id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
44,984 |
10001 = 73*137
|
-18,253 |
\frac{x\cdot (x + 7\cdot (-1))}{(7\cdot \left(-1\right) + x)\cdot (x + 2\cdot (-1))} = \dfrac{1}{14 + x^2 - x\cdot 9}\cdot (x^2 - 7\cdot x)
|
523 |
\cos{2*t} = 1 - \sin^2{t}*2
|
5,496 |
256 * 256^2 = 255^3 + 9^3 + 58^3
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39,201 |
(3\cdot \sqrt{3} + 5\cdot (-1))/2 = -5/2 + \sqrt{3}\cdot 3/2
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15,084 |
\frac1f*(g + h) = \frac{g}{f} + h/f
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12,929 |
\arccos(\frac{(-1) + z^2}{1 + z \cdot z}) = q \cdot 2 \Rightarrow \cos(2 \cdot q) = \dfrac{z^2 + (-1)}{1 + z \cdot z}
|
5,883 |
r\cdot (x_1 + x_2) = r\cdot x_1 + r\cdot x_2
|
27,029 |
6^2 + 6*36 + 36^2 = 36*(1^2 + 6 + 6 * 6) = 36*43
|
2,368 |
\left(-1\right) + 2\cdot x = 2\cdot \left(-\frac12 + x\right)
|
22,920 |
F \cdot F^x = F^x \cdot F
|
-11,517 |
-20 i + 10 + 10 \left(-1\right) = -20 i
|
25,665 |
-7 * 7 + 1^2 - 3^2 + 5 * 5 = -2*4^2
|
12,792 |
-(-z' + x')^2 + \left(z' + x'\right)^2 = z'\cdot x'\cdot 4
|
-19,467 |
\frac{\dfrac12*3}{8*1/3} = \tfrac18*3*3/2
|
-4,902 |
10^{2 \cdot (-1) + 3} \cdot 0.18 = 0.18 \cdot 10^1
|
21,556 |
\frac12 + \frac14 \cdot (l + (-1)) = \frac{1}{4} \cdot (1 + l)
|
20,997 |
5 = \sqrt{9 + p} \Rightarrow 25 + 9 \cdot \left(-1\right) = p
|
39,804 |
|55 + 50 \times (-1)| = 5
|
-5,902 |
\frac{1}{q^2 + 4\cdot q + 32\cdot (-1)}\cdot 4 = \frac{1}{(8 + q)\cdot (q + 4\cdot (-1))}\cdot 4
|
-11,641 |
-4 + 6 \cdot (-1) + 10 \cdot i = 10 \cdot i - 10
|
31,034 |
2^3 - \dfrac42 = 6
|
11,503 |
5 - 5 \times p^2 - 24 \times p = -(5 \times p^2 + 24 \times p + 5 \times (-1)) = -(p + 5) \times (5 \times p + \left(-1\right))
|
-14,110 |
5 + \dfrac{28}{7} = 5 + 4 = 9
|
-16,340 |
6\sqrt{80} = 6\sqrt{16 \cdot 5}
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24,502 |
l^2 - k^2 = \left(l - k\right)*\left(l + k\right)
|
18,955 |
(\frac35)^3 + \dfrac{1}{5} 2 (\frac{3}{5})^2 \cdot 3 = 81/125
|
14,370 |
n^2*2 = n*2 + k*4 \implies n^2*2 = (n + 2*k)*2
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-20,423 |
\frac{y + 5}{y + 5}\cdot (-\frac{1}{5}\cdot 2) = \frac{-2\cdot y + 10\cdot (-1)}{5\cdot y + 25}
|
21,735 |
h\cdot a^{1 + i} = h\cdot a^{i + 1}
