id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
30,463 |
2 \times 61 = 122
|
1,192 |
\cos(x - \beta) = \sin{x}\cdot \sin{\beta} + \cos{\beta}\cdot \cos{x}
|
21,195 |
x^2 - xz*2 + z^2 = (x - z) * (x - z)
|
-485 |
(e^{\frac{\pi\cdot i}{12}\cdot 11})^{10} = e^{10\cdot 11\cdot i\cdot \pi/12}
|
36,851 |
M \cdot x = x \cdot M
|
24,482 |
\cos{\pi}\cdot \sin{z} + \sin{\pi}\cdot \cos{z} = \sin\left(\pi + z\right)
|
2,843 |
\frac{4}{2} + \frac{8}{2} = (4 + 8)/2 = \dfrac{1}{2}*12
|
12,237 |
\pi\times 2 = 0 + 2\times \pi
|
7,314 |
\tfrac{1}{3!*2^3}(-1)^3 = -\frac{1}{48}
|
10,836 |
1 = -3032\cdot (14995 - 2\cdot 7479) + 15\cdot 7479
|
39,979 |
{10 \choose 3} = \frac{1}{7!*3!}*10! = 10*9*8/(3*2) = 10*3*4 = 120
|
16,910 |
e^{y + 1} = e^y\cdot e
|
-20,260 |
\tfrac{1}{(-30) x} (36 (-1) + x*18) = 6/6 (6 \left(-1\right) + x*3)/(x*(-5))
|
5,335 |
(3 + y) \cdot (5 \cdot \left(-1\right) + y) = ((-3) \cdot (-1) + y) \cdot (y + 5 \cdot (-1))
|
42,230 |
67 + 22 (-1) + 6(-1) + 2 = 41
|
29,071 |
((-1) + y^2)\cdot (y^4 + y^2 + 1) = \left(-1\right) + y^6
|
10,718 |
e^E e^B = e^{B + E}
|
-22,149 |
\frac{12}{40} = 3/10
|
909 |
-c^2 + g^2 = (g + c) (-c + g)
|
3,857 |
y^n*y = y^{n + 1}
|
-475 |
(e^{5\cdot i\cdot π/3})^8 = e^{\dfrac53\cdot π\cdot i\cdot 8}
|
10,120 |
3^{z/2} = 2^z + (-1) = 4^{z/2} + (-1)
|
44,623 |
\frac{1}{(q + \dfrac{g_1}{2})^2 + g_2 - \dfrac14 \cdot g_1^2} \cdot k_1 = \frac{1}{g_2 + q^2 + q \cdot g_1} \cdot k_1
|
-2,779 |
10^{\frac{1}{2}} + 10^{\frac{1}{2}} \cdot 16^{\frac{1}{2}} + 9^{\frac{1}{2}} \cdot 10^{1 / 2} = 10^{\frac{1}{2}} + 4 \cdot 10^{1 / 2} + 10^{\dfrac{1}{2}} \cdot 3
|
-10,577 |
\dfrac{1}{x \cdot 8 + 4 \left(-1\right)} (8 + x \cdot 6) = \frac{3 x + 4}{2 (-1) + x \cdot 4} \cdot \frac{2}{2}
|
25,965 |
b\cdot y = y\cdot b
|
17,827 |
\frac{1}{k} \cdot (k + 1 + 3 \cdot (-1)) = -2/k + 1
|
2,125 |
\left( r, i\right) + \left( x, i'\right) \coloneqq ( r + x, i + i')
|
4,213 |
\frac{2*1/3}{x + 2(-1)} - \frac{1/3*2}{x + 1} = \dfrac{1}{2(-1) + x^2 - x}2
|
21,633 |
\frac{2\cdot \frac{1}{5}}{4} = \frac{1}{10}
|
-5,658 |
\frac{4*n}{6 + n * n + n*5} = \frac{4*n}{(3 + n)*\left(n + 2\right)}
|
17,082 |
x^2 + z * z = z^2 + x^2
|
-3,327 |
2\sqrt{6} + 3\sqrt{6} = \sqrt{9} \sqrt{6} + \sqrt{4} \sqrt{6}
|
11,833 |
1 + x^2 - x = \frac34 + (-\frac{1}{2} + x)^2
|
18,166 |
