id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
39,126 |
s + s = (s + s) \cdot (s + s) = s^2 + s^2 + s^2 + s^2 = s + s + s + s
|
14,167 |
\frac{t}{e^{q \times t}} = e^{-t \times q} \times t
|
-29,594 |
\frac{\mathrm{d}}{\mathrm{d}x} (3 \cdot x^4) = 3 \cdot \frac{\mathrm{d}}{\mathrm{d}x} x^4 = 3 \cdot 4 \cdot x^3 = 12 \cdot x \cdot x \cdot x
|
3,257 |
y\cdot B^2 + 5\cdot y\cdot B + 4\cdot y = (4 + B^2 + 5\cdot B)\cdot y
|
-5,002 |
15.8 \cdot 10^2 = 10^{3 - 1} \cdot 15.8
|
3,697 |
(a + b)\cdot (-a + b) = b \cdot b - a^2
|
14,411 |
3 \leq x \Rightarrow e^{x + \left(-1\right)} > 2^{x + (-1)} \geq 2^{x + \left(-1\right)} = \left(1 + 1\right)^{x + (-1)}
|
37,091 |
\tfrac{1}{x}\cdot \xi = 1/\left(1/\xi\cdot x\right)
|
9,038 |
\frac{1}{x + 2 \cdot (-1)} \cdot \left(2 \cdot x^3 - 10 \cdot x + 4\right) = 2 \cdot x^2 + 4 \cdot x + 2 \cdot (-1)
|
-460 |
e^{2 \times \pi \times i} = e^{\pi \times i} \times e^{\pi \times i} = (-1)^2 = 1
|
8,335 |
\sin{2*y} = 2*\sin{y}*\cos{y} rightarrow \sin^{22}{y} = 4*\sin^2{y}*\cos^2{y}
|
11,877 |
S*W = I \Rightarrow W*S = I
|
-5,016 |
10^3 \cdot 0.84 = 0.84 \cdot 10^{2 - -1}
|
11,795 |
x*3 = \frac{\mathrm{d}}{\mathrm{d}x} (\frac12 + \frac32 x^2)
|
5,484 |
\tfrac{35}{12} = 91/6 - (\dfrac72)^2
|
-6,053 |
\frac{1}{27 (-1) + m^2 + m \cdot 6}4 = \frac{1}{(m + 9) (m + 3(-1))}4
|
-20,958 |
\dfrac{3 \cdot x}{x \cdot 3} \cdot (-\frac14 \cdot 7) = \dfrac{(-21) \cdot x}{12 \cdot x}
|
4,425 |
\cos{x \cdot f} = \cos(0.5 \cdot x \cdot f + 0.5 \cdot x \cdot f) = \cos^2{0.5 \cdot x \cdot f} - \sin^2{0.5 \cdot x \cdot f}
|
-3,509 |
\frac{3*5}{5*20} = 15/100
|
3,906 |
\frac{x}{(x^2 + a^2)^2} = \dfrac{x}{a^2 + x^2}\frac{1}{x^2 + a^2}
|
30,543 |
4\cdot π\cdot 2 = 8\cdot π
|
-4,528 |
\frac{-z + 7}{z^2 - 5z + 4} = \frac{1}{z + 4(-1)} - \dfrac{2}{(-1) + z}
|
9,110 |
x \cdot y + 12 \cdot (-1) = (x + 3 \cdot \left(-1\right) + 3) \cdot (y + 4 \cdot (-1) + 4) + 12 \cdot (-1) = \left(x + 3 \cdot (-1)\right) \cdot \left(y + 4 \cdot (-1)\right) + 4 \cdot (x + 3 \cdot (-1)) + 3 \cdot (y + 4 \cdot (-1))
|
17,372 |
1 + 2*x + 3*x^2 + \dotsm + x^{n + (-1)}*n = \dfrac{1}{(1 - x)^2}*(1 + n*x^{1 + n} - (n + 1)*x^n)
|
-22,428 |
125^{\frac13} = 5
|
12,865 |
\|-\theta + y\| = \sqrt{(y - \theta) \cdot (y - \theta)}
|
-472 |
\left(e^{\dfrac{\pi i}{12} 5}\right)^9 = e^{9 i \pi\cdot 5/12}
|
42,282 |
0.3 \times 4 = 1.2
|
-525 |
(e^{\frac{i}{6}\cdot \pi})^4 = e^{\frac{i\cdot \pi}{6}\cdot 4}
|
-5,210 |
10^{\left(-4\right)*(-1) + 1}*7.1 = 7.1*10^5
