id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-6,736 |
\frac{9}{100} + 9/10 = \dfrac{9}{100} + \frac{90}{100}
|
5,579 |
m*4 + 2 = (1 + 2 m)*2
|
22,620 |
(-b + a) \times \left(a^{k + \left(-1\right)} + a^{k + 2 \times \left(-1\right)} \times b + a^{k + 3 \times (-1)} \times b \times b + \cdots + a \times a \times b^{3 \times \left(-1\right) + k} + b^{k + 2 \times \left(-1\right)} \times a + b^{(-1) + k}\right) = a^k - b^k
|
34,988 |
(2 \cdot 2 + 1^2)^{1 / 2} = 5^{\dfrac{1}{2}}
|
10,260 |
\tan^{-1}\left(1\right) = \frac14\pi
|
26,689 |
1 + \lambda * \lambda - \lambda*2 = (\lambda + (-1)) * (\lambda + (-1))
|
-1,452 |
-\frac{1}{4}*\dfrac{1}{8}3 = \left((-1)*1/4\right)/(8*1/3)
|
16,034 |
1111 = 1 + x + x^2 + x x^2 = x^{12}
|
-22,941 |
63/54 = \frac{9 \cdot 7}{6 \cdot 9}
|
34,896 |
24 = \left(-1\right) + \dfrac{100}{4}
|
18,933 |
\sin(3\cdot x) = \sin\left(2\cdot x + x\right) = \sin(2\cdot x)\cdot \cos(x) + \cos(2\cdot x)\cdot \sin(x)
|
35,035 |
|16 - x*2| = 5\Longrightarrow x = 5.5, 10.5
|
-509 |
-\pi*26 + \pi*\frac{323}{12} = \pi*11/12
|
-4,122 |
\dfrac78 \cdot \frac{m^3}{m^3} = \frac{7 \cdot m^3}{8 \cdot m^3}
|
29,354 |
c \gt -1 \Rightarrow c + 1 > 0
|
-18,347 |
\frac{1}{32 + k^2 + k \cdot 12} \cdot \left(k^2 + 4 \cdot k\right) = \frac{(k + 4) \cdot k}{(4 + k) \cdot (8 + k)}
|
16,079 |
(x + t)^1 = x + t = x^1 + t^1
|
-5,323 |
2.4\cdot 10^{3 - -2} = 10^5\cdot 2.4
|
8,704 |
\cos(x - y) = \sin{y}\cdot \sin{x} + \cos{y}\cdot \cos{x}
|
21,776 |
w' \cdot I + I \cdot w = I \cdot (w + w')
|
10,159 |
\frac{1}{5}*(5*y + 1) = 1/5 + y
|
3,212 |
x \cdot \Sigma \cdot x^R = x \cdot \Sigma \cdot x^R \cdot x \cdot \Sigma \cdot x^R = x \cdot \Sigma^2 \cdot x^R
|
7,718 |
\frac{x}{y} \cdot x \cdot y = \dfrac{x}{y} \cdot y \cdot x
|
50,003 |
15 = 5 + 0 + 1 + 2 + 3 + 4
|
24,051 |
M'_{ii}=M_{ii}
|
-24,496 |
1 + \frac166 = 1 + 1 = 1 + 1 = 2
|
29,249 |
2^n - 2^{2 \cdot (-1) + n} \cdot ((-1) + n) + 2^{4 \cdot (-1) + n} \cdot \left(2 \cdot \left(-1\right) + n\right) \cdot \left(n + 3 \cdot (-1)\right)/2! - ... = 1 + n
|
-25,765 |
\frac{d}{dp} (-\dfrac3p) = \frac{1}{p^2} \cdot 3
|
1,320 |
\dfrac{\sin(z)}{z} = \dfrac1z(z - z^3/6 + \cdots) = 1 - \frac{z^2}{6} + \cdots
|
39,041 |
7*12 + 13(-1) = 71
|
3,422 |
e^{-\int_W^T s*r\,\mathrm{d}s} = e^{-\int_W^T s*r\,\mathrm{d}s}
|
4,891 |
\frac{1}{\dfrac1a\times c} = a/c
|
16,407 |
\frac{1}{\cos^2\left(y\right)} = 1 + \tan^2(y)
|
30,361 |
\frac{1}{100}84*83/99 = 6972/9900 \approx 0.704
|
11,621 |
