Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
-22,322
(z + 6)\cdot (3\cdot (-1) + z) = 18\cdot (-1) + z^2 + 3\cdot z
6,803
\frac{1}{x}*(x + 1) = \frac{1}{-\frac{1}{1 + x} + 1}
43,103
t*\cos{t} = \frac{\frac{\text{d}z}{\text{d}t}}{t} - z*\frac{1}{t^2}*2 \implies \cos{t}*t^2 = \frac{\text{d}z}{\text{d}t} - z*2/t
25,613
\sqrt{5}/2 + 1 = 1 + \sqrt{5}/2
14,844
27 + 26\cdot F + L = (1 + F)\cdot 26 + L + 1
7,819
\frac47 + \frac173*\dfrac{3}{4} = \frac{1}{28}25
19,619
2^0 \cdot a = a
8,829
2*\left(4*x^2 - 3*x + (-1)\right) = 2*(x + (-1))*(x + 1/4) = \frac{1}{2*(x + (-1))*(4*x + 1)}
46,275
(0.3)(0.4)=0.12
16,428
(z + 4) \cdot (3 + z^2 - z \cdot 4) + (\left(-1\right) + z) \cdot 13 = \left(-1\right) + z \cdot z^2
24,095
1 - \frac{1}{1 + x} = \frac{x}{1 + x}
34,489
|-7^2 \cdot 7 + 2 \cdot 2 \cdot 2| = 335
2,188
0*\cdots = i
1,242
\gamma \cdot (k + n') = k \cdot \gamma + n' \cdot \gamma
29,437
(y^2 - 1 - y) \cdot (1 - y + 2 \cdot y^2) = 2 \cdot y^4 - 1 - y \cdot y^2 \cdot 3
-22,963
72/63 = \frac{72}{7*9}*1
27,157
a^2 - 2\times x\times a + 2\times x \times x = (-x + a)^2 + x^2
-28,859
11 + 4\cdot \left(-1\right) + 1 = 8
22,655
\mathbb{E}(X_x^2) \cdot \mathbb{E}(X_k^2) = \mathbb{E}(X_x^2 \cdot X_k \cdot X_k)
31,923
0.2112 = 2 \cdot 0.88 \cdot (1 - 0.88)
-5,042
36.4\cdot 10^{1 + 3} = 36.4\cdot 10^4
-19,283
\frac{2}{\frac18 \cdot 9} \cdot \frac{1}{9} = 8/9 \cdot \frac{1}{9} \cdot 2
-16,573
4*\sqrt{75} = 4*\sqrt{25*3}
22,791
Z^k\times Z^n = Z^{n + k}
-1,466
-18/28 = \frac{\left(-18\right) \cdot \frac{1}{2}}{28 \cdot 1/2} = -9/14
9,319
-\phi_1 + 2\phi_2 = \phi_1 + 2\pi n\Longrightarrow \phi_2 = n\pi + \phi_1
12,977
x = \frac12\cdot (3\cdot (-1) + x) + \frac{1}{2}\cdot (3\cdot (-1) + x) + 3
-9,901
22/25 (-2/25) = 22 (-2)/(25\cdot 25) = -\frac{1}{625}44
-2,830
6^{\dfrac{1}{2}} \cdot 25^{1 / 2} + 6^{\frac{1}{2}} = 6^{1 / 2} + 6^{1 / 2} \cdot 5
9,631
x^0 \times x^n = x^{n + 0} = x^n
-20,365
5/5\cdot \frac{t + (-1)}{1 + 6\cdot t} = \frac{1}{t\cdot 30 + 5}\cdot (5\cdot t + 5\cdot (-1))
-27,339
\cos{z}*\sin{z}*2 = \sin{z*2}
1,098
E_2 * E_2 + E_2*E_1 + E_1*E_2 + E_1^2 = E_2^2 + 2*E_2*E_1 + E_1^2
-20,697
\tfrac{1}{20*(-1) + 45*r}*(5*r + 20) = 5/5*\dfrac{1}{4*\left(-1\right) + 9*r}*\left(4 + r\right)
