id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
15,344
|
-\sqrt{26} + x \leq 0 \Rightarrow x \leq \sqrt{26}
|
-27,335
|
\frac32 (1 + \sin{x}) = \frac{\cos^2{x}}{2 - 2 \sin{x}} 3
|
30,231
|
128/6 \cdot (45340.8 + 184680 + 484269.6) = 15238195.2
|
11,569
|
a\cdot x = 1/(1/a\cdot \frac1x) = \frac{1}{1/x\cdot \frac1a} = x\cdot a
|
-20,501
|
\dfrac{72 (-1) + x\cdot 8}{3x + 27 (-1)} = \frac{x + 9(-1)}{9\left(-1\right) + x}\cdot 8/3
|
10,993
|
0.9996 \cdot 0.972 \cdot 0.96 \cdot 0.96 \cdot 0.95 \cdot 2.86 \cdot 10^{18} = 20!
|
35,069
|
\frac{\frac12\cdot \frac12}{2} = 1/8
|
-10,411
|
\dfrac{4r - 10}{2r - 2} \times \dfrac{5}{5} = \dfrac{20r - 50}{10r - 10}
|
36,717
|
C_i = C_i^1
|
8,751
|
G^2 x = 0 \Rightarrow Gx = 0
|
-18,935
|
\dfrac{1}{36} \cdot 31 = \frac{A_s}{81 \cdot \pi} \cdot 81 \cdot \pi = A_s
|
23,306
|
0.02\cdot x = k\cdot 0.05 \implies \frac{x}{k} = 5/2
|
-11,580
|
-8 - 6 \cdot i = -9 + 1 - i \cdot 6
|
32,788
|
\pi\cdot 3/4 = \pi - \frac{1}{4}\pi
|
7,706
|
D^2\cdot E^2 = (D\cdot E)^2
|
-18,390
|
\frac{k*(5 + k)}{(6 + k) (k + 5)} = \dfrac{k*5 + k^2}{30 + k^2 + k*11}
|
9,820
|
x * x + \frac{1}{x^2} = (x + \tfrac1x) * (x + \tfrac1x) + 2*\left(-1\right)
|
-20,959
|
-\dfrac12\cdot 2/2 = -2/4
|
-4,400
|
\frac{x^2}{x^4} = \dfrac{x \cdot x}{x \cdot x \cdot x \cdot x} = \dfrac{1}{x^2}
|
15,499
|
(-1) + x^l = (x + (-1))*(x^{(-1) + l} + x^{l + 2*(-1)} + ... + x + 1)
|
-10,399
|
10 = -5*c + 9*(-1) + 5*\left(-1\right) = -5*c + 14*\left(-1\right)
|
-2,701
|
\sqrt{16} \times \sqrt{3} - \sqrt{3} \times \sqrt{9} = -3 \times \sqrt{3} + \sqrt{3} \times 4
|
4,294
|
2 i = -m + m^2 \implies m m = m + 2 i
|
19,083
|
\dfrac42\cdot 1/9 = \frac19\cdot 2
|
14,779
|
16*\left(-1\right) + x^8 = (x * x + 2*\left(-1\right))*(x^2 + 2)*(x^4 + 4)
|
26,217
|
\frac{800}{10}\cdot \frac{800}{1} = 80\cdot 800
|
21,944
|
(1 + 2^{33})\cdot (2^{33} + (-1)) = \left(-1\right) + 2^{66}
|
6,465
|
\left(71700 + 71000*\left(-1\right) - 717 + 71*(-1)\right)/(99*999) = \left(700 + 717*(-1) + 71\right)/(99*999) \gt 0
|
12,516
|
-\dfrac{1}{2\cdot (1 - \dfrac{x}{2})} = \tfrac{1}{2\cdot (-1) + x}
|
20,629
|
3^2 = 11 + 2*(-1)
|
27,805
|
(x^{22})^{N/2} \cdot B \cdot B \cdot 2 \cdot 3 \cdot \dots \cdot N/2 = B^2 \cdot (x^{22})^{N/2} \cdot (\frac{N}{2})!
