Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
-19,766
1.5 = \tfrac{1}{2} \cdot 3
12,133
\frac{2}{(1 - x^{k \cdot m \cdot 2})^2} \cdot m \cdot x^{m \cdot k \cdot 2 + (-1)} \cdot k = \frac{\partial}{\partial x} (\frac{1}{-x^{k \cdot m \cdot 2} + 1} \cdot x^{2 \cdot m \cdot k})
30,090
\tilde{K}\cdot d = 0.036\cdot K/(0.0018\cdot d) = \tfrac{20}{d}\cdot K
27,462
14 + 6 \cdot (-1) + \left(-1\right) = 7
23,883
\left(4 \cdot a + a \cdot 6 = 120 \Rightarrow 12 = a\right) \Rightarrow 144 = a^2
10,895
x_s + x_w = x_s - x_w + x_w*2
29,766
\frac{\partial}{\partial f} \left(u\cdot x\right) = \frac{\partial}{\partial f} (x\cdot u)
-10,520
\frac{7 + x}{(-1) + x \cdot 5} \cdot \tfrac55 = \frac{5 \cdot x + 35}{25 \cdot x + 5 \cdot (-1)}
42,644
7! \cdot 7! \cdot 8 = 8! \cdot 7!
3,114
102 \cdot 4 + 53 \cdot (-1) = 355
11,542
\frac{1}{\sqrt{3 * 3 + 2^2 + 6^2}}(35 + 7(-1)) = 4
44,809
14680057 = ((-1) + 2^{21}) \times 7
11,447
\tan\left(t\right) = \frac{1}{1/\left(\frac{1}{\cos(t)}\right)*1/\sin\left(t\right)}
16,314
(g + b)^2 = g^2 + 2\cdot b\cdot g + b^2 \Rightarrow g \cdot g + b^2 = (g + b)^2 - g\cdot b\cdot 2
-20,799
\frac{90 + 10*x}{63 + x*7} = 10/7*\tfrac{x + 9}{x + 9}
-20,364
\frac{1}{2\cdot r}\cdot (5\cdot r + 5\cdot (-1))\cdot \frac77 = (35\cdot \left(-1\right) + 35\cdot r)/(14\cdot r)
11,453
(y + 1)*\left(y * y - y + 2\right) = (y + 1)*\left(y^2 - y + 1\right) + y + 1 = y^3 + 1 + y + 1 = 6 + y
14,169
4\cdot (-1) + m = -7 \implies m = -3
12,774
(-f + h) \cdot (h + f) = h^2 - f \cdot f
-23,702
\left((-1)*0.73 + 1\right)^6 = 0.27^6
23,216
|dg| = |d| |g|
-17,037
2 = 2\cdot (-3\cdot p) + 2\cdot \left(-1\right) = -6\cdot p - 2 = -6\cdot p + 2\cdot \left(-1\right)
53,537
c = \frac{z}{3 + 10 \cdot k} \Rightarrow c \cdot 3 + k \cdot c \cdot 10 = z
9,136
\frac{1}{2^{l + (-1)}} = \frac{1 \cdot 2}{2^{l + (-1)} \cdot 2} = \dfrac{2}{2^l}
27,017
\dfrac{1}{d_2} \cdot f \cdot d_1/x = \tfrac{1/x \cdot d_1}{1/f \cdot d_2}
-4,214
x \cdot 8/7 = \frac{8}{7} \cdot x
-1,303
\frac{\left(-9\right)*1/7}{1/5} = 5/1 \left(-9/7\right)
-15,125
\frac{1}{\dfrac{1}{x^{10}\cdot y^6}}\cdot x^5 = \dfrac{1}{\frac{1}{x^{10}}\cdot \frac{1}{y^6}}\cdot x^5
940
n + 2*(-1) + n + n + (-1) = n*3 + 3*(-1)
-22,339
(1 + f)\cdot (f + 5\cdot \left(-1\right)) = 5\cdot (-1) + f^2 - 4\cdot f
28,730
2^1 = \frac{4}{2} = 2
30,694
\frac{\partial}{\partial z} z^n = n\cdot z^{n + \left(-1\right)}
