Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
31,756
\frac{1}{A*H} = 1/(H*A)
36,074
\binom{6}{2}/(\binom{7}{3}) = \dfrac{1}{35} \cdot 15 = 3/7
8,572
Y*V = V*Y
17,413
z \cdot 3 - z \cdot 2 = z
-14,927
440 = 90 + 87 + 95 + 85 + 83
-10,457
\frac{1}{10} \cdot 10 \cdot (-\dfrac{1}{q^2}) = -\frac{10}{10 \cdot q^2}
23,251
2^{3\times m} = 4^m\times 2^m
1,472
D^t = \frac{1}{(1/D)^t} = (\frac{1}{\frac1D})^t = D^t
-1,283
\frac{5}{7} \cdot (-7/2) = \frac{(-7) \cdot 1/2}{7 \cdot \dfrac15}
-18,567
-\dfrac{1}{6} = -1/6
11,544
u^2*m = m*u*u
-11,569
-9\cdot i = 0 + 0\cdot (-1) - i\cdot 9
8,456
\left(-b \cdot 8 + 1\right) \cdot (1 + b)^2 = 1 - 8 \cdot b^3 - b^2 \cdot 15 - b \cdot 6
-30,247
\left(9 + y\right) \left(y + 2\right) = y^2 + 11 y + 18
19,946
2m! = 2*1*2 \ldots m = 2*4 \ldots*2m
3,152
|\tfrac1x\times (x - x) + 0\times (-1)| = |\frac{1}{x}\times x| \lt \frac1x
-26,199
10 \cdot 5 + \frac{4^2}{4} = 50 + \dfrac{16}{4} = 50 + 4 = 54
-20,485
\frac{5}{5} \cdot \tfrac{5 + n}{-n + 9} = \frac{25 + 5 \cdot n}{-5 \cdot n + 45}
-29,339
(2x + 5) (2x + 5(-1)) = (2x)^2 - 5^2 = 4x * x + 25 \left(-1\right)
-7,107
\frac{5}{11} \cdot 2/12 = 5/66
31,055
(n + 1)^2 - n^2 = 2n + 1
468
0 = -i\cdot U + u \Rightarrow \dfrac{u}{U} = i
-24,445
\dfrac{1}{5 + 9} \cdot 98 = \frac{98}{14} = 98/14 = 7
-20,579
\frac185 (-\tfrac{1}{-3}3) = -15/\left(-24\right)
39,715
\tfrac143 = \frac{3}{4}
11,640
2010 \cdot \frac12 \cdot \frac13 \cdot 2 \cdot \dfrac15 \cdot 4 = 2010 \cdot \frac26 \cdot \frac{4}{5} = 2010 \cdot \frac{1}{15} \cdot 4 = 536
15,906
8 = \frac{1}{24} \times (1 \times 2^6 + 6 \times 0 + 2^4 \times 3 + 6 \times 2 \times 2 \times 2 + 8 \times 2^2)
8,389
a*b = x*y,-y^2 + x^2 = a^2 - b^2 \Rightarrow -b^2 + y^2 = -a * a + x^2
426
n = \frac{n*2}{2}
-1,656
0 - \frac{3}{2} \cdot \pi = -\dfrac32 \cdot \pi
-1,740
0 + 5/4*\pi = 5/4*\pi
21,465
l!*2 = l! + l!
