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ddrg
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math_formulas

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int64
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11,597
\left(100 + 1 + 10\right)*10^j = 10^j + 10^{j + 1} + 10^{j + 2}
-19,514
\dfrac{1}{2\cdot 1/8} = \frac82\cdot 1
51,879
2 + 2 + 2 + 1 + 1 + 2 + 1 + 1 + 1 + 1 + 1 = 15
20,865
\left(d + \mu\right)^2 = 2*\mu*d + \mu^2 + d * d
-2,216
-\frac{2}{12} + 7/12 = 5/12
7,883
\dfrac{1}{2^{n + 1}}(3(-1) + 2n + 4 - n) = \tfrac{1 + n}{2^{1 + n}}
37,724
(-b + x)^2 = x^2 + b^2 - 2bx \Rightarrow 2xb = -(-b + x)^2 + x^2 + b^2
3,367
z^3 - 12 \cdot z + 16 = (z + 2 \cdot (-1)) \cdot (g \cdot z^2 + h \cdot z + f) = g \cdot z^3 + (h - 2 \cdot g) \cdot z^2 + (f - 2 \cdot h) \cdot z - 2 \cdot f
14,691
(-1) + \cos^2(r) \cdot 2 = \cos\left(2 \cdot r\right)
26,811
1/t\cdot a/(p\cdot \frac{1}{t'}) = \frac{t'\cdot a}{t\cdot p\cdot 1^{-1}}\cdot 1
-20,182
-\frac{4}{t\cdot 9 + 2\cdot \left(-1\right)}\cdot \frac99 = -\dfrac{36}{18\cdot (-1) + 81\cdot t}
4,720
o \cdot o^2 + o \cdot o = 2 \cdot o - o^2 = 2 \cdot o - 2 - 2 \cdot o = 4 \cdot o + 2 \cdot (-1)
4,467
y/z = w \Rightarrow y = z*w
15,729
v^3 + (-1) = ((-1) + v) \cdot (1 + v \cdot v + v)
23,656
80^3 + 1 = 7^2 \cdot 3^5 \cdot 43
31,466
2 + \sqrt{3} = e^{-i*x} = \cos{x} - i*\sin{x}
26,167
6*z * z - z*15 + 9*(-1) = 3*\left(2*z^2 - 5*z + 3*(-1)\right)
4,606
W\cdot x/I = x\cdot W/I
21,953
{32 \choose 16} = {31 \choose 16} \cdot 2
36,503
1 + \frac{1}{1 - p}*p = \frac{1}{-p + 1}
7,996
\left(a = 2a\Longrightarrow a \cdot (2 + (-1)) = 0\right)\Longrightarrow a = 0
4,596
\frac{1}{17} = 60 \cdot 2/17 + 7 (-1)
3,259
0 = \theta^2 - 2 \cdot \theta + 1 = (\theta + (-1))^2
-25,789
\frac{1}{40}\cdot 4 = 4/(5\cdot 8)
26,527
\left(1 + r\right)^2 = 2\cdot r + r^2 + 1
-7,882
\frac{1}{17}(72 + 52 i - 18 i + 13) = \frac{1}{17}\left(85 + 34 i\right) = 5 + 2i
28,313
28/p = 7/p\cdot 4/p = \dfrac{1}{p}\cdot 7
1,171
\left(x^4 + (-1)\right)\cdot (-\frac{1}{x^4}) = \frac{1}{x^4} + (-1)
8,283
h \cdot d = \frac{1}{\tfrac{1}{h \cdot d}} = \frac{1}{1/h \cdot 1/d} = \dfrac{1}{1/d \cdot \frac{1}{h}} = d \cdot h
5,904
\frac{1}{p! (x - p)!}x! = \binom{x}{p}
-20,720
\frac{10\times (-1) + 10\times a}{5 - 5\times a} = -2/1\times \dfrac{5 - a\times 5}{5 - 5\times a}
1,271
\binom{17}{3} = \frac{17!}{14!\cdot 3!} = 680
