id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
34,081 |
\cos(2*x) = \cos^2\left(x\right) - \sin^2(x) = 2*\cos^2(x) + \left(-1\right)
|
-4,840 |
7.2/10 = \tfrac{7.2}{10}
|
19,659 |
\int_{-1}^1 (x^2 \cdot c_2 + c_0)\,\mathrm{d}x = \left(\int\limits_0^1 \left(c_0 + c_2 \cdot x^2\right)\,\mathrm{d}x\right) \cdot 2
|
-5,887 |
6/6*\frac{1}{(x + 3*(-1))*(2*(-1) + x)}*5 = \frac{30}{\left(3*\left(-1\right) + x\right)*\left(2*(-1) + x\right)*6}
|
13,698 |
y = \int (-\cos\left(p + |y|\right)*y/|y|)\,\text{d}p = -\sin(p + |y|)*y/|y|
|
18,150 |
1 = 3\cdot \left(x\cdot y\cdot z\right)^{2/3} + 2\cdot (-1) \leq x\cdot y + y\cdot z + z\cdot x + 2\cdot (-1)
|
1,904 |
h_2 + g_2\cdot \sqrt{2} + h_1 + \sqrt{2}\cdot g_1 = (g_2 + g_1)\cdot \sqrt{2} + h_1 + h_2
|
24,495 |
\sin(x \times 2) = 2 \times \sin(x) \times \cos\left(x\right)
|
9,515 |
c = 2, b = 1 \implies \frac{1}{c c + b^2} c = \dfrac{2}{2 2 + 1 1} = 2/5
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27,721 |
3616 = 1/6\cdot 21696
|
24,121 |
2^5 \cdot 3^2 = 288
|
12,620 |
((1 + i)/i)^i = (1 + \frac1i)^i
|
11,983 |
-(l^2 - 5 l + 13)*108 = 729 (-1) - (l*2 + 5 \left(-1\right)) (l*2 + 5 \left(-1\right))*27
|
22,876 |
\overline{F} = x \Rightarrow F = x
|
19,545 |
H' \cdot g' = H \cdot g \Rightarrow \frac{g}{g'} \cdot H = H'
|
14,452 |
gfN = Ngf
|
8,886 |
(n + 1) * (n + 1) - 1 + n = n^2 + n
|
-8,901 |
(-1) \cdot (-1) \cdot (-1) \cdot (-1) \cdot \left(-1\right) = -1^5
|
-22,139 |
\frac{6}{9} = \frac{1}{3} \cdot 2
|
-20,667 |
-\frac{3}{30} = 3/3 (-1/10)
|
-16,440 |
8 \cdot 4^{\frac{1}{2}} \cdot 11^{\frac{1}{2}} = 8 \cdot 2 \cdot 11^{\dfrac{1}{2}} = 16 \cdot 11^{\frac{1}{2}}
|
2,145 |
(z + (-1)) \cdot (z + 1) = (z + \left(-1\right)) \cdot z + z + (-1) = z \cdot z - z + z + (-1) = z \cdot z + (-1)
|
13,073 |
I_n = A\cdot B \Rightarrow A\cdot B = I_n
|
-20,300 |
\frac{1}{4\cdot s + 16}\cdot \left(3\cdot s + 12\right) = \frac{3}{4}\cdot \frac{s + 4}{4 + s}
|
41,876 |
1/e^x = e^{-x}
|
5,348 |
\left(\dfrac{(r + (-1)) r}{(r + 1) r} = 1/2 \implies r + 1 = 2r + 2(-1)\right) \implies r = 3
|
-20,696 |
\frac{45}{-10\cdot t + 15\cdot (-1)} = \frac{9}{3\cdot \left(-1\right) - 2\cdot t}\cdot \frac55
|
-7,232 |
2/5*3/4 = 3/10
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20,281 |
O*A/\sin\left(B\right) = \frac{O*B}{\sin(A)} = A*B/\sin\left(O\right)
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-18,617 |
