id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
11,597 |
\left(100 + 1 + 10\right)*10^j = 10^j + 10^{j + 1} + 10^{j + 2}
|
-19,514 |
\dfrac{1}{2\cdot 1/8} = \frac82\cdot 1
|
51,879 |
2 + 2 + 2 + 1 + 1 + 2 + 1 + 1 + 1 + 1 + 1 = 15
|
20,865 |
\left(d + \mu\right)^2 = 2*\mu*d + \mu^2 + d * d
|
-2,216 |
-\frac{2}{12} + 7/12 = 5/12
|
7,883 |
\dfrac{1}{2^{n + 1}}(3(-1) + 2n + 4 - n) = \tfrac{1 + n}{2^{1 + n}}
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37,724 |
(-b + x)^2 = x^2 + b^2 - 2bx \Rightarrow 2xb = -(-b + x)^2 + x^2 + b^2
|
3,367 |
z^3 - 12 \cdot z + 16 = (z + 2 \cdot (-1)) \cdot (g \cdot z^2 + h \cdot z + f) = g \cdot z^3 + (h - 2 \cdot g) \cdot z^2 + (f - 2 \cdot h) \cdot z - 2 \cdot f
|
14,691 |
(-1) + \cos^2(r) \cdot 2 = \cos\left(2 \cdot r\right)
|
26,811 |
1/t\cdot a/(p\cdot \frac{1}{t'}) = \frac{t'\cdot a}{t\cdot p\cdot 1^{-1}}\cdot 1
|
-20,182 |
-\frac{4}{t\cdot 9 + 2\cdot \left(-1\right)}\cdot \frac99 = -\dfrac{36}{18\cdot (-1) + 81\cdot t}
|
4,720 |
o \cdot o^2 + o \cdot o = 2 \cdot o - o^2 = 2 \cdot o - 2 - 2 \cdot o = 4 \cdot o + 2 \cdot (-1)
|
4,467 |
y/z = w \Rightarrow y = z*w
|
15,729 |
v^3 + (-1) = ((-1) + v) \cdot (1 + v \cdot v + v)
|
23,656 |
80^3 + 1 = 7^2 \cdot 3^5 \cdot 43
|
31,466 |
2 + \sqrt{3} = e^{-i*x} = \cos{x} - i*\sin{x}
|
26,167 |
6*z * z - z*15 + 9*(-1) = 3*\left(2*z^2 - 5*z + 3*(-1)\right)
|
4,606 |
W\cdot x/I = x\cdot W/I
|
21,953 |
{32 \choose 16} = {31 \choose 16} \cdot 2
|
36,503 |
1 + \frac{1}{1 - p}*p = \frac{1}{-p + 1}
|
7,996 |
\left(a = 2a\Longrightarrow a \cdot (2 + (-1)) = 0\right)\Longrightarrow a = 0
|
4,596 |
\frac{1}{17} = 60 \cdot 2/17 + 7 (-1)
|
3,259 |
0 = \theta^2 - 2 \cdot \theta + 1 = (\theta + (-1))^2
|
-25,789 |
\frac{1}{40}\cdot 4 = 4/(5\cdot 8)
|
26,527 |
\left(1 + r\right)^2 = 2\cdot r + r^2 + 1
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-7,882 |
\frac{1}{17}(72 + 52 i - 18 i + 13) = \frac{1}{17}\left(85 + 34 i\right) = 5 + 2i
|
28,313 |
28/p = 7/p\cdot 4/p = \dfrac{1}{p}\cdot 7
|
1,171 |
\left(x^4 + (-1)\right)\cdot (-\frac{1}{x^4}) = \frac{1}{x^4} + (-1)
|
8,283 |
h \cdot d = \frac{1}{\tfrac{1}{h \cdot d}} = \frac{1}{1/h \cdot 1/d} = \dfrac{1}{1/d \cdot \frac{1}{h}} = d \cdot h
|
5,904 |
\frac{1}{p! (x - p)!}x! = \binom{x}{p}
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-20,720 |
\frac{10\times (-1) + 10\times a}{5 - 5\times a} = -2/1\times \dfrac{5 - a\times 5}{5 - 5\times a}
|
1,271 |
\binom{17}{3} = \frac{17!}{14!\cdot 3!} = 680
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5,557 |
