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ddrg
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math_formulas

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int64
-30,985
55.9k
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10,597
|f\times a| = |f|\times |a|
7,396
\left(a + 0*(-1)\right)*\left(a + 0*(-1)\right) = (a + 0)*(a + 0*(-1)) = a
20,249
10*\frac{654321}{123456} = 6*9 + (-1) + 6*7/123456 \approx 53
7,833
e^a\cdot e^{x\cdot i} = e^{x\cdot i + a}
26,929
\frac{(-1) + y^2}{y + (-1)} = 1 + y
29,870
\frac12 \cdot (a + \left(-1\right)) = \frac{1}{-1} \cdot (b + 3 \cdot \left(-1\right)) = \frac11 \cdot \left(c + 4 \cdot (-1)\right) = k \Rightarrow k \cdot 2 + 1 = a, -k + 3 = b, k + 4 = c
93
30 = 1^2 + 2 * 2 + 5 * 5 = 1^2 + 2 * 2 + 3^2 + 4^2
6,836
1/\left(\alpha\cdot x\right) = \frac{1}{\alpha\cdot x}
5,657
\left( c, f\right) \cdot \left(x + b'\right) = \left( x \cdot c - f \cdot b', b' \cdot c + b' \cdot c\right)
-5,374
48\cdot 10^{1 + 2} = 10 \cdot 10 \cdot 10\cdot 48
13,236
\dfrac{1}{2 v^2} = \frac{1}{2 v v} = \dfrac{1}{2 v^2}
1,358
\left(x = 15 + 84 - x\times 2 \Rightarrow 3\times x = 99\right) \Rightarrow x = 33
18,319
|g_l| = \sqrt{|g_l|^2}
-17,284
0.47 = 47/100
31,474
x^2 - y\cdot x\cdot 5 + 6\cdot y^2 = (-3\cdot y + x)\cdot \left(x - y\cdot 2\right)
23,138
\frac{38962}{97527} = 1 - \frac{{56 \choose 7}}{{60 \choose 7}}
15,843
H \times k \times g = g \times k \times H
36,007
\frac{15}{16} + \frac{3}{64} = 63/64 = 1 - \frac{1}{64}
-20,318
\tfrac{3*z + 21}{z + 7} = \frac{z + 7}{z + 7}*\frac31
2,999
2*\left(0*(-1) + x\right) = z + (-1) \implies z = 2*x + 1
10,516
7^4 - 7^3 + 7 * 7 + 7(-1) + 1 = 2101 = 11*191
-8,419
2 = -\dfrac{10}{-5}
-3,757
\frac{1}{y^3}y^3*96/120 = \dfrac{y^3*96}{y^3*120}
-22,720
\frac{1}{81}\cdot 90 = 9\cdot 10/(9\cdot 9)
-945
\frac92 = 9/2
4,317
0 = -(x - 9/2) \implies -9/2 = x
12,842
\mathbb{E}[y]\cdot \mathbb{E}[x] = \mathbb{E}[x\cdot y]
15,469
(f \cdot g)^2 = (f \cdot g)^2
15,645
\left(-x\right)^2 = (-1)^2\cdot x^2 = x^2
15,788
\frac{1}{8} \cdot 7 \cdot \pi = \pi - \pi/8
8,148
1 + l + \left(-1\right) + b + (-1) = l + b + \left(-1\right)
18,462
4 = (2\cdot h + b)^2 + 3\cdot b^2 \geq \left(2\cdot h + b\right) \cdot \left(2\cdot h + b\right) + 12
-20,271
4/4 \frac{-7y + 6\left(-1\right)}{6 - y*2} = \dfrac{1}{24 - 8y}(-28 y + 24 (-1))
5,356
x \implies (x^2 - 3 x + 1)^2 - 3 \left(x^2 - 3 x + 1\right) + 1 = x x - 3 x + 1 = x
22,788
\cos{2 \cdot F} - \cos{2 \cdot E} = -2 \cdot (\sin^2{F} - \sin^2{E}) = -2 \cdot (\sin{F} - \sin{E}) \cdot (\sin{F} + \sin{E})
-9,581
-0.8 = -8/10 = -\frac45
31,416
\|z\|_2^2 = z*z = z^2
27,261
(\left(-1\right) + p^2)^2 = p^4 - 2\times p^2 + 1
25,605
{12 \choose 4} = \frac{1}{4! \cdot 8!} 12!