0 = x^4 + 6*x^2 + 25 = \left(x^2 + 5\right)^2 - 4*x * x = (x^2 - 2*x + 5)*(x^2 + 2*x + 5)
|
29,611 |
(-2\cdot 3 + 2) + \left(2\cdot (-1) + 3\right)\cdot 3 - 1\cdot (2\cdot (-1) + 1) = 0
|
12,565 |
x^{5/2} = \frac{1}{x^{\frac12}}\cdot x^3
|
-20,418 |
-\frac25\cdot \frac{9}{9} = -\frac{18}{45}
|
-10,414 |
\frac{1}{r*10 + 10 (-1)} 60 = \dfrac{10}{10}*\frac{1}{(-1) + r} 6
|
20,971 |
\frac{\mathrm{d}}{\mathrm{d}y} \cosh(y) = \sinh(y)
|
40,600 |
i^2 \cdot i = i^{2 + 1} = i^2\cdot i = -i = -i
|
5,020 |
|x| = (x \times x)^{\frac{1}{2}} \lt (x^2 + 1)^{\frac{1}{2}}
|
8,351 |
\left(b + a\right)/d = \frac{1}{d}b + \frac{1}{d}a
|
-24,591 |
4*4 4 = 4*16 = 64
|
21,809 |
\frac{\sin^2{z}}{1 + \sin^2{z}} = 1 - \frac{1}{1 + \sin^2{z}} = 1 - \tfrac{\sec^2{z}}{2 \cdot \tan^2{z} + 1}
|
-2,458 |
4 \cdot \sqrt{7} - \sqrt{7} \cdot 2 = -\sqrt{7} \cdot \sqrt{4} + \sqrt{16} \cdot \sqrt{7}
|
4,869 |
\cos{z} = \sin(-z + \frac{π}{2})
|
-12,157 |
\frac35 = \dfrac{t}{10 \cdot \pi} \cdot 10 \cdot \pi = t
|
16,904 |
7^{5 + 10 \cdot 427} = \left(7^{10}\right)^{427} \cdot 7^5
|
5,713 |
1 - y^2 + 1 = -y \cdot y + 2
|
-18,948 |
3/10 = A_s/(64\cdot \pi)\cdot 64\cdot \pi = A_s
|
-22,379 |
42 + x * x + 13*x = (x + 6)*(x + 7)
|
16,739 |
A\times A\times B = -A\times B\times A = B\times A\times A
|
1,854 |
|p| E_2 |x| E_1 = |p| |x| E_2 E_1
|
24,028 |
\sin^2{y/2} = \frac{1}{2} \cdot \left(1 - \cos{y}\right) = (1 - \sqrt{1 - \sin^2{y}})/2
|
9,000 |
\sqrt{y^2 - 5y + 4} = \sqrt{\left(y + (-1)\right) (y + 4(-1))} = \sqrt{y + (-1)} \sqrt{y + 4(-1)}
|
-6,352 |
\frac{3}{4\cdot r + 8\cdot \left(-1\right)} = \frac{3}{4\cdot (2\cdot \left(-1\right) + r)}
|
29,073 |
\lim_{x \to \infty} (1 - \frac{1}{x})^x = \lim_{x \to \infty} (\frac1x\cdot (x + (-1)))^x = \lim_{x \to \infty} (\frac{1}{x + (-1)}\cdot x)^{-x} = \lim_{x \to \infty} (1 + \frac{1}{x + (-1)})^{-x}
|
10,175 |
2 \cdot \left(a \cdot a + d^2\right) = (d + a)^2 + (-d + a)^2
|
47,886 |
\cos(A + G) + \cos\left(A - G\right) = 2*\cos{A}*\cos{G} = 2*\cos{\dfrac{1}{2}*(A + G + A - G)}*\cos{(A + G - A + G)/2}
|
32,407 |
-y + p \cdot p - y \cdot p = 0 \implies p = (y \pm \sqrt{y^2 + 4 \cdot y})/2
|
22,789 |
\frac{\mathrm{d}y}{\mathrm{d}z} \cdot \left(z + y^2\right) = 1\Longrightarrow \frac{\mathrm{d}z}{\mathrm{d}y} = z + y^2
|
-4,604 |
\frac{24\cdot (-1) + y\cdot 2}{y^2 - 3\cdot y + 10\cdot (-1)} = \frac{4}{y + 2} - \frac{2}{5\cdot \left(-1\right) + y}
|
-1,380 |
(1/7\cdot (-9))/(1/7\cdot (-9)) = -7/9\cdot (-9/7)
|
-23,220 |
5/9 = 1 - \tfrac19*4
|
55,290 |
2\implies 3
|
27,116 |