22,989
c + q/c = r\Longrightarrow \frac{1}{2}*(r ± \sqrt{-4*q + r^2}) = c
-15,356
\frac{z^8}{f^5\cdot z^5}\cdot f^6 = \dfrac{f^6}{f^5}\cdot \dfrac{1}{z^5}\cdot z^8 = f^{6 + 5\cdot (-1)}\cdot z^{8 + 5\cdot \left(-1\right)} = f\cdot z^3
10,212
a^2 + ba \cdot 2 + b^2 = (a + b) \cdot (a + b)
15,909
\binom{5}{3} = 5\cdot 4\cdot 3/\left(3\cdot 2\right) = 10
1,522
x^l - z^l = (x - z)*(x^{l + (-1)} + x^{l + 2*\left(-1\right)}*z + \dots + x*z^{2*(-1) + l} + z^{\left(-1\right) + l})
-11,636
-10 + 5 + 27 \cdot i = -5 + 27 \cdot i
19,122
\sqrt{( x^2, y^3)} = \sqrt{x^2 y^3} = \sqrt{x^2} \sqrt{y^3} = xy = \left[x,y\right]
9,756
xY^X = (xY)^X = (xIY)^X = Y^X xI
13,665
(\frac{d*x}{d}*1)^{n + 1} = (x*d/d)^n*x*d/d = x^n*d/d*\frac{x*d}{d}
7,557
U + V + W = U + V + W
-487
e^{6\cdot 17\cdot i\cdot \pi/12} = (e^{17\cdot \pi\cdot i/12})^6
-17,404
1.473 = \frac{147.3}{100}
23,150
6 = 3\cdot 2 + 7\cdot 0
-626
-4\pi + \frac{65}{12} \pi = \dfrac{17}{12} \pi
42,464
e^{i \cdot x} = \cos(x) + i \cdot \sin(x) = \cosh(i) + x \cdot \sinh\left(i\right)
3,947
(x*n) * (x*n) = (n*x)^2
-21,342
\tfrac36 = \frac12
21,971
e = 1/\left(\frac1e\right)
12,194
\frac{\text{d}x}{\text{d}x} = \frac{\text{d}x}{\text{d}Z}\cdot \frac{\text{d}Z}{\text{d}x} = \frac{\text{d}x}{\text{d}Z}\cdot \frac2Z
7,595
bp^m = cxp\Longrightarrow bp^{m + (-1)} = xc
-18,391
\tfrac{42 + k \cdot k + 13 \cdot k}{k^2 + 7 \cdot k} = \frac{(k + 6) \cdot (k + 7)}{(k + 7) \cdot k}
15,028
\frac12\cdot (\left(-b + a\right) \cdot \left(-b + a\right) + \left(b - c\right)^2 + (c - a)^2) = a^2 + b^2 + c^2 - a\cdot b - c\cdot b - c\cdot a
28,988
\frac{a^2}{(c-b)}+\frac{b^2}{(c-a)}=\frac{c(a^2+b^2)-a^3-b^3}{(c-b)(c-a)}=\frac{c(a^2+b^2-c^2)}{(c-b)(c-a)}........(3)
28,325
g - \frac{f}{x} = -f/x + g
-1,139
\frac{1}{(-4)\cdot 1/9}\cdot ((-9)\cdot \tfrac17) = -\frac94\cdot (-\frac{9}{7})
3,743
3/4 = \dfrac{1^{-1}}{4} \cdot 3
-10,650
3/3\cdot (-\frac1r\cdot \left(r\cdot 4 + 7\cdot (-1)\right)) = -(r\cdot 12 + 21\cdot \left(-1\right))/(r\cdot 3)
-475
e^{8 \cdot i \cdot \pi \cdot 5/3} = (e^{i \cdot \pi \cdot 5/3})^8
5,704
\frac{1}{z^d + z^{-d}} = \dfrac{z^d}{z^{2\cdot d} + 1} \approx \frac{1}{z^d}
24,216
-\pi/6 = \arcsin(-\dfrac{1}{2})
12,154
((2\cdot n)!)! = 2\cdot n\cdot 2\cdot \left(n + (-1)\right)\cdot 2\cdot \left(n + 2\cdot (-1)\right)\cdot \dots\cdot 2 = 2^n\cdot n!