|
7,758 |
(-1) + 2y < 1 + y\Longrightarrow 2 > y
|
-3,757 |
96/120 \cdot \frac{1}{z^3} \cdot z^3 = \frac{96 \cdot z^3}{120 \cdot z^3}
|
21,546 |
\frac{n \cdot (k + 2 \cdot \left(-1\right))}{2 \cdot \left(-1\right) + n \cdot k} = \frac{1}{n \cdot k + 2 \cdot \left(-1\right)} \cdot (k \cdot n + 2 \cdot (-1) - (n + (-1)) \cdot 2)
|
16,278 |
(1 + x)^{\delta + 1} = \left(1 + x\right) (1 + x)^\delta \geq (1 + x) \left(1 + \delta x\right)
|
32,465 |
2\times \cos(x)\times \sin(x) = \sin\left(2\times x\right)
|
-4,427 |
\frac{-5 \cdot x + 8 \cdot (-1)}{x^2 + x \cdot 3 + 2} = -\frac{3}{1 + x} - \dfrac{2}{x + 2}
|
14,839 |
(2 + k * k + 3*k)/2 - \dfrac{1}{2}*(k + k^2) = 1 + k
|
700 |
a^{-z} = (e^{\ln\left(a\right)})^{-z} = e^{-z\cdot \ln\left(a\right)}
|
15,850 |
{v + (-1) + l + 2*(-1) \choose l + 2*\left(-1\right)} = {3*(-1) + v + l \choose l + 2*(-1)}
|
4,212 |
2\cdot (3\cdot (-1) + 6\cdot 8) = 90
|
8,419 |
\cosh(2*x) = \cosh^2(x) + \sinh^2\left(x\right) = 1 + 2*\sinh^2(x)
|
32,126 |
2*s - s^2 + s - 2*s^2 + s^3 = s*3 - 3*s^2 + s^3
|
20,469 |
5/7 = \dfrac{2 + 3}{5 + 2}
|
19,612 |
|\dfrac{A}{E}| = |A|/|E|
|
16,704 |
27*\left(1 + \frac13 + 0.12/27\right) = 36.12
|
18,331 |
\operatorname{asin}(-1/2) = (\pi*(-1))/6
|
25,725 |
(x + \left(-1\right))*(5*(-1) + 3*x^3 - x^2*5 - x*5) = 3*x^4 - 8*x^2 * x + 5
|
3,041 |
\dfrac{l}{l + 1} = 1 - \frac{1}{1 + l}
|
31,420 |
A - A - B = A \cap A \cap B^\complement^\complement = A \cap \left(B \cup A^\complement\right) = A \cap B
|
22,875 |
x^3 + x*3 + 4\left(-1\right) = \left(x + (-1)\right) (x * x + x + 4)
|
16,887 |
\cos{\theta_2} \sin{\theta_1} + \cos{\theta_1} \sin{\theta_2} = \sin\left(\theta_2 + \theta_1\right)
|
-6,128 |
\frac{1}{x^2 - 14 \cdot x + 45} \cdot 3 = \frac{1}{(x + 9 \cdot \left(-1\right)) \cdot (x + 5 \cdot (-1))} \cdot 3
|
1,263 |
\cos(2 \cdot Z) = 1 - 2 \cdot \sin^2(Z) = 2 \cdot \cos^2(Z) + \left(-1\right)
|
-4,284 |
\frac{1}{z^2}z^2 * z = zz z/(zz) = z
|
34,522 |
\int \sin^2{z}\,dz = \int \sin{z}*\sin{z}\,dz
|
2,011 |
\dfrac{1}{2 z^2 + y z - y^2} (-y^2 + z^2*2 - y z) = 1 - \frac{2 z y}{-y^2 + 2 z^2 + y z}
|
22,844 |
x^2 - r^2 = (r + x) \cdot (x - r)
|
35,619 |
\frac{1}{12321} + 12319/24642 = \tfrac{1}{2}
|
-20,459 |
\frac{n*2 + 5*(-1)}{n*2 + 5*(-1)}*(-\dfrac71) = \tfrac{35 - 14*n}{n*2 + 5*(-1)}
|
12,253 |
\frac{1}{3}\cdot 2\cdot 1/3\cdot \frac23 = \tfrac{4}{27}
|
-5,282 |
10^{3 + (-1)} \cdot 0.97 = 0.97 \cdot 10 \cdot 10
|
807 |
1 - -\sin\left(x\right) + 1 = \sin(x)
|
-6,429 |
