h\times \left(f^2 + h^2\right) + 6\times f \times f\times h^2
|
50,442 |
2*11 + 5 = 27
|
28,226 |
4 + y^8 = (y^4 + 2*y^2 + 2)*(y^4 - 2*y^2 + 2)
|
-1,833 |
\frac{2}{3}\cdot \pi + \frac{\pi}{2} = \pi\cdot 7/6
|
9,480 |
z^{1/2} \cdot z^{\frac12} = z^1 = z
|
2,253 |
2*(-1) + (1/y + y)^2 = \frac{1}{y^2} + y^2
|
-6,672 |
\frac{4}{(q + 4) \cdot \left(5 \cdot (-1) + q\right)} = \frac{4}{20 \cdot \left(-1\right) + q^2 - q}
|
22,507 |
\left|{I - E\cdot D}\right| = \left|{I - E\cdot D}\right|
|
6,202 |
(3 + m*2) (2 + m) = 2 m^2 + 7 m + 6
|
11,052 |
\int 1\cdot \frac{2}{x^2 + 1}\,dx = \tan^{-1}{x}\cdot 2
|
4,583 |
2/3 = (3 + (-1))/3
|
6,991 |
\frac{1}{2}y = y - \frac12y
|
24,866 |
0.6 = \dfrac{9}{15}
|
24,967 |
1^{1/4}=1
|
4,855 |
(k + 1)^3 = k^3 + 3\cdot k \cdot k + 3\cdot k + 1 \lt k^3 + k^3 + k^3
|
27,090 |
\frac{1}{5}\cdot 3 = \dfrac{1}{2 + 3}\cdot 3
|
-11,540 |
i \cdot 6 + 4 + 0 \cdot (-1) = 6 \cdot i + 4
|
40,243 |
x*s = s*x
|
-20,856 |
\frac{30 - p \cdot 20}{5 \cdot (-1) + 25 \cdot p} = \dfrac{5}{5} \cdot \dfrac{-4 \cdot p + 6}{5 \cdot p + (-1)}
|
33,386 |
b \cdot z \cdot E = E \cdot z \cdot b
|
20,447 |
a_1\cdot a_2\cdot z = z\cdot a_2\cdot a_1
|
7,432 |
\cos\left(a + g\right) = -\sin(g)\cdot \sin(a) + \cos\left(a\right)\cdot \cos(g)
|
29,379 |
|K l| = |K| |l|
|
-20,460 |
-9/7*\dfrac{2 - 2*g}{2 - 2*g} = \frac{1}{-g*14 + 14}*(18*g + 18*(-1))
|
21,303 |
\left(-3,3\right) = (-3, 3)
|
12,387 |
10 \cdot 10 = 7^2 + 5^2 + 4 \cdot 4 + 3^2 + 1^2
|
-24,001 |
(4 + 5)^2 = 9 * 9 = 9^2 = 81
|
6,300 |
(\sqrt{x})^2 \cdot \sqrt{d} \cdot \sqrt{d} = d \cdot x
|
-15,571 |
\frac{1}{x^{25}\cdot (\frac{1}{k^5}\cdot x)^3} = \frac{1}{x^{25}\cdot \frac{1}{k^{15}}\cdot x^2 \cdot x}
|
-20,909 |
(4\cdot \left(-1\right) + n)\cdot \frac{1}{n + 4\cdot (-1)}/7 = \dfrac{1}{28\cdot (-1) + n\cdot 7}\cdot (n + 4\cdot (-1))
|
24,387 |
x!/x = \left((-1) + x\right)!