800/5 \cdot \tfrac12 \cdot 800 = 400 \cdot 160
|
9,345 |
\frac{-y + 1}{1 + y} = \frac{2}{y + 1} + \left(-1\right)
|
18,647 |
(-1) + z^5 = (z^4 + z^3 + z^2 + z + 1)*((-1) + z)
|
-29,594 |
d/dz (3 \times z^4) = 3 \times d/dz z^4 = 3 \times 4 \times z^3 = 12 \times z \times z^2
|
23,807 |
\binom{n}{r} = \binom{n + (-1)}{(-1) + r} + \binom{n + (-1)}{r}
|
12,797 |
24 = 3\cdot \left(-1\right) + 3 \cdot 3 \cdot 3
|
36,082 |
(\frac14*3) * (\frac14*3) = \tfrac{9}{16}
|
-1,643 |
3/4\cdot \pi = 2/3\cdot \pi + \pi/12
|
22,221 |
\lim_{t \to 0} |2\times \left(-1\right) + t|/t = \lim_{t \to 0} \frac1t\times ((-1)\times \left(t + 2\times (-1)\right))
|
5,515 |
\dfrac{1}{2l} = \frac{1}{l*2} = 1/\left(2l\right)
|
-20,849 |
\frac{1}{t + 2}\cdot (7\cdot t + 14) = \frac{t + 2}{t + 2}\cdot \tfrac11\cdot 7
|
16,223 |
c \times c + d^2 = d \times c \times 2 + c^2 - c \times d \times 2 + d^2
|
5,934 |
z = \tfrac{1}{R}*x*r \implies r = z*\frac{R}{x}
|
-7,120 |
\dfrac{1}{11}\cdot 2 = 4/10\cdot \tfrac{1}{11}\cdot 5
|
-1,805 |
-\frac{1}{6}*π = -π*\frac14*3 + π*7/12
|
2,304 |
e^z \cdot e^a = e^{z + a}
|
1,625 |
(-f + a)^3 = -f^3 + a^3 - fa^2\cdot 3 + f^2 a\cdot 3
|
-163 |
{10 \choose 3} = \frac{1}{(10 + 3 \cdot (-1))! \cdot 3!} \cdot 10!
|
15,848 |
1 - \left((-1) \cdot 0.25 + 1\right)^2 = 0.4375
|
29,328 |
-c = a\cdot x^2 + x\cdot b \Rightarrow (-c)^3 = (a\cdot x \cdot x + x\cdot b)^3
|
32,951 |
\frac{1}{A^2} = (\frac1A)^2
|
34,332 |
10 + 6*\left(-1\right) + 1 = 5
|
20,740 |
\dfrac{5\cdot 1/9}{3/8 + 5/9} = 40/67
|
18,512 |
d = c \Rightarrow 0 = d - c
|
4,808 |
-s^2 + x * x = (x - s)*(x + s)
|
-10,107 |
\phantom{ -\dfrac{3}{8} \times \dfrac{27}{50} \times \dfrac{1}{4}} = \dfrac{-3 \times 27 \times 1}{8 \times 50 \times 4} = -\dfrac{81}{1600}
|
33,688 |
\cos(C) = 1/\sec(C)
|
5,459 |
(-c + x)^2 = c^2 + x^2 - 2\cdot x\cdot c
|
8,729 |
\left(-1\right) + z^3 = ((-1) + z)\cdot (1 + z^2 + z)
|
-20,103 |
\frac{1}{21*\left(-1\right) + x*7}*63 = 7/7*\tfrac{9}{x + 3*(-1)}
|
37,907 |
350 = {7 \choose 3} {5 \choose 3}
|
5,609 |
(1 - 1/3)/6 = \frac19
|
-5,863 |
\dfrac{x \cdot 4}{(x + 7 \cdot (-1)) \cdot (x + 10 \cdot (-1))} = \frac{x \cdot 4}{70 + x^2 - x \cdot 17} \cdot 1
|
3,339 |
\operatorname{E}(E\cdot v) = E^2\cdot v = E\cdot v = E\cdot v
|
-12,131 |
\dfrac{9}{20} = \frac{t}{10 \cdot \pi} \cdot 10 \cdot \pi = t
|
42,392 |