|
24,856
|
\frac{12}{\sqrt{2}} \cdot \frac{2}{\sqrt{3}} = \frac{12}{\sqrt{2}} \cdot \tfrac{\sqrt{2}}{\sqrt{3}} \cdot \sqrt{2} = 12 \cdot \frac{\sqrt{2}}{\sqrt{3}} = 12 \cdot \frac{\sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} \cdot \sqrt{2} = 12 \cdot \sqrt{6}/3 = \ldots \cdot \ldots
|
24,801
|
b*Q^4 = 4*Q^2 * Q*b*Q + \frac{12*Q^2*b*x}{2} = 4*Q^3*b*Q + 6*Q^2*b*x
|
20,642
|
\cos(A + B) = -\sin(B) \sin\left(A\right) + \cos(B) \cos\left(A\right)
|
8,073
|
(-1) + r^{1 + n} = (1 + r + \cdots + r^n)\cdot \left((-1) + r\right)
|
1,715
|
1 + 10^{k_2} = k_1^2 \Rightarrow \left(k_1 + 1\right) ((-1) + k_1) = 10^{k_2}
|
-11,860
|
6.776\times 0.1 = 0.6776
|
-15,857
|
-10 \cdot \frac{9}{10} + 10/10 = -\dfrac{1}{10}80
|
29,830
|
hA = A = Ah
|
27,862
|
1/4 = \dfrac{1}{1296}\cdot 324
|
20,087
|
8! \cdot 84 = 9! \binom{4}{2} \cdot 2 - 24 \cdot 8!
|
21,341
|
\frac{8}{15} = \frac13 + \frac{1}{5}
|
33,212
|
8 = 2 \cdot 5 + 2\left(-1\right)
|
-7,197
|
\dfrac{2}{7} \cdot 3/7 = 6/49
|
-10,619
|
\dfrac44\cdot \frac{8}{6z + 9} = \tfrac{1}{24 z + 36}32
|
2,669
|
\left(y + x\right)\cdot 2 = x\cdot 2 + 2\cdot y
|
27,201
|
\dfrac{1}{\tan(b)} = \tan\left(\pi/2 - b\right)
|
16,359
|
\sin\left(-B + A\right) = \sin(A) \cos(B) - \sin\left(B\right) \cos\left(A\right)
|
2,809
|
-\frac{1}{1 + n} + \dfrac{n + 1}{1 + n} = 1 - \frac{1}{1 + n}
|
25,467
|
\sin^2(x) = \dfrac12*(-\cos(2*x) + 1)
|
24,703
|
x^{12} + (-1) = (x^6 + 1)\cdot (x^6 + \left(-1\right))
|
-3,409
|
\sqrt{11} \cdot 2 = (1 + 5 + 4 \cdot \left(-1\right)) \cdot \sqrt{11}
|
35,741
|
-x*|x|^{2*(-1) + p} + a = 0 \Rightarrow x*|x|^{2*(-1) + p} = a
|
34,732
|
0 = \sinh^2(x) = \cosh^2(x) + (-1)
|
23,920
|
1 - \dfrac{1}{998}\cdot 332 = 666/998
|
-4,508
|
z^2 - z + 12 (-1) = (z + 4(-1)) (z + 3)
|
-23,029
|
3\cdot 7/(7\cdot 7) = \frac{21}{49}
|
20,553
|
(-2)*\left(-1\right) = 2 \Rightarrow \left(-2\right)*(-2) = 4
|
-6,726
|
10^{-1} + \frac{1}{100} \cdot 2 = \frac{1}{100} \cdot 10 + 2/100
|
32,271
|
\cos(p\cdot y^2 + q\cdot y + r) \leq -1 \implies -1 = \cos(y^2\cdot p + q\cdot y + r)
|
15,033
|
0.0324 = \dfrac{81 \cdot \pi}{\pi \cdot 50 \cdot 50} \cdot 1
|
27
|
\sin^2{y} \cos^2{y} = \sin^{22}{y}/4 = \dfrac18 (1 - \cos{4 y})
|
-7,121
|
\dfrac{5}{42} = \frac{5}{14} \cdot 5/15
|
6,366
|
(1 + x - g + 1)! = (x - g)!
