id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
14,009 |
s*x + x*s*2 + s*3*x + \cdots + x*s*36 = 1 - x*s*0
|
13,600 |
\frac13 + \dfrac{2}{9} = \tfrac39 + 2/9 = \dfrac59
|
41,602 |
X^4 + 1 = X^4 - a * a = (X^2 + a) (X * X - a)
|
17,802 |
\left(1 + x\right)^2 = x \cdot x + 2\cdot x + 1
|
36,855 |
114 = 166 - 4\cdot (-1) + 33 + 23
|
11,190 |
\tfrac{1}{15}\cdot \left(2 + 3\right) = \frac{1}{15}\cdot 5
|
14,290 |
2\cdot \sin{r}\cdot \cos{r} = \sin{r\cdot 2}
|
14,540 |
\dfrac{b}{h} = \frac{1}{\frac{1}{b} \cdot h}
|
-11,531 |
i - 13 = i - 3 + 10*\left(-1\right)
|
16,552 |
(\cos(y) + i\sin\left(y\right))^n = e^{iny} = \cos\left(ny\right) + i\sin(ny)
|
4,442 |
12*y^3 + 8*y^2 - y + \left(-1\right) = (y + 1/2)*(12*y^2 + 2*y + 2*(-1)) = 2*(y - \frac{1}{2})*\left(6*y^2 + y + (-1)\right)
|
19,710 |
65 = 1 * 1 + 8 * 8
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7,678 |
\frac{1}{\frac{1}{\frac{1}{1/2 + 42} + 5} + 1} + 0 = \frac{427}{512}
|
-25,802 |
5*\dfrac13/7 = 5/21
|
-24,656 |
5/30 = \frac{5}{6*5}1
|
-20,847 |
\frac{x \cdot (-48)}{18 \cdot x} = -8/3 \cdot \frac{6}{x \cdot 6} \cdot x
|
1,821 |
-\frac13 + \frac12 = \tfrac16
|
14,588 |
(1 + k) \left(2 + k\right) ... \cdot 2 = (k + 2)!
|
15,151 |
(3 - \sqrt{2})^4 = \left(\left(3 - \sqrt{2}\right)^2\right)^2 = (11 - 6\cdot \sqrt{2}) \cdot (11 - 6\cdot \sqrt{2}) = 193 - 132\cdot \sqrt{2}
|
4,055 |
y_2 \cdot y_2 = y_1 \cdot y_1 \implies y_2 = y_1
|
5,811 |
\frac12\cdot (x \cdot x + x) = x + \dfrac12\cdot (x^2 - x)
|
-11,136 |
(y + 9(-1)) * (y + 9(-1)) + b = (y + 9\left(-1\right)) (y + 9(-1)) + b = y^2 - 18 y + 81 + b
|
14,451 |
1 + y - 2\cdot y \cdot y = (1 + 2\cdot y)\cdot (-y + 1)
|
13,679 |
v = (x^2\cdot 4 + 4)^{\frac{1}{2}} \Rightarrow x^2\cdot 4 + 4 = v \cdot v,(v^2 + 4\cdot (-1))/4 = x \cdot x
|
37,808 |
4! = (12 + 8(-1))!