35,161
17^{0.3} = 1 + 0.84 + \frac{1}{2}0.84^2 + 0.84^3/3! = 2.292
12,987
S^{k \cdot l} \cdot \Lambda_l^j \cdot \Lambda_k^i = \Lambda_l^j \cdot S^{k \cdot l} \cdot \Lambda_k^i
1,785
B = 5/6*\left(B + 1\right) + \frac{1}{6}*\left(y + 1\right)\Longrightarrow B = 6 + y
11,199
z \cdot R/I = R \cdot z/I
9,798
\frac{\left(-3\right) \frac{1}{2}}{(-5)\cdot 1/4} = 6/5
-2,629
(2 + 4 \cdot (-1) + 5) \cdot \sqrt{3} = 3 \cdot \sqrt{3}
8,154
i \cdot \sin{\frac{\pi}{2} \cdot 3} + \cos{3 \cdot \pi/2} = -i
909
-b^2 + a^2 = (b + a)*\left(-b + a\right)
11,461
\left(1 + 2 + 3 + \dotsm + 20\right)/20 = \frac{1}{2}*21 = 10.5
24,282
\left(f - \alpha\right)*(f + \alpha) = -\alpha^2 + f^2
6,481
B A^k = A B A^{k + \left(-1\right)} = A^2 B A^{k + 2 (-1)} = \dotsm = A^k B
190
2\cdot \frac{1}{2}\cdot \pi + \cos{\frac{\pi}{2}} + \frac{8}{\pi^3}\cdot (\pi/2)^3 = \pi + 1
22,366
y^2 + (-1) = y^2 + 1 = (y + 1) \cdot (y + 1)
1,066
(h/c*c)^k = h^k/c*c
17,331
y^4 - 7 \cdot y^2 + 1 = (y^2 + 1)^2 - 9 \cdot y^2 = \left(y^2 + 1 + 3 \cdot y\right) \cdot \left(y^2 + 1 - 3 \cdot y\right)
16,829
(d_1 - d_2)\cdot (d_2 + d_1) = d_1^2 - d_2^2
20,112
y < b \Rightarrow y * y < b^2 = \frac19
-1,094
\dfrac{30}{21} = \frac{10}{21*\frac{1}{3}}1 = 10/7
9,956
z * z + z + 1 = z^2 + z + \frac{1}{4} + \dfrac34 = \left(z + 1/2\right)^2 + 3/4
10,825
x*\left(-0.95^6 + 1\right) = -0.95^6 x + x
22,623
0 = y^2 + 2\cdot i\cdot y + 2\cdot \left(-1\right) = (y + i) \cdot (y + i) + (-1) = \left(y + \left(-1\right) + i\right)\cdot (y + 1 + i)
5,040
\left(1 + x\right)! - x! = x! \cdot x
7,526
10^{81} + (-1) = (10^9)^9 + (-1) = 5185^9 + \left(-1\right) = 5185\cdot \left(5185^2\right)^4 + (-1) = \cdots = 729
-23,646
4/25 = 4*\frac{1}{5}/5
-6,565
\frac{5}{x\cdot 2 + 18\cdot (-1)} = \dfrac{1}{(9\cdot (-1) + x)\cdot 2}\cdot 5
-3,759
121 d^3/\left(d*99\right) = \tfrac{121}{99} d d^2/d
6,519
\frac{|a|}{|x|} = |a/x|
-6,575
\frac{1}{\left(3 \times (-1) + y\right) \times (y + 9 \times \left(-1\right))} \times (2 \times \left(y + 9 \times (-1)\right) - 5 \times (3 \times (-1) + y) + 6 \times (-1)) = \dfrac{2 \times (y + 9 \times (-1))}{(y + 3 \times (-1)) \times (9 \times (-1) + y)} - \dfrac{5 \times \left(y + 3 \times \left(-1\right)\right)}{(3 \times (-1) + y) \times (y + 9 \times (-1))} - \frac{6}{(y + 3 \times (-1)) \times (9 \times (-1) + y)}
5,588
(f - 5\cdot h)\cdot \left(-2\cdot h + f\right) = f^2 + h \cdot h\cdot 10 - 7\cdot h\cdot f
-17,301
\frac{1}{100} \cdot 71.8 = 0.718
-10,741
\dfrac{50}{r\cdot 25 + 20} = \dfrac{1}{r\cdot 5 + 4}\cdot 10\cdot \dfrac{5}{5}
