id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-20,044 |
\tfrac{l + 10}{10 + l\cdot 3}\cdot \frac{8}{8} = \frac{l\cdot 8 + 80}{24\cdot l + 80}
|
22,725 |
(2*m + 1) * (2*m + 1) = 4*m * m + 4*m + 1 = 4*(m^2 + m) + 1
|
4,052 |
\sin(\frac{\pi}{4} + y) = \cos(\frac{\pi}{4}) \cdot \sin\left(y\right) + \cos(y) \cdot \sin(\frac{\pi}{4})
|
7,328 |
\frac{1}{1 - y^2} = 1 + y^2 + y^4 + y^6*...
|
-22,295 |
q^2 - 6q + 5 = (q + 5(-1)) (q + (-1))
|
23,039 |
2\cdot \left(-1\right) + (1/z + z)^2 = \frac{1}{z^2} + z^2
|
2,221 |
(s + t + x)^2 = s^2 + t^2 + x^2 + 2\cdot s\cdot t + 2\cdot x\cdot s + x\cdot t\cdot 2
|
27,167 |
1 = 1.0 = ... = 1*...
|
3,002 |
-(5^{1 / 2} \cdot 2 - 11^{1 / 2}) + 5^{1 / 2} \cdot 2 + 11^{1 / 2} = 2 \cdot 11^{1 / 2}
|
35,002 |
-l^2 + i^2 = 0 \Rightarrow i^2 = l^2
|
14,915 |
\cos\left(2 \cdot y\right) = \cos^2(y) - \sin^2\left(y\right) = 1 - 2 \cdot \sin^2(y)
|
-30,887 |
\frac{1}{8}*48 = 6
|
-20,103 |
\frac{9}{3(-1) + x} \dfrac77 = \frac{63}{21 \left(-1\right) + 7x}
|
3,182 |
3 + 2\cdot (3\cdot n + (-1) + 2\cdot n^2 - n) = 4\cdot n \cdot n + 4\cdot n + 1 = (2\cdot n + 1)^2
|
4,966 |
1 - \dfrac{1}{y_{1 + j} + (-1)} = \frac{1}{(-1) + y_{1 + j}}\times (y_{1 + j} + 2\times (-1))
|
16,638 |
r*x*8 = x*r*8
|
23,490 |
d*y = g \implies y = g/d
|
25,812 |
2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7 = 2016
|
3,570 |
3^{2\cdot (-1) + k}\cdot \left(9 + \left(-1\right)\right) = -3^{k + 2\cdot (-1)} + 3^k
|
25,970 |
z^{2 \times 2}\times z^{2^6}\times z^{2^8}\times z^{2^9}\times z^{2^{10}}\times z^{2^7}\times z^{2^4}\times z^{2^3} = z^{2012}
|
23,853 |
\binom{3}{2}\cdot 2^{3 + 2\cdot (-1)} = 3\cdot 2 = 6
|
200 |
(n + 1)^2 - n \times n = n \times 2 + 1
|
25,471 |
\dfrac{0.96}{0.01 + 0.96} = 96/97
|
-1,624 |
-5/4\cdot \pi = 0 - 5/4\cdot \pi
|
14,180 |
\alpha = \alpha^{p^d} \Rightarrow (\alpha^{p^{d + (-1)}})^p = \alpha
|
28,698 |
\frac{2*\pi}{3} = 2/3*\pi
|
31,853 |
9 = 6 \cdot (-1) + 3 \cdot 5
|
-20,422 |
\frac{1}{2 + x\cdot 5}\cdot \left(10\cdot x + 2\cdot (-1)\right)\cdot \frac77 = \dfrac{14\cdot (-1) + 70\cdot x}{14 + x\cdot 35}
|
12,487 |
4\tan^{-1}(∞) = \pi\cdot 2
|
5,204 |
(n + 1)^2 = 1 + 3 + ... + 2n + 1
|
7,381 |
z^2 + z = z \cdot z + 2\cdot z - z = z \cdot z - z + 2\cdot z = z^2 - z + 2\cdot z
|
45,540 |
(b/3 + \frac{2}{3} \cdot x)^0 \cdot (-x + b) \cdot \dfrac34 + b^0 \cdot (b - x)/4 = b - x
|
-23,811 |
(2 + 5)^2 = 7^2 = 7 \cdot 7 = 49
|
26,226 |
1 + 2 + \cdots + 9 = \frac12\cdot 90 = 45