|
38,390 |
(e^0)^{1 / 2} = e^0
|
5,015 |
84\times 9 = 84\times 10 + 84\times (-1) = 840 + 84\times (-1) = 800 + 44\times (-1) = 756
|
6,726 |
\left(2 \cdot k\right)^2 = 0 + 2 \cdot k \cdot k \cdot 2
|
21,594 |
x R y rightarrow y R x
|
-11,084 |
(z + 7\cdot (-1)) \cdot (z + 7\cdot (-1)) + f = (z + 7\cdot (-1))\cdot (z + 7\cdot (-1)) + f = z^2 - 14\cdot z + 49 + f
|
4,477 |
(g h/h)^2 = g h g h/h/h = g^2 h/h
|
-1,579 |
\pi*3/2 = \pi/6 + \pi \frac{1}{3} 4
|
18,040 |
\int_1^\infty \cos{t}/t\,\mathrm{d}t = \sum_{m=0}^\infty \int_{1 + m \cdot \pi}^{1 + (m + 1) \cdot \pi} \cos{t}/t\,\mathrm{d}t = \int_1^{\pi + 1} \cos{t} \cdot \sum_{m=0}^\infty \frac{(-1)^m}{t + m \cdot \pi}\,\mathrm{d}t
|
12,403 |
\frac{1}{10 \times 10} = 1/100
|
-20,153 |
-\dfrac{7}{2} \cdot \frac{t \cdot (-3)}{(-3) \cdot t} = \frac{21 \cdot t}{t \cdot (-6)}
|
39,303 |
260 = 4^4+4^1
|
27,276 |
6\cdot l + 9\cdot x = 2\cdot 3\cdot l + 3\cdot 3\cdot x = 3\cdot \left(2\cdot l + 3\cdot x\right)
|
25,701 |
r^2 + r\cdot 6 + 9 = \left(r + 3\right)^2
|
23,098 |
h\frac{d}{d + h} = \frac{1}{1/d + \frac{1}{h}}
|
18,412 |
\dfrac{1}{2}\cdot (1 - \sqrt{5}) = \frac12 - \sqrt{5}/2
|
29,110 |
\|x\| = 0 \Rightarrow 0 = x
|
-5,970 |
\frac{4}{y\cdot 5 + 40} = \frac{4}{5 (y + 8)}
|
34,591 |
E_x = E_x
|
3,571 |
1 + x^4 = 1 + 2\times x^2 + x^4 - 2\times x^2 = \left(1 + x^2\right)^2 - \left(\sqrt{2}\times x\right)^2
|
-30,831 |
\frac134 \pi \cdot 9 \cdot 9 \cdot 9 = 972 \pi
|
11,007 |
\left(|d| = 1 \Rightarrow d \in A\right) \Rightarrow |A\cdot d| = 1!
|
33,120 |
2x+5x = (2+5)x = 7x
|
29,966 |
20!/\left(3!\cdot 17!\right) = 1140
|
33,735 |
0 = q^2 + (-1) = (q + (-1))*\left(q + 1\right)
|
22,641 |
(h_2 + h_1 + b) \cdot (h_1^2 + b^2 + h_2^2 - h_1 \cdot b - h_1 \cdot h_2 - b \cdot h_2) = h_1 \cdot h_1 \cdot h_1 + b^3 + h_2^3 - h_2 \cdot b \cdot h_1 \cdot 3
|
-4,761 |
\frac{-z + 17 (-1)}{3 \left(-1\right) + z z - z\cdot 2} = \frac{4}{1 + z} - \tfrac{5}{3 (-1) + z}
|
14,971 |
2\cdot 2\cdot y + 4\cdot y = 8\cdot y
|
18,759 |
\frac{1}{2}20! = 18! \frac{19}{2}20
|
28,708 |
\frac{1}{n! + (1 + n)! + (n + 2)!} = \frac{1}{(n + 2)^2\cdot n!}
|
19,997 |
7 = 3^2 - 3 + 1 \cdot 1
|
-13,927 |
\frac{36}{2 + 7} = \frac1936 = \tfrac{36}{9} = 4
|
24,730 |
\sum_{k=1}^{1 + m} k^3 = \left(m + 1\right)^3 + \sum_{k=1}^m k^3
|
-10,509 |
-\frac{y \cdot 4}{12 \cdot \left(-1\right) + 12 \cdot y} \cdot 1 = 4/4 \cdot (-\frac{y}{3 \cdot y + 3 \cdot (-1)})
|
9,776 |
(x + y) \cdot (x + l \cdot y) = x^2 + l \cdot x \cdot y + x \cdot y + l \cdot y^2 \geq x^2 + (l + 1) \cdot x \cdot y
|
14,249 |
13\cdot \left(-1\right) + 7\cdot a = 71 \Rightarrow a = 12
|
-2,253 |
2/16 = 7/16 - \frac{1}{16}*5
|
31,169 |
-\sin{G} = \sin{-G}