18,893
\sin(z + s) = 2\cdot \sin((s + z)/2)\cdot \cos(\dfrac12\cdot \left(s + z\right))
36,915
\alpha_k = \alpha_k
953
\left(\sqrt{(-1) + d^2} = -i\cdot d \Rightarrow d^2 + \left(-1\right) = -d \cdot d\right) \Rightarrow d = -\frac{1}{\sqrt{2}}
2,752
\frac{1}{n!} \cdot (n! - (n + \left(-1\right))!) = \dfrac{1}{n} \cdot (n + (-1))
2,627
\binom{6}{5} \cdot \frac{5^1}{6^6} = 30/46656
9,301
G_{11}\cdot Z = Z\cdot G_{11}
13,395
15 \cdot 0.9 \cdot 0.1 = 1.35
-29,240
0(-1) + 5 \cdot 0 = 0
-10,552
4/4\cdot \dfrac{z + 3}{z\cdot 5 + 10} = \dfrac{z\cdot 4 + 12}{z\cdot 20 + 40}
17,724
\dfrac{3}{8} + 9/16 = \dfrac{15}{16} \leq 1
34,440
\dfrac{\binom{7}{5}}{7!} = 1/240
-8,061
\frac{1}{-i*5 - 2}*\left(26 + 7*i\right) = \frac{1}{-2 + i*5}*(-2 + 5*i)*\frac{1}{-2 - i*5}*(26 + i*7)
26,924
39 = (-1) + 10 \cdot 4
-7,338
1/6 = \frac{1}{10}\cdot 3\cdot \frac59
21,167
0 = 60 + g^2 - 16 \cdot g \Rightarrow g = \frac{1}{2} \cdot (16 \pm \left(256 + 240 \cdot (-1)\right)^{\dfrac{1}{2}}) = 6,10
-18,954
\tfrac{3}{4} = \frac{1}{4 \cdot π} \cdot A_s \cdot 4 \cdot π = A_s
22,179
0 = 1 - \cos(c)*\cosh\left(c\right)\Longrightarrow \cos(c) - 1/\cosh(c) = 0
36,107
3^{1997} = \left(3^{20}\right)^{99} \cdot 3^{17}
23,857
4 + 9\times 7 = 67
-4,877
\tfrac{1}{100} \cdot 27.2 = 27.2/100
40,810
630 - 3\cdot 180 + 3\cdot 60 + 24\cdot \left(-1\right) = 246
8,301
0 = z^3 - 2\cdot z^2 - 5\cdot z + 6 = (z + \left(-1\right))\cdot \left(z + 2\right)\cdot (z + 3\cdot (-1))
24,702
2 \left(a_x + 2 (-1)\right) = 2 a_x + 4 (-1) > a_x
3,267
z^2 + z\cdot 5 + 6 = (2 + z) (3 + z)
9,870
\frac{1}{2!\cdot 2!\cdot 4!}8! + \frac{8!}{2!\cdot 4!} = 1260
-3,357
-\sqrt{13} + \sqrt{117} + \sqrt{325} = \sqrt{9\cdot 13} + \sqrt{25\cdot 13} - \sqrt{13}
14,676
36 \cdot (-1) + 16 = 45 \cdot (-1) + 25
8,440
z_2 \cdot z_1 = \frac{1}{z_2 \cdot z_1} = z_1 \cdot z_2
2,272
r_l - r \lt x \implies r_l \lt x + r
31,219
\dfrac16 \cdot (\sin(\pi) - \sin(0)) = 0
31,313
\cos\left(2\cdot \pi + x\right) = \cos(x)
9,520
\sin^2{x} = \cos^2{x}/4 = \dfrac{1}{4}*(1 - \sin^2{x})
-12,044
\frac{3}{4} = \tfrac{p}{16 \pi}*16 \pi = p
16,425
(a - b)^2 = \left(-a + b\right) \cdot \left(-a + b\right)
-15,794
67/10 = -\dfrac{5}{10} + 9/10\cdot 8
1,070