|
37,303 |
1 + 1 + 5 + 5 = 12
|
18,669 |
(y + 3\cdot (-1))\cdot (y + 5) - (y + 4)\cdot (y + 5\cdot (-1)) = y^2 + 2\cdot y + 15\cdot \left(-1\right) - y^2 - y + 20\cdot (-1) = 3\cdot y + 5
|
-1,920 |
7/12 \cdot \pi + \pi \cdot 13/12 = 5/3 \cdot \pi
|
-20,032 |
\frac{50 \cdot (-1) + t \cdot 100}{70 \cdot t + 35 \cdot \left(-1\right)} = \frac{10}{7} \cdot \frac{1}{5 \cdot (-1) + 10 \cdot t} \cdot (10 \cdot t + 5 \cdot (-1))
|
1,707 |
x = \tan(G) \Rightarrow G = \operatorname{atan}\left(x\right)
|
11,017 |
B*X*2 = B*X + X*B
|
18,034 |
3^{1/2} = \cot{\frac{1}{6}\cdot \pi}
|
32,881 |
\frac{1}{0.25 + 1} = 1 - 0.2
|
31,508 |
2 + m + (-1) = m + 1
|
10,236 |
x\cdot e\cdot z = x\cdot z = x\cdot e\cdot z
|
-26,367 |
\left(-1\right)*(-1) = 1
|
586 |
4^2+28^2+46^2=4*27^2
|
-2,900 |
(3 \cdot (-1) + 5) \cdot 13^{1/2} = 13^{1/2} \cdot 2
|
11,154 |
\left(8 \cdot (-1) + 7\right)^2 + (8 + 10 \cdot (-1)) \cdot (8 + 10 \cdot (-1)) = 5
|
40,925 |
5 \times 20 = 100
|
-26,368 |
(-1)\cdot (-1)\cdot \left(-1\right) = -1
|
3,454 |
-\frac{1}{2^k} + 1 = 1/2 + 1/4 + \dotsm + \frac{1}{2^k}
|
7,818 |
f*d + f*h = f*\left(d + h\right)
|
-15,782 |
10/10 - 7\cdot \frac{1}{10}\cdot 9 = -\frac{53}{10}
|
507 |
eh + xh = \left(e + x\right) h
|
-1,614 |
23/12\cdot \pi - 19/12\cdot \pi = \frac{\pi}{3}
|
-27,513 |
x^2\cdot 21 = 3\cdot 7xx
|
14,492 |
e_2 + e_3 + \cdots + e_x + e_{x + 1} = e_2 + e_3 + \cdots + e_x + e_{x + 1}
|
-19,058 |
3/4 = A_Y/\left(49*\pi\right)*49*\pi = A_Y
|
33,520 |
10 \cdot \frac{1}{12345} \cdot 54321 = 5 \cdot 9 + (-1) + 5 \cdot 6/12345 \approx 44
|
-26,148 |
-4\cdot 25^{\frac123} - -4\cdot 0^{\frac123} = -500 + 0 = -500
|
19,016 |
\sin\left(z*2\right) = 2*\cos(z)*\sin(z)
|
-26,153 |
[4\cdot4-24\cdot4^{-1}]-[4\cdot3-24\cdot3^{-1}] = 10-4 = 6
|
29,804 |
\frac{z^2}{(-1) + z^2} = \frac{z^2}{2}*(\frac{1}{(-1) + z} - \dfrac{1}{1 + z})
|
8,998 |
\frac{1}{y + 2} = \tfrac{1/2}{1 + \dfrac{y}{2}}
|
-3,825 |
7/9*x * x = 7*x^2/9
|
31,137 |
1 - 125/216 = \frac{1}{216}\cdot 91
|
24,503 |
2 = (6 + 34^{1/2})\cdot (-34^{1/2} + 6)
|
32,786 |
(-1)*4.5 + 110 + 18*(-1) + 4*(-1) - 3.5 + 9*(-1) + 2*(-1) = 69
|
55,133 |
\sqrt{t^2 + d \cdot d} - t \approx \sqrt{t^2 + d \cdot d + \frac{1}{4 \cdot t^2} \cdot d^4} - t = \sqrt{(t^2 + \dfrac{d^2}{2 \cdot t})^2} - t = \frac{1}{2 \cdot t} \cdot d^2
|
399 |
1/n - \frac{1}{1 + n} = \frac{1}{n \cdot n + n}
|
26,615 |
e*c*b = c*e*b
|
-20,026 |