\operatorname{E}\left(x \cdot x\right) = \operatorname{E}\left(U^2\right)\cdot \operatorname{E}\left((1 + x)^2\right) = \operatorname{E}\left(U\right)\cdot (1 + 2\cdot \operatorname{E}\left(x\right) + \operatorname{E}\left(x^2\right))
|
6,148 |
\dfrac{1}{\sqrt{(-1) + x^2}} = \dfrac{x}{x*\sqrt{(-1) + x^2}}
|
-11,180 |
(x + 2 \cdot (-1))^2 + b = (x + 2 \cdot \left(-1\right)) \cdot (x + 2 \cdot (-1)) + b = x^2 - 4 \cdot x + 4 + b
|
28,083 |
( |d|, |f|) = 1 \Rightarrow \left(d, f\right) = 1
|
-11,698 |
1/36 = (\tfrac16)^2
|
42,281 |
\rho \cdot \beta = \beta \cdot \rho
|
8,088 |
(z^4 + (-1))*(z^4 + 1) = (-1) + z^8
|
23,612 |
\sin(z) \sin\left(K\right) + \cos(z) \cos(K) = \cos(K - z)
|
-21,671 |
\dfrac13\cdot 2 = 2/3
|
458 |
5*\pi/12 = \frac{1}{2}*(\pi - \frac16*\pi)
|
22,696 |
3^{70} + 2^{70} = ((\frac{2}{3})^{70} + 1) \cdot 3^{70}
|
1,431 |
\frac{2}{n^2 + (-1)} = \frac{1}{n + (-1)} - \frac{1}{1 + n}
|
-5,067 |
0.3*10^{(-2)*(-1) + 1} = 10^2 * 10*0.3
|
30,041 |
\dfrac{1}{2^6} \cdot (1^2 + 3 \cdot 3 + 3^2 + 1 \cdot 1) = 20/64 = 5/16
|
-18,334 |
\dfrac{a * a + 9*a}{81*(-1) + a^2} = \frac{a*\left(9 + a\right)}{\left(a + 9\right)*(a + 9*(-1))}
|
-10,312 |
\frac22\cdot 7/(25\cdot s) = 14/(s\cdot 50)
|
-16,355 |
6\sqrt{16} \cdot \sqrt{5} = 6 \cdot 4 \cdot \sqrt{5} = 24\sqrt{5}
|
5,454 |
0 = J^{s + (-1)} + (-1) = (J + (-1))*(1 + J + \dotsm*J^{s + 2*(-1)})
|
32,778 |
m - 2i + i = -i + m
|
11,918 |
V*S = (V^{\frac{1}{2}}*S^{\frac{1}{2}}) * (V^{\frac{1}{2}}*S^{\frac{1}{2}})
|
-22,336 |
(s + 2) \left(s + 6\right) = 12 + s * s + 8s
|
-2,813 |
2*\sqrt{10} = ((-1) + 3)*\sqrt{10}
|
19,295 |
\dfrac{1}{2^{1/2}} = \sin(\pi \cdot 3/4)
|
-20,930 |
-8/5 \cdot \frac{(-1) \cdot 5 \cdot y}{(-5) \cdot y} = \frac{y \cdot 40}{y \cdot (-25)}
|
11,584 |
\pi \cdot 64 = 16 \cdot \pi \cdot 2 \cdot 2
|
22,913 |
b^m = \left((b^{\dfrac1q})^q\right)^m = (b^{\frac{1}{q}})^{q \cdot m}
|
-29,755 |
d/dx (3x^5) = 3d/dx x^5 = 3\cdot 5x^4 = 15 x^4
|
-1,334 |
\frac{\frac19 \cdot (-1)}{3 \cdot \frac{1}{7}} = 7/3 \cdot (-\frac{1}{9})
|
39,021 |
\pi/4 = \tan^{-1}{1}
|
39,200 |
\dfrac1z = \frac{1}{z}
|
40,243 |
x \cdot \Delta = \Delta \cdot x
|
3,862 |
(U + A)^{n + 1} = (U + A)^n\cdot (U + A) = (U + A)^n U + (U + A)^n A
|
4,486 |
\cos\left(-b + c\right) = \sin{c} \cdot \sin{b} + \cos{b} \cdot \cos{c}
|
31,454 |
\frac{96 + 10}{2*96 + 10} = \frac{1}{202}*106 = \frac{1}{101}*53 \approx 0.524752
|
29,929 |
\binom{5}{2}\cdot 3\cdot \binom{5}{4}\cdot 4! = 3600
|
26,400 |
\sec\left(\theta\right) = 1/\cos(\theta)
|
8,225 |
\frac{Z_l}{B_l} = \tfrac{\left(-1\right) Z_l}{(-1) B_l}