\left(x - a\right) (x - b) = x \cdot x - x\cdot (b + a) + ba
-4,751
\frac{1}{5 \cdot (-1) + x} \cdot 4 - \frac{3}{x + 4} = \frac{1}{x^2 - x + 20 \cdot \left(-1\right)} \cdot (31 + x)
28,226
y^8 + 4 = (2 + y^4 + 2 \cdot y^2) \cdot (2 + y^4 - 2 \cdot y^2)
-20,221
\dfrac19*8*9/9 = \frac{72}{81}
2,117
x + 1 - j + (-1) = 2 + x - j
-20,826
54\cdot s/(s\cdot \left(-45\right)) = ((-9)\cdot s)/(\left(-9\right)\cdot s)\cdot (-\frac65)
9,537
-\sin(b)*\cos(f) + \sin(f)*\cos(b) = \sin\left(f - b\right)
24,165
\sin\left(x\right) = 0\Longrightarrow 0 \neq \cos\left(x\right)
40,710
200\cdot 0.5 = 100
40,877
0 = 4\cdot x^2 - y^2 = (2\cdot x + y)\cdot (2\cdot x - y)
15,037
47^4 + 3\cdot 28^4 = 2593 \cdot 2593
8,159
3 = (12^{1 / 2}/2) \times (12^{1 / 2}/2)
9,878
\left(x^X\cdot A\cdot x\right)^X = x^X\cdot A^X\cdot x = -x^X\cdot A\cdot x
37,567
-\frac{33}{16} = -2 - 1/16
-10,269
\dfrac{9\cdot p + 6\cdot (-1)}{12\cdot (-1) + 24\cdot p} = \frac{3\cdot p + 2\cdot \left(-1\right)}{4\cdot (-1) + 8\cdot p}\cdot \frac{1}{3}\cdot 3
34,547
-5\cdot (5 + a\cdot 4) = -a\cdot 20 + 25\cdot (-1)
-25,213
\frac{\mathrm{d}}{\mathrm{d}\vartheta} \cos(e^\vartheta) = -e^\vartheta \cdot \sin\left(e^\vartheta\right)
9,530
p\cdot 2 = \beta + \alpha \Rightarrow 2\cdot p - \beta = \alpha
17,550
b + a' x a + a b' = a x a' + b a' + b'
-19,187
9/10 = X_p/(4\cdot \pi)\cdot 4\cdot \pi = X_p
12,118
(n + 5*(-1))*2 + (6*(-1) + n)*\left(n + 5*(-1)\right) = (5*(-1) + n)*(n + 4*(-1))
29,649
(n \cdot n + n \cdot 3 + 2 + 4 \cdot n + 4 + 6)/2 = \dfrac12 \cdot (n^2 + n \cdot 7 + 12)
54,714
\frac{49}{1.001} + \frac{1}{0.951} = 48.951048951 + 1.051524711 = 50.002573662
-17,812
65\times (-1) + 71 = 6
-3,371
275^{1 / 2} + 99^{1 / 2} = (9 \cdot 11)^{1 / 2} + \left(25 \cdot 11\right)^{1 / 2}
25,106
-y^n + z^n = \left(-y + z\right)*(z^{n + (-1)} + z^{2*(-1) + n}*y + y^2*z^{n + 3*(-1)} + \cdots + z*y^{n + 2*(-1)} + y^{n + (-1)})
26,944
3^{2*\frac14*3} = 9*((3^3)^{\frac{1}{2}})^{\dfrac{1}{2}} \approx 20.5
22,814
x_1 - x_4*1/2 = 0 \Rightarrow x_4*1/2 = x_1
6,901
\sin^2(z) = \frac{1}{-4}(e^{iz} - e^{-iz})^2 = -\dfrac{1}{4}\left(e^{2iz} + 2\left(-1\right) + e^{-2iz}\right)
1,389
g^{\frac{1}{2}}*g^{1 / 2} = g
24,878
\left(x^2 + x\right)^2 = x \cdot x + x + x^3 + x^3 = x^2 + x