|
-7,821 |
\frac{-3 + i*15}{-i*2 + 3}*\frac{1}{3 + 2*i}*(3 + 2*i) = \frac{1}{-2*i + 3}*(-3 + i*15)
|
-29,559 |
y^5 \cdot 6/y = 6 \cdot y^4
|
-3,321 |
208^{1/2} - 117^{1/2} = (16*13)^{1/2} - (9*13)^{1/2}
|
26,013 |
5 * 5 = \frac{1}{2}(7^2 + 1^2)
|
22,944 |
\left(-1\right) + x^l = ((-1) + x)\cdot (-e^{\frac{2}{l}\cdot \pi} + x)\cdot \cdots\cdot e^{\dfrac{2}{l}\cdot \pi\cdot \left(l + (-1)\right)}
|
-10,440 |
3/3 \cdot (-\dfrac{t}{t^3}) = -\frac{t \cdot 3}{3 \cdot t^3}
|
6,640 |
\tanh{x} = \sinh{x}/\cosh{x} = \frac{1}{e^x + e^{-x}} \cdot \left(e^x - e^{-x}\right)
|
10,383 |
\int_d^c j\,\mathrm{d}y = \int_d^c j\,\mathrm{d}y
|
17,191 |
\cos(x + z) = -\sin(x)*\sin(z) + \cos(z)*\cos(x)
|
19,144 |
\pi/3 = \frac{\pi}{\sin(\pi/6) \cdot 6}
|
15,841 |
\left|{X\cdot x\cdot x^T}\right| = \left|{X}\right|\cdot \left|{x\cdot x^T}\right| = \left|{X}\right|\cdot x\cdot x^T
|
33,921 |
6 * 6 * 6 + \left(y*5\right)^3 = 216 + 125 y^2 * y
|
-22,221 |
((-1) + t) (t + 6) = t^2 + t\cdot 5 + 6\left(-1\right)
|
21,737 |
x^3 - x^2\cdot 12 + x\cdot 36 + 32 (-1) = (x + 2(-1))^2 (8(-1) + x)
|
16,167 |
{n \choose k} = \frac{n!}{k! \cdot (n - k)!} = {n \choose n - k}
|
11,377 |
1/2 + \frac14*4 + 9/8 = 21/8
|
26,625 |
\sin{\theta \cdot 2}/2 = \cos{\theta} \cdot \sin{\theta}
|
22,706 |
1^2 \times \tfrac{1}{2^{\frac{1}{2}}} \times 2 = 2^{1 / 2}
|
16,331 |
(x + 4\cdot (-1))\cdot (x + 1) = 4\cdot (-1) + x^2 - 3\cdot x
|
-1,741 |
\pi*\frac{13}{6} = 19/12*\pi + 7/12*\pi
|
14,188 |
\frac{1}{3}(16 + 4\left(-1\right)) = 6 \lt 7
|
-9,318 |
-30t - 50 = - (2\cdot3\cdot5 \cdot t) - (2\cdot5\cdot5)
|
-9,429 |
-10 t^3 = -2*5 t t t
|
-3,060 |
\sqrt{11} + \sqrt{11}\cdot 2 = \sqrt{11}\cdot \sqrt{4} + \sqrt{11}
|
-26,706 |
\sum_{k=1}^\infty \dfrac{5^k}{k \cdot 5^k} = \sum_{k=1}^\infty 1/k
|
-5,969 |
\tfrac{3}{(s + 1) \cdot \left(6 + s\right)} = \frac{1}{6 + s \cdot s + s \cdot 7} \cdot 3
|
5,920 |
\cos\left(x + s\right) = \cos(s)*\cos\left(x\right) - \sin(x)*\sin\left(s\right)
|
11,795 |
z\cdot 3 = \frac{\mathrm{d}}{\mathrm{d}z} (z^2\cdot 3/2 + 1/2)
|
13,323 |
-\frac{D_{15}}{15!^2} \cdot 15! + 1 = -D_{15}/15! + 1
|
51,658 |
100040004 = 10002^2
|
-10,494 |
-\frac{3}{60\cdot q^2} = 3/3\cdot (-\frac{1}{20\cdot q^2})
|
14,474 |
r = \cos(\arccos{r})
|
-10,807 |
\dfrac19*189 = 21
|
10,281 |
a/g \cdot g = \frac{g}{g^2} \cdot g \cdot a
|
-23,014 |
\frac{1}{56}63 = \frac{7\cdot 9}{7\cdot 8}
|
16,241 |
{(-1) + n \choose k + \left(-1\right)} n/k = {n \choose k}
|
18,956 |
a \cdot a \cdot a - b^3 = \left(a \cdot a + b \cdot a + b^2\right) \cdot \left(a - b\right)
|
18,948 |
1 = (z_1 + z_2)^2 \leq 2(z_1 \cdot z_1 + z_2^2)
|
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