\frac{56 \times \left(-1\right) + 56 \times r}{48 \times (-1) + r \times 48} = \frac{8 \times \left(-1\right) + 8 \times r}{8 \times (-1) + 8 \times r} \times \dfrac{7}{6}
|
9,715 |
-2\times y^2 + 12 \geq 16 + y^2 - y\times 8 \implies 3\times y \times y - y\times 8 + 4 \leq 0
|
31,124 |
\frac{1}{2} \cdot \left(n + (-1)\right)! = \frac{n!}{n \cdot 2}
|
-22,091 |
\frac{20}{36} = \frac59
|
-2,536 |
125^{1 / 2} - 45^{1 / 2} + 80^{1 / 2} = (16 \cdot 5)^{\dfrac{1}{2}} + (25 \cdot 5)^{1 / 2} - \left(9 \cdot 5\right)^{\dfrac{1}{2}}
|
20,549 |
250^2*250^{y*3 + (-1)} = 250^{y*3 + 1}
|
47,308 |
\sum_{n=0}^\infty(-1)^n\frac{4^{n-2}(x-2)}{(n-2)!} = (x-2) \sum_{n=0}^\infty\frac{(-4)^{n-2}}{(n-2)!} = (x-2) \left(\sum_{n=0}^\infty\frac{(-4)^{n}}{n!} \right)
|
6,417 |
\sin(\alpha) \cdot \cos(\beta) + \sin(\beta) \cdot \cos(\alpha) = \sin\left(\beta + \alpha\right)
|
21,350 |
\sin(x \cdot 2) = \sin(x + x)
|
4,222 |
9 a^4 = x^2 \implies 900 a^4 = x^2\cdot 100
|
24,196 |
y^2 + (-1) = (y + 1)*\left(y + (-1)\right)
|
6,759 |
\frac{1}{z + B}z = 1 - \dfrac{B}{B + z}
|
33,312 |
\dfrac{76!}{76! - 75!} = \frac{76 \cdot 75!}{75! \cdot (76 + (-1))} \cdot 1 = \frac{1}{75} \cdot 76
|
1,768 |
[g,d] = \left[f, e\right] \Rightarrow f = e,g = d
|
23,349 |
\binom{24}{8} \binom{16}{8} = \frac{24!}{8!^3} = 9465511770
|
33,777 |
2*\frac{1}{3}*2*2 = 8/3
|
-18,388 |
\dfrac{p\cdot \left(3 + p\right)}{\left(3 + p\right)\cdot \left(3\cdot (-1) + p\right)} = \frac{1}{9\cdot (-1) + p^2}\cdot (p\cdot 3 + p^2)
|
7,376 |
1 - \tfrac{1}{m + 1} + \frac{1}{(m + 2)*(1 + m)} = 1 - \dfrac{1}{2 + m}
|
29,749 |
Y'\cdot Z + x\cdot Y' + X\cdot Z = X\cdot Y'\cdot Z + x\cdot Y'\cdot Z + x\cdot Y' + X\cdot Z = x\cdot Y' + X\cdot Z
|
20,120 |
v*(-\lambda) = -v\lambda
|
-3,396 |
2\cdot 3^{1 / 2} + 3^{1 / 2}\cdot 5 = 25^{1 / 2}\cdot 3^{1 / 2} + 4^{1 / 2}\cdot 3^{1 / 2}
|
-7,532 |
(6 - i \times 12)/3 = 6/3 - 12 \times i/3
|
2,587 |
|h\cdot g| = |h|\cdot |g| \leq |h|\cdot \|g\|_\infty
|
-28,797 |
24 = 2\pi/\left(\pi*2*\frac{1}{24}\right)
|
-9,399 |
24 \cdot q + 18 = q \cdot 2 \cdot 2 \cdot 2 \cdot 3 + 2 \cdot 3 \cdot 3
|
5,326 |
\frac{\partial}{\partial x} (v \cdot w) = v \cdot \frac{\mathrm{d}w}{\mathrm{d}x} + w \cdot \frac{\mathrm{d}v}{\mathrm{d}x}
|
-6,493 |
\dfrac{3}{z - 2} \times \dfrac{5(z + 5)}{5(z + 5)} = \dfrac{15(z + 5)}{5(z + 5)(z - 2)}
|
-22,794 |
\frac{1}{40}60 = 20*3/(2*20)
|
16,097 |
w \cdot v^U \cdot z = z \cdot v^U \cdot w
|
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