|
31,133 |
\frac88 + \sqrt{8 + 8}\cdot (8\cdot 8\cdot 8 + 8\cdot \left(-1\right)) = 2017
|
4,453 |
-(y^2 + x^2) + 1 = 1 - x^2 - y^2
|
31,057 |
k\cdot \frac{1}{h}\cdot a\cdot b = \dfrac{a\cdot b}{h}\cdot 1\cdot k
|
30,527 |
\mathbb{E}\left(m_1\cdot m_2\right) = \mathbb{E}\left(m_1\right)\cdot \mathbb{E}\left(m_2\right)
|
759 |
\binom{n}{j}\cdot j = \frac{n!}{(j + (-1))!\cdot (n - j)!} = n\cdot \binom{n + (-1)}{j + (-1)}
|
-29,358 |
(4 + y) (4 - y) = 4 \cdot 4 - y^2 = 16 - y^2
|
-5,223 |
3.2\cdot 10^1 = 3.2\cdot 10^{-2 - -3}
|
-12,787 |
18 = 29 + 11 \left(-1\right)
|
40,188 |
\overline{e^{i\cdot p}} = \overline{\cos{p} + i\cdot \sin{p}} = \cos{p} - i\cdot \sin{p} = \cos{-p} + i\cdot \sin{-p} = e^{-i\cdot p}
|
13,151 |
g\cdot(h_1+h_2) = (g\cdot h_1) + (g\cdot h_2)
|
33,691 |
6\cdot 1/3/2 = 6/(2\cdot 3)
|
18,397 |
2^{n + 1} = 2 \cdot 2^n \geq 2 \cdot 4 \cdot n \cdot n > 4 \cdot n^2 + 8 \cdot n + 4 = 4 \cdot (n^2 + 2 \cdot n + 1) = 4 \cdot \left(n + 1\right) \cdot \left(n + 1\right)
|
5,297 |
(a_1 + a_2)/r = \frac{a_2}{r} + a_1/r
|
17,753 |
H \cdot D = 0 = D \cdot H
|
9,432 |
|f \cdot a| = |a \cdot f|
|
22,885 |
(B \cdot B - x^2) \cdot (B \cdot B - x^2) + (x\cdot B\cdot 2) \cdot (x\cdot B\cdot 2) = (B^2 + x^2)^2
|
-15,327 |
\frac{1}{\zeta^9\cdot t^{15}\cdot \frac{1}{\frac{1}{\zeta^{15}}\cdot \frac{1}{t^{10}}}} = \frac{\frac{1}{t^{15}}}{t^{10}\cdot \zeta^{15}}\cdot \frac{1}{\zeta^9}
|
19,568 |
\left(y \cdot y = y + 3 \Leftrightarrow 0 = y \cdot y - y + 3\cdot (-1)\right) \Rightarrow \dfrac{1}{2}\cdot (1 \pm \sqrt{13}) = y
|
32,972 |
((6 + 5\cdot (-1))^2 + (0 + 3)^2)^{1/2} = (1 + 9)^{1/2} = 10^{1/2} \leq 4
|
-5,205 |
10^1\cdot 58.8 = 10^{2 - 1}\cdot 58.8
|
14,672 |
(2 \times (-1) + V) \times (V + (-1)) + 4 = V^2 - 3 \times V + 6
|
1,913 |
(s + (-1))*\frac{1}{(-1) + s}*\left((-1) + s^i\right) = s^i + (-1)
|
-20,741 |
\frac{8(-1) + p}{p + 8(-1)} (-3/1) = \frac{24 - 3p}{p + 8(-1)}
|
1,474 |
(4n^2 - 1) = (2n-1)(2n+1)
|
4,248 |
g_1 \cdot h \cdot g_2 = g_2 \cdot g_1 \cdot h
|
-2,411 |
3*\sqrt{6} + \sqrt{6} = \sqrt{9}*\sqrt{6} + \sqrt{6}
|
-9,125 |
x\cdot 2\cdot 3\cdot 3\cdot 3\cdot x = x^2\cdot 54
|
-4,360 |
\frac{66 q}{48 q^4} = \frac{1}{q^4} q\cdot 66/48
|
-20,145 |
\tfrac{1}{3\cdot \left(-1\right) - y\cdot 3}\cdot (-y\cdot 3 + 3\cdot (-1))\cdot (-5/1) = \frac{1}{-3\cdot y + 3\cdot (-1)}\cdot \left(15\cdot y + 15\right)
|
34,243 |
Q^1\cdot \cdots\cdot Q^k = \overline{Q}^k
|
17,040 |
\frac{V\cdot e^x}{V} = e^{V\cdot x/V}
|
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