id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
13,502 |
\frac{z}{z^3} = \frac{1}{z * z}
|
-26,594 |
(x*2)^2 = 4*x^2
|
14,941 |
\tan(x) = \frac{\sin(x)}{\cos(x)} = \frac{1}{\sqrt{1 - \sin^2\left(x\right)}}\cdot \sin(x)
|
-19,628 |
\tfrac{6}{\frac18} \cdot 1/5 = \frac65 \cdot \frac{1}{1} \cdot 8
|
7,264 |
1 = \tfrac17*(11 - 2*2)
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-20,872 |
\frac{1}{90 + 9*t}*\left(2*t + 20\right) = \dfrac{1}{t + 10}*(t + 10)*\frac{2}{9}
|
-3,170 |
-63^{1/2} + 112^{1/2} = (16 \cdot 7)^{1/2} - (9 \cdot 7)^{1/2}
|
6,011 |
25 = 4^2 + 3 * 3
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-4,733 |
\dfrac{1}{2 + y^2 + 3*y}*(-2*y + 5*\left(-1\right)) = \frac{1}{2 + y} - \frac{3}{y + 1}
|
964 |
(1 + 4 + 9)\cdot 999 = 14\cdot \left(1000 + (-1)\right) = 13986
|
32,996 |
4 = (1^3 + 1^3)*(1^3 + 1^3)
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-20,929 |
-9/(-9)*(-9/2) = 81/(-18)
|
1,350 |
s + s\cdot 0 = s
|
-10,785 |
-\frac{y + 8\cdot \left(-1\right)}{y^3\cdot 20}\cdot 4/4 = -\frac{1}{80\cdot y^3}\cdot (32\cdot \left(-1\right) + y\cdot 4)
|
14,997 |
\cos(\pi/17) \cdot 2 = 2 \cdot \cos(2 \cdot \pi/34)
|
-26,639 |
81\cdot \left(-1\right) + 16\cdot x^6 = (4\cdot x^3 + 9\cdot \left(-1\right))\cdot \left(9 + 4\cdot x \cdot x \cdot x\right)
|
-10,601 |
\frac{7}{q + 3 \cdot \left(-1\right)} \cdot \frac{5}{5} = \frac{1}{15 \cdot (-1) + 5 \cdot q} \cdot 35
|
-15,167 |
\dfrac{x^5}{\frac{1}{\frac{1}{t^{10}} \cdot \dfrac{1}{x^{10}}}} = \frac{x^5}{x^{10} \cdot t^{10}}
|
-3,020 |
\sqrt{96} + \sqrt{150} + \sqrt{24} = \sqrt{16*6} + \sqrt{25*6} + \sqrt{4*6}
|
-25,984 |
840 = \frac{1}{0.1}84
|
24,263 |
1225/5050 = \frac{1}{202} 49
|
32,125 |
\left(t + (-1)\right)^2 = t \cdot t - 2 \cdot t + 1
|
6,482 |
((-1) + \frac{k*u*h}{i*g*x})*100 = \dfrac{1}{i*g*x}*(-x*i*g + k*h*u)*100
|
-7,000 |
\frac{3}{2}\cdot \frac{1}{7} = \frac{1}{14}\cdot 3
|
4,609 |
1/l + 3*(1 + l^2) + 3*\left(-1\right) = 3*l^2 + \dfrac{1}{l}
|
19,120 |
n + \left(-1\right) + n + 2(-1) = 3(-1) + n\cdot 2
|
16,795 |
3\cdot \left(\dfrac13\cdot (d + 7) + 4\right) = 3\cdot \dfrac13\cdot \left(d + 7\right) + 3\cdot 4 = d + 7 + 12
|
6,916 |
6\cdot m\cdot 8 + k\cdot 48 = 48\cdot (k + m)
|
26,890 |
\sin{\frac14\cdot \pi} = \frac{1}{\sqrt{2}} = \cos{\pi/4}
|
22,106 |
(1 + y^4 + y^3 + y \cdot y + y)\cdot ((-1) + y) = (-1) + y^5
|
16,761 |
\frac{\mathrm{d}n}{\mathrm{d}n} - r = \frac{\partial}{\partial n} (n - r)
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18,879 |