|
37,964 |
\frac{1}{2}*24 = 12
|
-3,985 |
16/32 \cdot \frac{m^3}{m^5} = \frac{16 \cdot m^3}{m^5 \cdot 32}
|
14,718 |
0 > 144 - 12\cdot a \Rightarrow a > 12
|
10,404 |
\frac12\cdot (3 + \sqrt{5}) = ((1 + \sqrt{5})/2)^2
|
30,606 |
y^2 + y + 8 = y^2 - 9 \cdot y + 8 = \left(y + (-1)\right) \cdot (y + 8 \cdot (-1)) = (y + 9) \cdot (y + 2)
|
8,659 |
v = h + x\Longrightarrow v - h = x
|
-5,252 |
\frac{1}{1000} \cdot 0.3 = 0.3/1000
|
33,168 |
\frac{1}{-z + 1} = 1 + z + z^2 + z * z^2 + \cdots
|
5,076 |
(1 - z)^{n + 3\cdot (-1)} = \left(-1\right)^{n + 3\cdot (-1)}\cdot (z + (-1))^{n + 3\cdot (-1)} = \left(-1\right)^{n + \left(-1\right)}\cdot (z + (-1))^{n + 3\cdot (-1)}
|
15,999 |
(y^2 - \sqrt{3} \cdot y + 1) \cdot (1 + y^2 + y \cdot \sqrt{3}) = y^4 - y^2 + 1
|
6,520 |
5/83 = \frac{\binom{13}{4}}{39\cdot \binom{13}{3} + \binom{13}{4}}
|
405 |
\left(1 + t^2\right) * \left(1 + t^2\right) - 2*t^2 = t^4 + 1
|
18,893 |
2\sin{\frac{1}{2}(M + y)} \cos{\left(M + y\right)/2} = \sin(M + y)
|
18,807 |
y*G*c/(c*y) = c*y*G/\left(c*y\right)
|
-22,047 |
\dfrac{35}{10} = \tfrac72
|
-11,482 |
-15 + 2 + 13 \cdot i = -13 + 13 \cdot i
|
10,001 |
-3\cdot (y + 2\cdot (-1))^2 = -3\cdot (2\cdot (-1) + y)\cdot (2\cdot (-1) + y)
|
14,892 |
0 = -((-1) + x) + (2 + x) \cdot (x + (-1)) \Rightarrow \left(x + 1\right) \cdot (x + (-1)) = 0
|
1,059 |
\frac1p = \frac{-\dfrac1p + 1}{(-1) + p}
|
29,046 |
\frac{0.054}{0.3 \cdot 0.6} \cdot 1 = 0.3
|
19,568 |
\left(3 + x = x^2 \Leftrightarrow 3\cdot (-1) + x^2 - x = 0\right)\Longrightarrow x = \frac{1}{2}\cdot \left(1 ± \sqrt{13}\right)
|
2,655 |
x^4 + a^4 = -x^3 a \cdot 4 + (a + x)^4 - 4 x a^3 - 6 x^2 a^2
|
24,633 |
4^n*4^n = 4^{2n} = 16^n
|
12,606 |
p = \frac{q}{q}\cdot p = q\cdot p\cdot q^2\cdot p\cdot q\cdot p
|
-3,823 |
\frac{r^4 \cdot 40}{70 \cdot r^3} = \frac{r^4}{r \cdot r \cdot r} \cdot 40/70
|
31,582 |
\cos(A + A) = \cos(A)*\cos\left(A\right) - \sin\left(A\right)*\sin\left(A\right) = \cos^2(A) - \sin^2(A)
|
-2,766 |
7^{\dfrac{1}{2}}*9^{1 / 2} + 7^{\dfrac{1}{2}} = 7^{1 / 2}*3 + 7^{\frac{1}{2}}
|
-10,599 |
\frac{1}{9 \cdot \left(-1\right) + 3 \cdot q} \cdot 3 = \frac{3 \cdot 1/3}{3 \cdot \left(-1\right) + q}
|
-18,538 |
42/30 = \dfrac{1}{5}7
|
13,959 |
\sin{z} = z \cdot (1 - \frac{1}{3!} \cdot z^2 + z^4/5! - ...)