|
36,074
|
\dfrac{{6 \choose 2}}{{7 \choose 3}} = 15/35 = \frac37
|
15,731
|
x/f = \frac{1}{1/x f}
|
905
|
4 = b^0\cdot 0 + b^2 + b^1\cdot 0 \implies 2 = b
|
5,617
|
a_n * a_n = a_{\left(-1\right) + n}*a_{n + 2*\left(-1\right)} \implies a_n*a_{2*(-1) + n}*a_{n + (-1)} = a_n^3
|
24,465
|
0 + 0 \cdot 5^3 + 5^2 + 4 \cdot 5 = 45
|
16,896
|
\cos{e} \cdot \sin{f} + \sin{e} \cdot \cos{f} = \sin(f + e)
|
7,368
|
P(x) = (x - a - b \cdot d^{1/2}) \cdot (x - a + b \cdot d^{1/2}) = x^2 - 2 \cdot a \cdot x + a \cdot a - b^2 \cdot d
|
7,693
|
\sin(x) = x - x \cdot x/2! - x^3/3! - x^4/4! - \frac{1}{5!} \cdot x^5 - \dots
|
933
|
0 \cdot (-2) = 0
|
24,838
|
\mathbb{E}[YV] = \mathbb{E}[V] \mathbb{E}[Y]
|
33,483
|
(-3 \cdot y^2 + y^3) \cdot (3 \cdot (-1) + y) + 1 = y^4 - 3 \cdot y^3 - 3 \cdot y^3 + y^2 \cdot 9 + 1
|
33,429
|
1 + a - x = a - x + 1
|
3,451
|
e^{e*0}*e = e
|
-465
|
e^{9*\frac{7*i*\pi}{4}} = (e^{\frac74*i*\pi})^9
|
24,789
|
1 + d = 0 \implies -1 = d
|
833
|
(M + N) \left(M - N\right) = M^2 + MN - MN - N^2
|
27,986
|
\frac{2}{2(-1) + 3} = 2
|
-30,343
|
0 = (s*q_0)^2 + 3*s*q_0 + 18*(-1) = (s*q_0 + 6)*(s*q_0 + 3*(-1))
|
18,891
|
(\left(-1\right) + 2^4) \cdot \left(4 \cdot (-1) + 2^4\right) \cdot (2^4 + 8 \cdot (-1)) \cdot (2^4 + 2 \cdot (-1)) = 20160
|
13,021
|
6/q - \frac{6}{q + 7} = \dfrac{42}{q^2 + 7q}
|
30,006
|
3^{2\cdot r} + 3^{r\cdot 2 + 1} = (2\cdot 3^r)^2
|
29,047
|
2^{n + (-1)} + (-1) = (2^{\frac{1}{2}*(n + \left(-1\right))} + 1)*(2^{\frac{1}{2}*\left(n + (-1)\right)} + (-1))
|
-2,598
|
(1 + 2)\cdot \sqrt{5} = 3\cdot \sqrt{5}
|
1,587
|
1 = 2 - 2 \cdot \left(-1/2 + 1\right)^3 - 3 \cdot (-\frac{1}{2} + 1)^2
|
-17,551
|
6(-1) + 59 = 53
|
567
|
Y^2 + \mu\cdot Y\cdot 2 + \mu^2 = \left(Y + \mu\right) \cdot \left(Y + \mu\right)
|
17,962
|
(c \cdot g + d \cdot b)^2 + (g \cdot d - c \cdot b)^2 = (c^2 + d^2) \cdot (g^2 + b^2)
|
-19,464
|
\dfrac{1/5 \cdot 8}{7 \cdot \frac18} = \tfrac15 \cdot 8 \cdot 8/7
|
-4,600
|
\frac{1}{x^2 + x + 20\cdot (-1)}\cdot (2\cdot x + 26\cdot \left(-1\right)) = -\dfrac{2}{4\cdot (-1) + x} + \frac{1}{x + 5}\cdot 4
|
24,527
|
3^2 = 2*2^2 + 1
|
-28,844
|
15 = 415 + 400\times (-1)
|
-10,563
|
50 = -2 \cdot a + 3 + 50 \cdot (-1) = -2 \cdot a + 47 \cdot \left(-1\right)
|
-20,333
|
-3/2 \frac{9M + 8}{M \cdot 9 + 8} = \frac{-M \cdot 27 + 24 (-1)}{16 + M \cdot 18}
|
8,123
|
m^6 = (m \cdot m)^3
|
54,533
|
60 = 5*4*3
|
14,886
|
|B - A| + |A| \geq |B| \implies |B| - |A| \leq |B - A| = |A - B|
|
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