5 \cdot q + 5 = 7 \cdot (3 \cdot q + 9) = 21 \cdot q + 63
|
5,154 |
w + w + S + S = (w + S) \times (1 + 1) = w + S + w + S
|
4,506 |
\frac{1}{1024}256 = 1/4
|
-16,730 |
2 = a^2 - a + 2\cdot a + 2\cdot (-1) = a^2 - a + 2\cdot a + 2\cdot (-1)
|
25,401 |
z\cdot (a + 1) + 100\cdot a + 56 = z + 1000\cdot a \Rightarrow z = 900 - \dfrac{56}{a}
|
9,082 |
2^m + i = 2 \cdot 2^{m + \left(-1\right)} + 2 \cdot i/2 = 2 \cdot \left(2^{m + (-1)} + \frac{1}{2} \cdot i\right)
|
30,640 |
c \cdot c\cdot c\cdot c^2 = c^5
|
30,303 |
E[Z]\times E[X] = E[X\times Z]
|
-11,740 |
\frac{81}{16} = (\frac94)^2
|
38,755 |
15/60 = \tfrac14
|
-1,772 |
-\pi\cdot \dfrac{11}{12} = -\pi + \pi/12
|
-2,689 |
\sqrt{9} \times \sqrt{5} + \sqrt{5} \times \sqrt{16} = \sqrt{5} \times 3 + 4 \times \sqrt{5}
|
24,963 |
a \cdot f^2 = a \cdot f^2
|
52,262 |
\frac{1}{12} \cdot (q^2 + (-1)) = \left\lfloor{\sqrt{q}}\right\rfloor + \left\lfloor{\sqrt{2 \cdot q}}\right\rfloor + \dots + \left\lfloor{\sqrt{q \cdot \left(q + (-1)\right)/4}}\right\rfloor
|
12,109 |
3\cdot j \cdot j + j\cdot 3 + 1 = (1 + j)^3 - j^3
|
2,478 |
1 + 24541/56660 = \frac{81201}{56660}
|
29,072 |
(-1) + z^3 = (z \cdot z + z + 1)\cdot (z + (-1))
|
30,507 |
f\frac{-r^k + 1}{-r + 1} = f\dfrac{1}{(-1) + r}\left((-1) + r^k\right)
|
31,749 |
(1 + 1) (d + h) = d + h + d + h = d + h + d + h
|
29,775 |
i_1 xi_2 = xi_1 i_2
|
-1,692 |
-\pi*2 + \pi*7/3 = \frac{\pi}{3}
|
1,215 |
0.3\cdot \cos(3\cdot x) + 0.4\cdot \sin(3\cdot x) = U\cdot \sin(3\cdot x + X) = U\cdot \sin(3\cdot x)\cdot \cos\left(X\right) + U\cdot \cos(3\cdot x)\cdot \sin(X)
|
107 |
\rho^2 + b \cdot b + d^2 + \rho \cdot b \cdot d = 4 \geq \rho \cdot b + b \cdot d + \rho \cdot d + \rho \cdot b \cdot d
|
29,221 |
\cos(\arctan(n)) = \tfrac{1}{\sqrt{1 + n \cdot n}}
|
8,063 |
648 = 3^4\cdot 2 \cdot 2 \cdot 2
|
27,277 |
3^{4 \cdot n + 3} = 3^3 \cdot (10 + (-1))^{2 \cdot n} = 3^3 \cdot (1 + 10 \cdot \left(-1\right))^{2 \cdot n}
|
-10,592 |
-9 = -5*y + 4 + 21*(-1) = -5*y + 17*\left(-1\right)
|
8,035 |
\frac 1p + \frac 1q=1 \implies (p-1)(q-1)=1
|
16,312 |
\dfrac{1}{2^{-\sqrt{l}}}l \cdot l = 2^{\sqrt{l}} l^2
|
21,022 |
b = x A \implies b/A = x
|
1,336 |
\frac{1}{((-1) + x)^2}*(x + 2*(-1))*e^x = \frac{\mathrm{d}}{\mathrm{d}x} (\frac{e^x}{(-1) + x})
|
10,876 |
\frac{1}{2}*(\sin(c + g) + \sin(c - g)) = \sin(c)*\cos(g)
|
19,592 |
(f, g) = \frac{1}{g}*f*g/f = f^g/f
|
-11,622 |