1 + (74 + 1)/100 + \frac14 + 1 + \frac{1}{100}\cdot \left(74 + 1\right) = 3.75
|
-27,696 |
\cos(z)\cdot 16 = d/dz \left(16\cdot \sin(z)\right)
|
394 |
0\times \dots\times \pi\times 2 = 0
|
16,656 |
\frac{3/4*\dfrac34}{2} = 9/32
|
9,857 |
144=2\times72
|
11,286 |
\frac{2}{8} - \frac{5}{4} - \frac{k}{2} + 3 = 0 \implies k = 4
|
4,107 |
(\frac{1}{\zeta_j} + \zeta_j) * (\frac{1}{\zeta_j} + \zeta_j) = \zeta_j^2 + 2 + \frac{1}{\zeta_j * \zeta_j}
|
-3,194 |
(2 + 1 + 4) \cdot 13^{1/2} = 13^{1/2} \cdot 7
|
3,848 |
|-ba + b_n a_n| = |-ba + a_n b_n - ba_n + a_n b|
|
869 |
2 = \left(0 + 1\right) \cdot 2^1
|
-2,430 |
\sqrt{13}\times 7 = \sqrt{13}\times (3 + 5 + \left(-1\right))
|
2,214 |
\sin{\frac{π}{4}} = \cos{π/4} = \sqrt{2}/2
|
-5,530 |
\frac{3}{q \cdot 3 + 30 \cdot (-1)} = \tfrac{3}{(10 \cdot (-1) + q) \cdot 3}
|
-28,922 |
\dfrac{1}{7 \times \frac{1}{20}} \times 7 = 7 \times \frac{20}{7} = 20
|
21,439 |
E((A - E(A))^2) = E(A \cdot A) - E(A)^2
|
-7,197 |
6/49 = \frac{2}{7}*\frac{1}{7} 3
|
5,124 |
\frac38 = 1/8 \cdot 3
|
368 |
\frac{5}{12} = \frac{1}{3\cdot 2} + 1/(2\cdot 2)
|
36,370 |
n^2 - n \cdot n - n = n
|
16,897 |
36 + 24 \left(-1\right) = 12
|
23,131 |
\left(x/2 + 5(-1)\right)^2 + x^2 = (3 + x/2)^2 + (x + 4(-1))^2
|
-15,255 |
\frac{1}{\frac{z^4}{q^{20}}*q^5} = \frac{1}{(\frac{z}{q^5})^4*q^5}
|
-1,210 |
-\frac{3}{5} \cdot 9/1 = ((-3) \cdot 1/5)/(1/9)
|
506 |
\frac{1}{g*h} = 1/\left(g*h\right) \Rightarrow g*h = g*h
|
1,389 |
g = \sqrt{g} \cdot \sqrt{g}
|
23,261 |
x^{d + c} = x^c x^d
|
3,744 |
g \cdot 7 - 3 \cdot f = g + 6 \cdot g - 3 \cdot f
|
11,492 |
\tfrac11*(10 + 6*(-1)) = \frac15*(18 + 2) = (26 + 2)/7
|
-20,804 |
\frac{1}{-6*k + 10*\left(-1\right)}*7*\frac99 = \frac{63}{-54*k + 90*(-1)}
|
12,182 |
k - 2\cdot n + 1 = k - n - n + (-1)
|
2,713 |
\left(2(k + 1)\right)! = \left(2k + 2\right)! = 2k! (2k + 1) (2k + 2)
|
-7,606 |
\frac{1}{-(-4*i)^2 + 1 * 1}*(1 + 4*i)*(-14 + i*5) = \frac{(-14 + i*5)*\left(i*4 + 1\right)}{\left(-i*4 + 1\right)*\left(i*4 + 1\right)}
|
36,449 |
\left(3\cdot q\right)^2 = 3\cdot q\cdot 3\cdot q = 9\cdot q^2
|
-2,428 |
\sqrt{13} \cdot \left(5 + 1\right) = 6 \cdot \sqrt{13}
|
26,481 |
\left(4 \cdot \left(-1\right) + z\right)^2 = z^2 - 8 \cdot z + 16
|
40,839 |
1 = X X + 2 = X^3 + X + 1
|
-19,386 |
8\cdot \frac{1}{3}/(5\cdot \dfrac18) = \tfrac{8}{5}\cdot \frac{1}{3} 8
|
2,038 |
|x| = \|x\times h_0\| = \|-x\times h_0\|
|
-20,355 |