15,331
\frac{1}{36} = \frac{6}{6^3}
14,135
2 \cdot \pi/5 \cdot 1.25 = \dfrac{2}{5} \cdot \pi \cdot 5/4 = \frac{\pi}{2}
32,719
\frac8x = \dfrac8x
38,155
a*\frac1b/d = a/(b*d) = a*1/b/d = \tfrac{1}{b*d}*a
14,063
\mathbb{E}[Z_t^2 \cdot Z_{-j + t}^2] = \mathbb{E}[Z_{t - j}^2] \cdot \mathbb{E}[Z_t^2]
-10,617
3 = 30 \cdot \beta + 30 \cdot (-1) + 15 = 30 \cdot \beta + 15 \cdot (-1)
22,302
\frac{210}{2}1 = 105
20,788
15 = -10^0 \cdot 5 + 10^1 \cdot 2
2,482
\left(y + 2(-1)\right) (2(-1) + y) = (y + 2(-1))^2
13,286
347720 = \binom{26}{7} - \binom{20}{7} - \binom{20}{6}\cdot 6
22,424
\dfrac{10}{\dfrac{10}{2} + 1} = 5/3
11,006
\sin^2(A) + \sin^2(B) + \sin^2\left(H\right) = 2\Longrightarrow 1 - \cos^2(A) + 1 - \cos^2\left(B\right) - \sin^2(H) = 2
2,415
2 + 8 + 24 + 64 + \dotsm + 2^n\cdot n = 2\cdot (\left(n + (-1)\right)\cdot 2^n + 1)
18,098
x^{b + (-1)} \cdot b = \frac{\partial}{\partial x} x^b
-22,172
\frac{1}{7} 9 = 45/35
8,846
2^{n*3} = (2^3)^n
18,073
1/(\sqrt{l}) = \frac{l^{3/2}}{l \cdot l}
19,235
|-x + Q| = |x - Q|
34,324
2^{200} - 2^{192} \cdot 31 + 2^{198} = (2^{96} \cdot 17) \cdot (2^{96} \cdot 17)
36,855
166 - 33 + 23 + 4\cdot (-1) = 114
-17,984
27\cdot (-1) + 64 = 37
28,677
(1/100 + 1)*10000 = 10000 + \frac{1}{100}*10000
26,576
\tan(\tan^{-1}\left(\dfrac{b}{g}\right)) = \frac{1}{g} \cdot b
29,118
\sin\left(x + \pi\cdot 2\right) = \sin(x)
13,278
0 = 2 + 4(-1) + y''\Longrightarrow 2 = y''
8,710
x^5 \cdot 6 + 15 \cdot x^4 + x^3 \cdot 20 + x^2 \cdot 15 + 6 \cdot x + 1 = -x^6 + \left(1 + x\right)^6
14,391
2 = 546 - 32 \cdot 17 = 5 \cdot h_2 - h_1 - 32 \cdot (2 \cdot h_1 - 9 \cdot h_2) = 293 \cdot h_2 - 65 \cdot h_1
53,231
15 = 6 + 4 + 5
-18,634
-\frac{1}{4}11 = -\frac{11}{4}
15,576
B = \begin{array}{rr}1 & 0\\0 & -1\end{array} = \dfrac{1}{B}
-7,184
\frac17*0 = 0
17,758
x * x + i = 0 rightarrow x = \left(-i\right)^{1/2}
-562
e^{3\cdot \frac{\pi\cdot i}{3}\cdot 1} = (e^{\frac{\pi\cdot i}{3}})^3
10,159
1/5 + y = \tfrac15(y \cdot 5 + 1)
-24,199
6 + \frac1848 = 6 + 6 = 12
28,201
\frac{\frac{1}{10^6}}{10^4} (10^6 + (-1)) = 9.99999 \cdot 10^{-5}
250
i = \sin{\dfrac{\pi}{2}}*i + \cos{\dfrac12*\pi}