12,842
\mathbb{E}(y*z) = \mathbb{E}(y)*\mathbb{E}(z)
-18,264
\frac{1}{k\cdot 6 + k^2}\cdot (54\cdot (-1) + k \cdot k - 3\cdot k) = \frac{(k + 6)\cdot (9\cdot (-1) + k)}{k\cdot (6 + k)}
22,696
3^{70} + 2^{70} = 3^{70} (1 + (2/3)^{70})
2,511
720 \cdot x^4 + 5280 \cdot x^3 + 12240 \cdot x^2 + x \cdot 11520 + 3840 = 240 \cdot (3 \cdot x + 4) \cdot (x + 4) \cdot (x + 1) \cdot (x + 1)
-7,755
\dfrac{1}{3 - i*5}(8 - i*2) \dfrac{3 + 5i}{5i + 3} = \frac{1}{-5i + 3}(8 - 2i)
35,281
5 \cdot \dfrac{16}{36} - 5 \cdot 20/36 = -\frac{20}{36} = -5/9
2,192
r = t_2 \cdot t_1 \Rightarrow r \cdot t_1 = t_2
-20,175
-\dfrac74\cdot \dfrac{2 - 6\cdot p}{2 - p\cdot 6} = \dfrac{1}{-24\cdot p + 8}\cdot (42\cdot p + 14\cdot (-1))
-20,327
\frac{1}{2x + 8(-1)}(8 - 20 x) = \frac{4 - x*10}{x + 4(-1)}*2/2
2,779
|h^2 + 2\cdot h\cdot b + b \cdot b| = |h^2 + h\cdot b + b^2 + h\cdot b| = |0 + h\cdot b| = |h\cdot b|
10,059
\frac{64}{72*2}1 = 32/72
16,192
\dfrac{1}{z^3 - d^3}\cdot z^3 = \frac{1}{z^3 - d^3}\cdot (z^3 - d^3 + d^3) = 1 + \frac{d^3}{z^3 - d^3}
33,628
3 \cdot 17 = 10 \cdot 10 - 7^2
33,856
\dfrac{2h}{2} = h
-11,099
(y + 3*(-1))^2 + f = \left(y + 3*(-1)\right)*\left(y + 3*(-1)\right) + f = y^2 - 6*y + 9 + f
-7,250
2/9 \cdot 5/8 = \frac{1}{36} \cdot 5
-18,935
31/36 = x_r/(81*π)*81*π = x_r
22,895
x\cdot 63\% = x\cdot 70\%\cdot 90\%
3,786
q^2 \cdot x = q \cdot q \cdot x
-26,364
-\dfrac14 \cdot 5 \cdot (-5/4) = 25/16
28,132
(X + U)^2 - X^2 - U^2 = U*X + U*X
11,852
-\tan(-\frac{\pi}{2} + x) = \cot(x)
30,156
(V + (-1))\cdot (V + 1) + 8\cdot 3 = 23 + V^2
5,233
99.75 = 3*\frac{1}{12}*(20 * 20 + (-1))
-19,012
17/18 = Y_s/(9\times \pi)\times 9\times \pi = Y_s
-2,345
-\dfrac{3}{20} + \frac{9}{20} = \tfrac{6}{20}
21,797
n^4\cdot n^3 = n^7
-5,494
\frac{1}{(6 + r) \cdot 5} \cdot 3 = \dfrac{3}{30 + 5 \cdot r}
24,957
\frac{1}{x^d}\cdot x^f = x^{f - d}
15,124
1/5 = \frac{12}{16}*4/15
20,424
\dotsm + h + \dotsm + a + \dotsm = \dotsm + a + \dotsm + h + \dotsm
5,091