\binom{6}{3} = \frac{1}{3! \cdot 3!} \cdot 6! = 20
|
-15,955 |
-\frac{9}{10} \times 9 + 6/10 = -75/10
|
18,970 |
37 \cdot \left(-1\right) + (10 + 1) \cdot 10/2 = 18
|
-2,541 |
6 \cdot 6^{1 / 2} = (4 + 5 + 3 \cdot (-1)) \cdot 6^{1 / 2}
|
10,539 |
b_j\cdot s_j = s_j\cdot b_j
|
27,745 |
1 + x^4 + 4\cdot x^3 + x \cdot x\cdot 6 + 4\cdot x = \left(x + 1\right)^4
|
10,315 |
\left(x\cdot b = x\cdot b/h = h \Rightarrow \frac{b}{h} = h/x\right) \Rightarrow b = h\cdot \frac1x\cdot h
|
24,872 |
3 = 4 \times x - \left(1 - x\right) \times 2\Longrightarrow x = 5/6
|
16,423 |
(z + 2 \cdot (-1)) \cdot (\bar{z} + 2) = z \cdot \bar{z} + 2 \cdot \left(z - \bar{z}\right) + 4 \cdot (-1) = |z|^2 + 4 \cdot (-1) + 4 \cdot i \cdot \Im{(z)}
|
463 |
\left(-1\right) + X^2 = \left((-1) + X\right)\cdot (X + 1)
|
13,779 |
Z^3 = Z\cdot x = x\cdot Z
|
12,637 |
5^n \cdot ((-1) + 6) + (-1) = 5 + 5^n \cdot 6 + 6 (-1) - 5^n
|
47,730 |
y[n+\frac{7}3]=\sin\left(\frac{6\pi}7\cdot(n+\frac{7}3)+1\right)=\sin\left(\frac{6\pi}7n+2\pi+1\right)=\sin\left(\frac{6\pi}7n+1\right)=y[n]
|
39,182 |
(YY^V)^V = (Y^V)^V Y^V = YY^V
|
-15,461 |
\dfrac{{r^{-2}}}{{r^{-12}n^{9}}} = \dfrac{{r^{-2}}}{{r^{-12}}} \cdot \dfrac{{1}}{{n^{9}}} = r^{{-2} - {(-12)}} \cdot n^{- {9}} = r^{10}n^{-9}
|
25,775 |
3/4 + \left(-2 \cdot x + (-1)\right) \cdot \left(-x/2 - \frac14\right) = x \cdot x + x + 1
|
9,232 |
(\sqrt{n})^3 = (n^{1/2})^3 = n^{\frac12 \cdot 3} = (n^3)^{1/2} = \sqrt{n^3}
|
32,864 |
\cosh{x} = d/dx \sinh{x}
|
21,439 |
E[(Y - E[Y])^2] = E[Y^2] - E[Y]^2
|
11,981 |
\sin\left(3\cdot x\right) = -\sin^3(x)\cdot 4 + 3\cdot \sin\left(x\right)
|
12,421 |
\pi r^2 \cdot \pi R \cdot 2 = \pi \cdot \pi Rr^2 \cdot 2
|
-25,264 |
\frac{\mathrm{d}}{\mathrm{d}z} z^m = m*z^{\left(-1\right) + m}
|
-22,210 |
2\cdot \left(-1\right) + t^2 - t = (t + 1)\cdot (2\cdot (-1) + t)
|
4,303 |
1/(3*2) = -1/3 + \dfrac{1}{2}
|
31,979 |
\frac{6}{36} = \frac{1}{6}
|
14,989 |
(x^2\cdot 2 + a a - x a\cdot 2) \left(2 x^2 + a^2 + 2 a x\right) = a^4 + 4 x^4
|
-29,020 |
z^m\cdot z^l = z^{l + m}
|
-11,738 |
\frac{9}{4} = (3/2)^2
|
-2,827 |
16^{1/2}*5^{1/2} + 25^{1/2}*5^{1/2} = 5^{1/2}*4 + 5^{1/2}*5
|
21,282 |
\dfrac36\cdot 4/7 = 2/7
|
31,346 |
z^2 x^2 = 1 + (x + z)^2 + 2(x + z) \Rightarrow (x + z + 1)^2 = x^2 z^2
|
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