\frac{1}{2}9 \frac{1}{z + 2(-1)}(z + 2(-1)) = \frac{1}{4\left(-1\right) + z*2}(z*9 + 18 (-1))
|
31,953 |
-z! + \theta^2 = 2001 \Rightarrow \theta \cdot \theta = z! + 2001
|
-16,586 |
99^{\frac{1}{2}}*4 = 4 (9*11)^{\frac{1}{2}}
|
-5,622 |
\dfrac{1}{3 \cdot (q + 9 \cdot (-1))} \cdot 4 = \frac{4}{27 \cdot (-1) + q \cdot 3}
|
-5,460 |
\frac{1}{98 \cdot (-1) + 2 \cdot x^2} \cdot (6 \cdot x + 42 \cdot (-1) - x + 7 \cdot (-1) + 4 \cdot (-1)) = \frac{1}{x^2 \cdot 2 + 98 \cdot (-1)} \cdot (x \cdot 5 + 53 \cdot (-1))
|
19,706 |
y^2 + z^2*4 + 5*z*y = (y + z)*(y + 4*z)
|
29,474 |
\frac{1}{x + 2} \cdot (b + x^3 + a \cdot x) = x^2 - 2 \cdot x + a + 4 + \frac{1}{x + 2} \cdot \left(-(a + 4) \cdot 2 + b\right)
|
7 |
-\operatorname{E}\left[X_2\right] + \operatorname{E}\left[X_1\right] = \operatorname{E}\left[-X_2 + X_1\right]
|
6,745 |
(\tfrac13) * (\tfrac13) + (\frac13*2) * (\frac13*2) = 5/9 \lt 1 + 1
|
9,423 |
4 + (-1) + 3\cdot (-1) = 10\cdot (-1) + 1 + 9
|
7,525 |
\sin(\left(-z\right)^2) = \sin{z \cdot z}
|
14,504 |
(7^{1/2}\cdot 3 + 7)/2 = 7/2 + \dfrac{3\cdot 7^{1/2}}{2}
|
-19,728 |
7\cdot 6/\left(8\right) = \dfrac{42}{8}
|
24,194 |
1^3 - 3 \cdot 1^2 + \left(-1\right) + 3 = 1 + 3 \cdot \left(-1\right) + (-1) + 3 = 0
|
-16,528 |
4*\sqrt{4}*\sqrt{3} = 4*2*\sqrt{3} = 8*\sqrt{3}
|
17,674 |
\left(n + 1\right)^3 = n^2 \cdot n + 3 \cdot n^2 + n \cdot 3 + 1
|
8,319 |
2N * N = (\sqrt{2} N)^2
|
-20,430 |
\frac{1}{3 + z} \cdot \left(z + 3\right) \cdot (-\frac{7}{4}) = \dfrac{1}{12 + z \cdot 4} \cdot (-z \cdot 7 + 21 \cdot (-1))
|
-29,166 |
2 \times 5 + 3 \times 2 = 16
|
16,155 |
(-1)^{-m + 1} = \left(-1\right)^{-m + 1} (-1)^{2m} = (-1)^{m + 1}
|
-20,561 |
\frac{-27*x + 12}{4 - 9*x} = \frac{1}{1}*3*\frac{4 - x*9}{4 - 9*x}
|
33,195 |
\frac{8*(-1) + 28}{4*\left(-1\right) + 8} = 5
|
13,980 |
Q^4 + 1 = \left(Q^2 + (-1)\right)^2 - \left(cQ\right)^2 = (Q^2 - cQ + (-1)) (Q^2 + cQ + (-1))
|
9,778 |
\frac{1}{40}\cdot (3000 + 2\cdot x) = \dfrac{3000}{40} + \frac{2\cdot x}{40} = 75 + x/20
|
-3,204 |
\sqrt{2} \sqrt{25} + \sqrt{9} \sqrt{2} = \sqrt{2}\cdot 5 + \sqrt{2}\cdot 3
|
2,185 |
x \cdot 6 + 5 \cdot \left(-1\right) = x + 5 \cdot x + 6 \cdot (-1) + 1
|
-20,595 |
\frac{20}{5*(-1) + 25*z}*z = \frac{4*z}{5*z + (-1)}*1*5/5
|
-22,057 |
\frac72 = \frac{21}{6}
|
11,287 |
\sin{\frac{5\cdot \pi}{2}} = \sin{\pi/2} = 1
|
10,584 |
E[A A] = E[A]^2 + VAR[A]
|
20,956 |
x^T\times A\times x = (x^T\times A\times x)^T = x^T\times A^T\times x = -x^T\times A\times x
|
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