-\frac{1}{2} + \frac3x = 6/(x*2) - x/(x*2)
5,077
\sin{y/2} = \cos{\tfrac{1}{2}y} = \sin(\pi/2 - \frac12y)
-29,321
-4 + 7*i = 7*i - 6 + 2
-9,146
z*2*2*2*2 + 2*2*2*2*2 = 16*z + 32
22,059
{l \choose Y} = {l + (-1) \choose (-1) + Y} + {(-1) + l \choose Y}
-7,748
a^2 - g^2 = (g + a)\cdot (a - g)
29,204
2 + a*b - a + b = 1 + ((-1) + b)*(a + (-1))
33,651
\frac{1}{y^2 \cdot 3 + 2} = \dfrac{1}{2 \cdot (1 + y^2 \cdot 3/2)}
6,526
(1 + 1) (z + y) = z + y + z + y = z + y + z + y
15,694
1 - 2 \times t + t^2 = \left(-t + 1\right)^2
18,485
(p\cdot e^{i\cdot 0})^3 = (p\cdot e^{i\cdot 2\cdot \pi}) \cdot (p\cdot e^{i\cdot 2\cdot \pi}) \cdot (p\cdot e^{i\cdot 2\cdot \pi}) = p^3
-20,517
-\frac{1}{z + 3\cdot (-1)}\cdot 5\cdot \frac19\cdot 9 = -\frac{45}{9\cdot z + 27\cdot (-1)}
29,538
2i = -1 + i \Rightarrow i = -1
15,727
|\frac{1}{2 + x} - \frac{1}{2 + z}| = \frac{|x - z|}{(2 + x) \cdot (2 + z)} \leq \dfrac{1}{4} \cdot |x - z|
-9,316
y \cdot 3 \cdot 3 \cdot 3 y - 3 \cdot 3 \cdot 13 y = -117 y + y y \cdot 27
-5,468
\dfrac{1}{4\cdot n + 20\cdot (-1)} = \frac{1}{(5\cdot (-1) + n)\cdot 4}
24,296
X*g*e rightarrow g*X*e
14,064
(b + 1) \cdot (b + a) = b \cdot \left(1 + a + b\right) + a
24,023
4 \cdot z_1^2 + x \cdot x + y^2 = 4 \cdot x \cdot y \cdot z_1 \cdot \dotsm \cdot \dotsm \cdot \dotsm \cdot \dotsm \cdot \dotsm \cdot \dotsm \cdot \dotsm \cdot \dotsm \cdot 2
31,876
7 + x^2 + 8x = (x + 1) (x + 7)
6,899
E[\bar{X}^2] = Var[\bar{X}] + E[\bar{X}]^2
-23,177
-\frac{1}{4} \cdot \left(-\frac18\right) = 1/32
-4,977
0.9 \cdot 10^{-3 - -3} = 10^0 \cdot 0.9
6,946
\cos(-\alpha + \pi/2) = \sin\left(\alpha\right)
28,091
\cos{C} \cdot \sin{B} + \sin{C} \cdot \cos{B} = \sin(B + C)
19,396
5 \cdot 5 - 2^2 \cdot 6 = 1 \cdot 1 \cdot 1
-6,705
6/100 + 10^{-1} = \frac{10}{100} + \frac{1}{100}\cdot 6
17,654
i^{-1} = -i\cdot (-i)^{-1}/i = \tfrac{1}{(-1)\cdot i^2}\cdot ((-1)\cdot i) = -i
-21,012
\frac{(-2)*r}{6 + r}*\frac14*4 = \frac{r*(-8)}{24 + 4*r}
-11,550
8 - 24 i = -i*24 - 8 + 16