\tfrac{2}{2\cdot (r + 8\cdot (-1))} = \frac{2}{16\cdot (-1) + r\cdot 2}
|
21,948 |
a*2 = 17 \Rightarrow \frac{17}{2} = a
|
19,409 |
|y^l| = \left(1 + |y| + (-1)\right)^l \gt 1 + (|y| + (-1))\times l
|
-2,661 |
3^{\dfrac{1}{2}} = (3(-1) + 4) \cdot 3^{\frac{1}{2}}
|
10,611 |
\frac{\mathrm{d}}{\mathrm{d}x} \sin(x \cdot x) = x \cdot \cos(x^2) \cdot 2
|
19,439 |
1 = z\cdot m + y\cdot n\Longrightarrow z\cdot m = -n\cdot y + 1
|
1,250 |
3*2!/36 = 6/36 = \frac{1}{6}
|
24,916 |
-y \cdot 8 + x^2 + y^2 - 6 \cdot x = 0 \implies (x + 3 \cdot (-1))^2 + (4 \cdot (-1) + y)^2 = 5^2
|
33,851 |
(2^7 + 2(-1))/7 = 18
|
17,602 |
-V/2 + V = \dfrac{V}{2}
|
16,623 |
\frac37\cdot \frac26/5 = 1/35
|
35,314 |
\frac{1}{4}\times \left(1 + 51\right) = 13
|
3,488 |
4*(-1) + 67 = 63
|
-1,244 |
-6/1 \cdot (-2/5) = \tfrac{\left(-2\right) \cdot \frac15}{\frac{1}{6} \cdot (-1)}
|
-29,169 |
0\cdot (-1) = 0
|
-11,642 |
2*i - 6 = 0 + 6*\left(-1\right) + i*2
|
6,998 |
15 \leq n \Rightarrow n \geq 1 + \frac{14}{15} \cdot n
|
-4,651 |
-\frac{1}{z + 5(-1)} + \frac{1}{z + 2\left(-1\right)}4 = \tfrac{1}{10 + z^2 - z\cdot 7}(18 (-1) + z\cdot 3)
|
12,755 |
(1 + n^2) \cdot (n \cdot n + (-1)) = n^4 + \left(-1\right)
|
18,591 |
(X + 3)^2 = X^2 + 6\cdot X + 9 = X^2 + 5\cdot X + 7 + X + 2
|
-1,091 |
-9/30 = \dfrac{(-9)*1/3}{30*1/3} = -3/10
|
2,379 |
2 \cdot (-1) + 2 \cdot \left(x + 1\right) + 5 \cdot x = 7 \cdot x
|
301 |
(h^2 + c^2 + c\cdot h)\cdot \left(-h + c\right) = -h^3 + c^3
|
-20,414 |
\frac{1}{24\cdot (-1) + p\cdot 4}\cdot (42\cdot (-1) + p\cdot 7) = 7/4\cdot \frac{6\cdot \left(-1\right) + p}{p + 6\cdot (-1)}
|
19,235 |
|-T + S| = |-S + T|
|
4,801 |
r^4 + 1 = (r^2 + (-1))^2 + 2r \cdot r = (r^2 + (-1))^2 - r \cdot r = (r^2 - r + (-1)) (r^2 + r + \left(-1\right))
|
-29,321 |
7i - 6 + 2 = 7i - 4
|
1,498 |
7^2 + (-2)^2 = 49 + 4 = 53 = r^2 \implies \sqrt{53} = r
|
285 |
\sin{2a} = \cos{a} \sin{a} \cdot 2
|
-12,771 |
15 = 4*(-1) + 19
|
33,617 |
U\cdot Y\cdot |X| = Y\cdot |X|\cdot U
|
8,450 |
a_n^3-a^3=(a_n-a)(a_n^2+aa_n+a^2)
|
3,974 |
S \coloneqq S_1 S_2 \dotsm S_l \coloneqq S_1 S_2 \dotsm S_l
|
1,972 |
a \cdot \zeta = a \cdot \zeta
|
23,197 |
G^r\cdot G^x = G^{x + r}
|
-3,664 |
\frac{9}{5 \times l^2} = \frac{9}{l^2} \times \dfrac15
|
14,746 |
2 \cdot m^2 + 6 = m \cdot m + m^2 + 6 \geq m^2 + 2 \cdot m + 6 = \left(m + 1\right)^2 + 5 > (m + 1)^2 + 3
|
1,256 |
h_1^3\cdot h_1^3\cdot h_2 = h_1^6\cdot h_2 = h_1 \cdot h_1\cdot h_2
|
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