|
-22,995 |
\tfrac{70}{98} = \tfrac{5 \cdot 14}{14 \cdot 7}
|
35,829 |
\cos^2(x) = \dfrac12*(1 + \cos(2*x))
|
5,074 |
\left(1 = x\cdot z\cdot \frac{1}{z}/x \Rightarrow z\cdot x/z = x\right) \Rightarrow x\cdot z = z\cdot x
|
-603 |
e^{11*\frac12*\pi*i} = (e^{\dfrac12*i*\pi})^{11}
|
8,322 |
T^p T^q = T^p T^q
|
1,768 |
[h, e] = \left[c, d\right] \implies h = e,d = c
|
-10,412 |
-\tfrac{1}{k\cdot 4}(k + 6) \frac155 = -\left(30 + 5k\right)/(20 k)
|
34,313 |
x + 2 = 0 \Rightarrow x = -2
|
7,871 |
\frac{1}{36} = 1/4 - \dfrac{2}{9}
|
-28,872 |
(-6^0 + 6^1) \cdot 6^x = 6^x \cdot 5
|
21,001 |
x^4 = (1 - x)^2 = x^2 - 2 \times x + 1 = 1 - x - 2 \times x + 1 = 2 - 3 \times x
|
12,733 |
900 = 360*(-1) + 1260
|
-17,226 |
-44/5 = -\frac1544
|
-1,719 |
0 - \pi*7/6 = -\pi*7/6
|
15,558 |
2 \cdot (a - g) = g^3 - a \cdot a \cdot a = (g - a) \cdot (g^2 + a \cdot g + a \cdot a)
|
5,430 |
b \cdot X \cdot x rightarrow b \cdot X \cdot x
|
-20,041 |
\frac{-t\cdot 27 + 18\cdot (-1)}{t\cdot 15 + 10} = \frac{2 + t\cdot 3}{2 + 3\cdot t}\cdot \left(-9/5\right)
|
-17,369 |
\frac{1}{100} \cdot 17.1 = 0.171
|
15,926 |
-(y + (-1)) (y + 3) = 3 - y^2 - y\cdot 2
|
-6,018 |
\dfrac{1}{l*5 + 50} 2 = \dfrac{1}{(10 + l)*5} 2
|
-10,316 |
2/2*(-\frac{4}{3*n + 3}) = -\frac{8}{6*n + 6}
|
-20,087 |
\frac{1}{4 + o \cdot 3} \cdot (o + 5 \cdot \left(-1\right)) \cdot 7/7 = \frac{1}{28 + o \cdot 21} \cdot (35 \cdot (-1) + o \cdot 7)
|
2,112 |
0 = (a - d) \cdot (a - d) + 3 \cdot c^2 \Rightarrow a = d, c = 0
|
-2,271 |
\tfrac{1}{3} 2 = 8/12
|
29,389 |
\cos{\pi/12} = \cos(\dfrac{1}{3} \cdot \pi - \pi/4) = \cos{\frac{\pi}{3}} \cdot \cos{\frac{\pi}{4}} + \sin{\pi/3} \cdot \sin{\frac14 \cdot \pi} = \frac12 \cdot 1/(\sqrt{2}) + \dfrac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{2}} = \frac{1 + \sqrt{3}}{2 \cdot \sqrt{2}}
|
2,271 |
x\cdot c/c\cdot c = c\cdot x
|
10,039 |
(l + 1)! = l!*(l + 1) \Rightarrow (1 + l)! - l! = l*l!
|
10,903 |
x = a,w = d \implies a\cdot w = d\cdot x
|
23,542 |
(r + 1)^3 - r^3 = 1 + r^2*3 + r*3
|
17,906 |
U\cdot B = B\cdot U
|
-24,892 |
2/15 = q/(12 \pi) \cdot 12 \pi = q
|
4,337 |
5^{3*m} + 2*5^{2*m} - 5^m + 2*(-1) = (5^m + 2)*(5^{2*m} + (-1)) = (5^m + 2)*\left(5^m + (-1)\right)*(5^m + 1)
|
25,238 |
\tan(x + \frac{1}{4}\times \pi) = \cot(-x + \dfrac{1}{4}\times \pi)
|
-18,368 |
\frac{(r + (-1))\cdot r}{(9\cdot (-1) + r)\cdot ((-1) + r)} = \tfrac{-r + r \cdot r}{r^2 - r\cdot 10 + 9}
|
42,703 |
2^7 = 2^4*(1 + {7 \choose 1})
|
-9,125 |
z \cdot z\cdot 54 = z\cdot 2\cdot 3\cdot 3\cdot 3 z
|
27,319 |
q - t + s = -s + q - t
|
24,279 |
\left(a^3\right)^n + n = (a^3)^n + n^3 - n^3 + n = (a^n + n)*((a^2)^n - n*a^n + n^2) - n^3 + n
|
-15,150 |
\frac{1}{x \cdot (a^4 \cdot x \cdot x)^5} = \frac{1}{a^{20} \cdot x^{10} \cdot x}
|
-18,364 |
\frac{x \cdot \left(8 \cdot \left(-1\right) + x\right)}{\left(x + 8 \cdot (-1)\right) \cdot \left(x + 5\right)} = \frac{-8 \cdot x + x \cdot x}{x^2 - 3 \cdot x + 40 \cdot (-1)}
|
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