5,557
\operatorname{E}\left(x \cdot x\right) = \operatorname{E}\left(U^2\right)\cdot \operatorname{E}\left((1 + x)^2\right) = \operatorname{E}\left(U\right)\cdot (1 + 2\cdot \operatorname{E}\left(x\right) + \operatorname{E}\left(x^2\right))
6,148
\dfrac{1}{\sqrt{(-1) + x^2}} = \dfrac{x}{x*\sqrt{(-1) + x^2}}
-11,180
(x + 2 \cdot (-1))^2 + b = (x + 2 \cdot \left(-1\right)) \cdot (x + 2 \cdot (-1)) + b = x^2 - 4 \cdot x + 4 + b
28,083
( |d|, |f|) = 1 \Rightarrow \left(d, f\right) = 1
-11,698
1/36 = (\tfrac16)^2
42,281
\rho \cdot \beta = \beta \cdot \rho
8,088
(z^4 + (-1))*(z^4 + 1) = (-1) + z^8
23,612
\sin(z) \sin\left(K\right) + \cos(z) \cos(K) = \cos(K - z)
-21,671
\dfrac13\cdot 2 = 2/3
458
5*\pi/12 = \frac{1}{2}*(\pi - \frac16*\pi)
22,696
3^{70} + 2^{70} = ((\frac{2}{3})^{70} + 1) \cdot 3^{70}
1,431
\frac{2}{n^2 + (-1)} = \frac{1}{n + (-1)} - \frac{1}{1 + n}
-5,067
0.3*10^{(-2)*(-1) + 1} = 10^2 * 10*0.3
30,041
\dfrac{1}{2^6} \cdot (1^2 + 3 \cdot 3 + 3^2 + 1 \cdot 1) = 20/64 = 5/16
-18,334
\dfrac{a * a + 9*a}{81*(-1) + a^2} = \frac{a*\left(9 + a\right)}{\left(a + 9\right)*(a + 9*(-1))}
-10,312
\frac22\cdot 7/(25\cdot s) = 14/(s\cdot 50)
-16,355
6\sqrt{16} \cdot \sqrt{5} = 6 \cdot 4 \cdot \sqrt{5} = 24\sqrt{5}
5,454
0 = J^{s + (-1)} + (-1) = (J + (-1))*(1 + J + \dotsm*J^{s + 2*(-1)})
32,778
m - 2i + i = -i + m
11,918
V*S = (V^{\frac{1}{2}}*S^{\frac{1}{2}}) * (V^{\frac{1}{2}}*S^{\frac{1}{2}})
-22,336
(s + 2) \left(s + 6\right) = 12 + s * s + 8s
-2,813
2*\sqrt{10} = ((-1) + 3)*\sqrt{10}
19,295
\dfrac{1}{2^{1/2}} = \sin(\pi \cdot 3/4)
-20,930
-8/5 \cdot \frac{(-1) \cdot 5 \cdot y}{(-5) \cdot y} = \frac{y \cdot 40}{y \cdot (-25)}
11,584
\pi \cdot 64 = 16 \cdot \pi \cdot 2 \cdot 2
22,913
b^m = \left((b^{\dfrac1q})^q\right)^m = (b^{\frac{1}{q}})^{q \cdot m}
-29,755
d/dx (3x^5) = 3d/dx x^5 = 3\cdot 5x^4 = 15 x^4
-1,334
\frac{\frac19 \cdot (-1)}{3 \cdot \frac{1}{7}} = 7/3 \cdot (-\frac{1}{9})
39,021
\pi/4 = \tan^{-1}{1}
39,200
\dfrac1z = \frac{1}{z}
40,243
x \cdot \Delta = \Delta \cdot x
3,862
(U + A)^{n + 1} = (U + A)^n\cdot (U + A) = (U + A)^n U + (U + A)^n A
4,486
\cos\left(-b + c\right) = \sin{c} \cdot \sin{b} + \cos{b} \cdot \cos{c}
31,454
\frac{96 + 10}{2*96 + 10} = \frac{1}{202}*106 = \frac{1}{101}*53 \approx 0.524752
29,929
\binom{5}{2}\cdot 3\cdot \binom{5}{4}\cdot 4! = 3600
26,400
\sec\left(\theta\right) = 1/\cos(\theta)
8,225