\left(h \cdot a + a^2 + h^2\right)/3 = ((a + h)/2) \cdot ((a + h)/2) + \left(h - a\right) \cdot \left(h - a\right)/12
|
-9,709 |
-\tfrac{1}{2} = -\dfrac24
|
18,282 |
\operatorname{E}(2 \operatorname{E}(r) r) = 2 \operatorname{E}(r) \operatorname{E}(r)
|
3,840 |
(\frac1a - x^2)/(\frac1a) = 1 - a*x * x
|
23,698 |
\tfrac{1}{6 \cdot 6 \cdot 6} \cdot {6 \choose 3} = 20/216 = 5/54
|
21,649 |
4*\tfrac{1}{5}/4 = \dfrac15
|
24,970 |
4^y = \left(2^2\right)^y = 2^{2y} = \left(2^y\right)^2
|
-18,964 |
3/5 = \frac{E_r}{4 \cdot \pi} \cdot 4 \cdot \pi = E_r
|
-22,206 |
g g - 12 g + 20 = (2 (-1) + g) (g + 10 (-1))
|
-5,463 |
\frac{2}{49 \cdot (-1) + k^2} = \frac{2}{\left(k + 7\right) \cdot (k + 7 \cdot (-1))}
|
-18,251 |
\frac{n^2 + n + 30 \cdot (-1)}{n \cdot 6 + n \cdot n} = \dfrac{1}{n \cdot \left(n + 6\right)} \cdot \left(6 + n\right) \cdot (5 \cdot \left(-1\right) + n)
|
8,816 |
a + b = a/b + \frac{b}{a} \lt a + b
|
18,355 |
2 \cdot 32 \cdot 4^4 + 8 \cdot 28 \cdot 4^4 = 73728
|
25,343 |
-8/2 + 3\cdot 3 = 9 + \dfrac12\cdot \left((-1)\cdot 8\right)
|
9,860 |
\frac12 \cdot (b \cdot b - d \cdot d) = \frac{1}{2} \cdot \left(b + d\right) \cdot (b - d)
|
30,007 |
5*\dfrac{1}{5}*18/2 = 9
|
7,636 |
(1 + l)^2 = 1 + 3 + 5 + \ldots + 2\cdot l + 1
|
7,039 |
\cos(-a + \pi/2) = \sin{a}
|
-3,061 |
\sqrt{7} \cdot 5 = \sqrt{7} \cdot (3 + 2)
|
32,038 |
1820 = {4 \choose 1} \cdot {(-1) + 12 + 4 \choose 12}
|
1,304 |
d^n\times d^m = d^{m + n}
|
12,113 |
3 \lt (1 + z^2 - 3*z)*z \implies 0 < z^3 - z^2*3 + z + 3*(-1)
|
-3,022 |
\left(2\cdot (-1) + 4\right)\cdot \sqrt{10} = \sqrt{10}\cdot 2
|
6,478 |
\{F\cdot S\cdot x,Q\cdot S\cdot F\} \Rightarrow S\cdot F\cdot Q = S\cdot F\cdot x
|
21,732 |
\dfrac16 = 1/3 - \dfrac{1}{6}
|
-7,979 |
(-54 + 12 \times i + 90 \times i + 20)/34 = \left(-34 + 102 \times i\right)/34 = -1 + 3 \times i
|
33,093 |
\frac{1}{Y \cdot X} = \tfrac{1}{X \cdot Y}
|
-18,353 |
\dfrac{6 \cdot n + n^2}{30 \cdot (-1) + n^2 + n} = \frac{(n + 6) \cdot n}{(n + 5 \cdot \left(-1\right)) \cdot (n + 6)}
|
11,041 |
\frac{g}{b^x\cdot h} = g\cdot b^{-x}/h
|
-1,080 |
1/(6\cdot (-5/9)) = (\dfrac{1}{5}\cdot (-9))/6
|
22,847 |
g_2 \cdot g_1 \cdot g_2 = g_2 \cdot g_1 \cdot g_2 = g_2 \cdot g_1 \cdot g_2
|
5,946 |
\sqrt{a \cdot a - 16 \cdot a + 48} = \sqrt{(a + 6 \cdot (-1))^2 + 12} \gt \sqrt{(a + 6 \cdot (-1))^2} = |a + 6 \cdot (-1)| = 6 - a
|
-4,883 |
10^{5*\left(-1\right) + 11}*0.49 = 10^6*0.49
|
16,915 |
\cos((-x + \pi)/2) = \sin(x/2)
|
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