-2 + 8i = i*8 + 3 + 5(-1)
|
421 |
\frac{(-2) \dfrac1x}{-e^{1/x} \frac{1}{x^2}} = \frac{1}{(-1) e^{\frac{1}{x}}}((-2) x) = 2xe^{-\frac1x}
|
53,102 |
(y + x)^2 = \frac{\mathrm{d}y}{\mathrm{d}x} rightarrow 1 + \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\partial}{\partial x} (y + x) = 1 + (y + x)^2
|
26,460 |
\cos{z} = \left(e^{iz} + e^{-iz}\right)/2 \sin{z} = \frac{1}{2i}(e^{iz} - e^{-iz})
|
-5,705 |
8/8*\frac{3}{(q + 9(-1)) \left(2(-1) + q\right)} = \frac{24}{8(q + 2(-1)) (9\left(-1\right) + q)}
|
5,902 |
\left(1 - \sqrt{5} \cdot 2\right)^2 = -\sqrt{5} \cdot 4 + 21
|
-8,467 |
36 = \left(-4\right)*\left(-9\right)
|
4,082 |
0 = \dfrac{1}{2}\times (1 - 1)
|
-2,320 |
\dfrac{2}{11} = -2/11 + \tfrac{4}{11}
|
36,937 |
-z_1 + 3 - 2\cdot z_2 = 0 \Rightarrow z_1 = -z_2\cdot 2 + 3
|
-3,659 |
5/(6*q) = 5*1/6/q
|
5,467 |
-\dfrac{y + 2\cdot (-1)}{2 + y} = \frac{2 - y}{2 + y}
|
809 |
y! = 10!\cdot 11\cdot 12\cdot ...\cdot y > 10!\cdot 11^{y + 10\cdot \left(-1\right)}
|
9,167 |
\cos{\frac{\pi}{4}} \cdot \sin{0} \cdot 2 = 0
|
639 |
25 + x^2 - 10*x = (x + 5*(-1))^2
|
15,505 |
\frac{Z}{2} = G \implies Z < G
|
23,765 |
\sec{\theta} \tan{\theta} = \frac{d}{d\theta} \sec{\theta}
|
-17,707 |
3 = 17 + 14 (-1)
|
-15,806 |
-71/10 = -9/10*9 + \frac{1}{10}*10
|
400 |
1 + 3*x = \frac{1 + x*3}{(1 - x)^8}
|
27,567 |
\overline{x} \cdot a = \overline{\overline{a} \cdot x}
|
427 |
\operatorname{E}[V \times x] = \operatorname{E}[V] \times \operatorname{E}[x]
|
9,029 |
x^2 + x y \cdot 2 + y^2 = \left(x + y\right)^2
|
20,442 |
5 + b^2 = 5 + a^2 \Rightarrow a^2 = b^2
|
20,452 |
z + (-1) + (z + (-1)) \cdot (z + (-1)) + z = z \cdot z
|
1,581 |
((-y + 1) \cdot (1 + y))^{1/2} = (1 - y^2)^{1/2}
|
25,303 |
\sin(\pi/3)\cdot 2 = \sqrt{3}
|
15,184 |
|x^2 - x| = |(-1) + x|*|x|
|
18,229 |
11/15 = \frac{12 + \left(-1\right)}{16 + (-1)}
|
-28,892 |
(100 + 200 + 150 + 150)/4 = \dfrac{1}{4}\cdot 600 = 150
|
5,086 |
-a \cdot a + z^2 = (-a + z) \cdot (a + z)
|
-15,772 |
-10\cdot \tfrac{1}{10}\cdot 8 + 2/10\cdot 10 = -\dfrac{1}{10}\cdot 60
|
-2,325 |
\frac{5}{15} = \dfrac{1}{3}
|
11,216 |
\frac36 \cdot \frac{1}{6} \cdot 4 + \tfrac46 \cdot 4/6 = 7/9
|
5,969 |
r^2 = 1 + ((-1) + r) \cdot (r + 1)
|
21,094 |
a*1/d/h = \frac{a*1/d}{h} = \frac{a}{d*h}
|
-28,939 |
\frac{1}{2}4 = 2
|
-16,335 |
(25 \cdot 2)^{1/2} \cdot 10 = 50^{1/2} \cdot 10
|
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