\frac{Z_l}{B_l} = \tfrac{\left(-1\right) Z_l}{(-1) B_l}
31,133
\frac88 + \sqrt{8 + 8}\cdot (8\cdot 8\cdot 8 + 8\cdot \left(-1\right)) = 2017
4,453
-(y^2 + x^2) + 1 = 1 - x^2 - y^2
31,057
k\cdot \frac{1}{h}\cdot a\cdot b = \dfrac{a\cdot b}{h}\cdot 1\cdot k
30,527
\mathbb{E}\left(m_1\cdot m_2\right) = \mathbb{E}\left(m_1\right)\cdot \mathbb{E}\left(m_2\right)
759
\binom{n}{j}\cdot j = \frac{n!}{(j + (-1))!\cdot (n - j)!} = n\cdot \binom{n + (-1)}{j + (-1)}
-29,358
(4 + y) (4 - y) = 4 \cdot 4 - y^2 = 16 - y^2
-5,223
3.2\cdot 10^1 = 3.2\cdot 10^{-2 - -3}
-12,787
18 = 29 + 11 \left(-1\right)
40,188
\overline{e^{i\cdot p}} = \overline{\cos{p} + i\cdot \sin{p}} = \cos{p} - i\cdot \sin{p} = \cos{-p} + i\cdot \sin{-p} = e^{-i\cdot p}
13,151
g\cdot(h_1+h_2) = (g\cdot h_1) + (g\cdot h_2)
33,691
6\cdot 1/3/2 = 6/(2\cdot 3)
18,397
2^{n + 1} = 2 \cdot 2^n \geq 2 \cdot 4 \cdot n \cdot n > 4 \cdot n^2 + 8 \cdot n + 4 = 4 \cdot (n^2 + 2 \cdot n + 1) = 4 \cdot \left(n + 1\right) \cdot \left(n + 1\right)
5,297
(a_1 + a_2)/r = \frac{a_2}{r} + a_1/r
17,753
H \cdot D = 0 = D \cdot H
9,432
|f \cdot a| = |a \cdot f|
22,885
(B \cdot B - x^2) \cdot (B \cdot B - x^2) + (x\cdot B\cdot 2) \cdot (x\cdot B\cdot 2) = (B^2 + x^2)^2
-15,327
\frac{1}{\zeta^9\cdot t^{15}\cdot \frac{1}{\frac{1}{\zeta^{15}}\cdot \frac{1}{t^{10}}}} = \frac{\frac{1}{t^{15}}}{t^{10}\cdot \zeta^{15}}\cdot \frac{1}{\zeta^9}
19,568
\left(y \cdot y = y + 3 \Leftrightarrow 0 = y \cdot y - y + 3\cdot (-1)\right) \Rightarrow \dfrac{1}{2}\cdot (1 \pm \sqrt{13}) = y
32,972
((6 + 5\cdot (-1))^2 + (0 + 3)^2)^{1/2} = (1 + 9)^{1/2} = 10^{1/2} \leq 4
-5,205
10^1\cdot 58.8 = 10^{2 - 1}\cdot 58.8
14,672
(2 \times (-1) + V) \times (V + (-1)) + 4 = V^2 - 3 \times V + 6
1,913
(s + (-1))*\frac{1}{(-1) + s}*\left((-1) + s^i\right) = s^i + (-1)
-20,741
\frac{8(-1) + p}{p + 8(-1)} (-3/1) = \frac{24 - 3p}{p + 8(-1)}
1,474
(4n^2 - 1) = (2n-1)(2n+1)
4,248
g_1 \cdot h \cdot g_2 = g_2 \cdot g_1 \cdot h
-2,411
3*\sqrt{6} + \sqrt{6} = \sqrt{9}*\sqrt{6} + \sqrt{6}
-9,125
x\cdot 2\cdot 3\cdot 3\cdot 3\cdot x = x^2\cdot 54
-4,360
\frac{66 q}{48 q^4} = \frac{1}{q^4} q\cdot 66/48
-20,145
\tfrac{1}{3\cdot \left(-1\right) - y\cdot 3}\cdot (-y\cdot 3 + 3\cdot (-1))\cdot (-5/1) = \frac{1}{-3\cdot y + 3\cdot (-1)}\cdot \left(15\cdot y + 15\right)
34,243
Q^1\cdot \cdots\cdot Q^k = \overline{Q}^k
17,040
\frac{V\cdot e^x}{V} = e^{V\cdot x/V}