|
22,911 |
(1 + n)*2^{1 + n} = (1 + n)*2*2^n
|
17,718 |
\cos\left(2*x\right) = \cos^2(x) - \sin^2(x) = \cos^2(x) - 1 - \cos^2\left(x\right) = 2*\cos^2(x) + (-1)
|
19,547 |
\pi x^3*2 + 4 Y^2 x \pi - 4 \pi x^3 = 4 Y^2 x \pi - 2 x^3 \pi
|
25,527 |
\tfrac{2*y}{y + (-1)} = \frac{2}{(-1) + y} + 2
|
30,403 |
\tfrac{1}{x + 3} \times (x^2 + 5 \times x + 7) = x + \frac{1}{x + 3} \times \left(2 \times x + 7\right) = x + 2 + \frac{1}{x + 3}
|
1,952 |
100!/102! = \frac{100!}{102*101*100!} = 1/10302
|
2,294 |
2^6\cdot 3^6\cdot 4^3 = 2^1\cdot 4^3\cdot 2^5\cdot 3^4\cdot 3^2
|
25,932 |
0.111111*\dotsm = x rightarrow x \lt 1 + 1 + 1 + 1 + \dotsm
|
811 |
\cos{x \times 2} = \left(-1\right) + 2 \times \cos^2{x}
|
15,118 |
\frac{1}{m \cdot 2 + (-1)} \cdot (2 + 2 \cdot m) \cdot \dfrac{1}{m + 1} \cdot (m \cdot 2 + 1) = \frac{2 \cdot m + 1}{m \cdot 2 + (-1)} \cdot 2
|
6,425 |
\dfrac{1}{a_{2^m}}\cdot a_{2^{m + 1}}\cdot 2 = \frac{a_{2^{m + 1}}}{a_{2^m}\cdot 2^m}\cdot 2^{1 + m}
|
10,592 |
\dfrac{1}{99 \cdot 999} \cdot ((100 + (-1)) \cdot 717 - ((-1) + 1000) \cdot 71) = -71/99 + \frac{717}{999}
|
-13,253 |
1 + \frac{1}{2}\cdot 2 = 1 + 1 = 1 + 1 = 2
|
6,971 |
1 + \left(-1\right) = -1 + 1
|
37,320 |
g_2 + g_1 + f = g_1 + f + g_2
|
3,999 |
(20 + 4 + 5 + 6 + 11 + 13)^3 = 4^4 + 5^4 + 6^4 + 11^4 + 13^4 + 20^4
|
16,936 |
g^2 - Q^2 = (g - Q) \cdot (g + Q)
|
-529 |
(e^{5 \cdot \pi \cdot i/12})^4 = e^{4 \cdot \frac{5}{12} \cdot i \cdot \pi}
|
-23,648 |
8/21 = 2/3\cdot \frac17\cdot 4
|
33,243 |
\dfrac{15}{36} = \frac{1}{12}*5
|
14,257 |
\cot(\dfrac{3}{2}\cdot \pi - z) = \cot(\pi - z - \frac{\pi}{2}) = -\cot(z - \pi/2) = \cot\left(\pi/2 - z\right) = \tan{z}
|
2,628 |
612 = 3*8*(2*8 + 1)*(8 + 1)/6
|
21,742 |
((-1) + z) \cdot ((-1) + z) = z^2 - 2 \cdot z + 1
|
14,924 |
x \approx e rightarrow e = x
|
33,059 |
\int f\,\mathrm{d}D = \int f\,\mathrm{d}D
|
-6,480 |
\frac{x \cdot 3}{40 + x^2 + x \cdot 13} \cdot 1 = \frac{3 \cdot x}{(8 + x) \cdot (x + 5)}
|
25,237 |
\frac{5}{6} \times \frac{5}{6}=\left(\frac{5}{6}\right)^2
|
12,992 |
(C_2 + C_1)^2 = C_1^2 + C_1 C_2 + C_2 C_1 + C_2^2
|
21,591 |
\mathbb{E}[A\cdot Y]^2 = (\mathbb{E}[A]\cdot \mathbb{E}[Y])^2
|
11,209 |
(d + 1) \left(d^{(-1) + r} - d^{r + 2(-1)} \ldots \ldots + 1\right) = d^r + 1
|
-1,490 |
\frac{1}{2 \cdot 1/7} \cdot (\left(-9\right) \cdot 1/5) = -\dfrac95 \cdot \frac72
|
-4,772 |
\frac{11 \cdot (-1) - 2 \cdot x}{x^2 + 5 \cdot x + 4} = -\dfrac{3}{x + 1} + \frac{1}{x + 4}
|
40,038 |
(-1)\cdot 0.01 + 1 = 0.99
|
-4,236 |
\frac{5}{\mu^2}\cdot \dfrac{1}{3} = \frac{5}{\mu^2\cdot 3}
|
9,445 |
4^n + n^4 = (2^n)^2 + n \cdot n \cdot n \cdot n = (n^2 + 2^n)^2 - 2\cdot 2^n\cdot n \cdot n
|
-9,869 |
0.125 = \frac{12.5}{100} = \dfrac{1}{8}
|
26,399 |
100*\dotsm*0 = 0
|
-5,735 |
\frac{4}{12 (-1) + 3x} = \frac{4}{(x + 4(-1))*3}
|
16,327 |
d_r + x_r = x_r + d_r
|
7,095 |
1/3\cdot \left(\frac13\cdot 2\right)^3 = 8/81
|
-20,592 |
\frac{56*(-1) + 7*k}{70 - k*42} = \dfrac{7}{7}*\frac{8*(-1) + k}{-k*6 + 10}
|
17,421 |
996 = 4\cdot (\frac{1}{8}\cdot (29\cdot \left(-1\right) + 2013) + 1)
|
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