7,219
\left\{1, \ldots, 2, 0\right\} = \mathbf{N}
-27,745
\frac{\mathrm{d}}{\mathrm{d}z} (3 \cdot \tan{z}) = 3 \cdot \frac{\mathrm{d}}{\mathrm{d}z} \tan{z} = 3 \cdot \sec^2{z}
-17,019
-6 = -6\times (-r) - 42 = 6\times r - 42 = 6\times r + 42\times (-1)
31,457
x\times 2 + 1 \leq 2 + y\Longrightarrow y + 1 \geq x\times 2
11,791
\cos(-x + 2\pi) = \cos(x)
-20,526
-\frac{10}{1}\cdot \frac{7\cdot (-1) + s}{s + 7\cdot (-1)} = \dfrac{1}{s + 7\cdot (-1)}\cdot (70 - s\cdot 10)
30,038
xA + Ay = \left(x + y\right) A
13,640
\lfloor x \rfloor = 2\Rightarrow 2\leq x<2.55\;
17,914
r*2/3 + 2*(-1) = \dfrac{1}{6}*(-12 + 4*r)
-5,020
\frac{10.8}{10} = \frac{1}{10}10.8
18,135
x^4 + 18\cdot x^3 + x \cdot x\cdot 122 - x\cdot 720 + 3240\cdot (-1) = (180 + x^2 + x\cdot 20)\cdot (x^2 - 2\cdot x + 18\cdot (-1))
35,667
4 = (y^2 + 1)^{\dfrac{1}{2}} + (1 + \left(1/y\right)^2)^{\dfrac{1}{2}} = (y^2 + 1)^{1 / 2} \cdot (1 + \frac1y)
-20,450
-\frac{5}{4}\cdot \frac{r + 4\cdot (-1)}{r + 4\cdot (-1)} = \tfrac{1}{r\cdot 4 + 16\cdot \left(-1\right)}\cdot \left(20 - 5\cdot r\right)
-7,147
\dfrac{3}{44} = 3/11\cdot 3/12
2,702
\left(p = \tan{x} - \sin{x} \implies p = \frac{2\cdot x \cdot x \cdot x}{-x^2 + 4}\right) \implies 0 = x \cdot x \cdot x\cdot 2 + p\cdot x \cdot x - p\cdot 4
8,921
a \cdot a \cdot b = a \cdot a \cdot b
25,221
A^4 \cdot A = A^5
4,542
\frac{0 \times (-1) + y}{z + 0 \times (-1)} = y/z
22,248
(1 + l)*((-1) + l) = (-1) + l^2
12,115
\frac{1}{x \cdot c} = \dfrac{1}{c \cdot x}
33,573
2/3 = 1 - \dfrac{1}{3}
30,142
18 + y^2 - y*11 = \left(y + 2*(-1)\right)*(y + 9*\left(-1\right))
-2,465
\sqrt{325} + \sqrt{13} = \sqrt{13} + \sqrt{25\cdot 13}
10,101
x^{l/n} = (x^l)^{\frac{1}{n}} = (x^{1/n})^l
-30,546
\frac{d}{dz_1} z_2 = -\frac14\cdot \frac{1}{z_2^2}\cdot e^{z_1} = -\dfrac{e^{z_1}}{4\cdot z_2^2}
29,776
f + \left(-1\right) + 99/9 = f + 10
-2,970
11^{1/2}*(5 + 4 + 2*(-1)) = 7*11^{1/2}
35,395
\cos(x + y) = -\sin{x} \sin{y} + \cos{x} \cos{y}
-17,430
55 = 26\cdot (-1) + 81
6,353
(k + l) \cdot g = -(-k - l) \cdot g = -(-k \cdot g + -l \cdot g) = --k \cdot g - -l \cdot g = k \cdot g + l \cdot g
27,991
0 = (r + 1)^2*(r + (-1))^2 \implies r = 1,-1
38,158
2^{1/3}/2 = 4^{-\dfrac{1}{3}}
39,244
2^{6}=64
22,341
\frac14 + \frac15 - \tfrac{1}{5 \times 4} = \frac15 \times 2
29,879
\dfrac{1}{52} \cdot 26 \cdot 4/25 = \dfrac{1}{1300} \cdot 104
-437
\left(e^{\dfrac{23 i\pi}{12}}\right)^5 = e^{23 \pi i/12*5}
10,939
0 = a \cdot \sin(m) + b \cdot \cos(m) \cdot 0 = -a \cdot \sin\left(m\right) + b \cdot \cos\left(m\right)