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ddrg
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math_formulas

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int64
-30,985
55.9k
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44,984
10001 = 73*137
-18,253
\frac{x\cdot (x + 7\cdot (-1))}{(7\cdot \left(-1\right) + x)\cdot (x + 2\cdot (-1))} = \dfrac{1}{14 + x^2 - x\cdot 9}\cdot (x^2 - 7\cdot x)
523
\cos{2*t} = 1 - \sin^2{t}*2
5,496
256 * 256^2 = 255^3 + 9^3 + 58^3
39,201
(3\cdot \sqrt{3} + 5\cdot (-1))/2 = -5/2 + \sqrt{3}\cdot 3/2
15,084
\frac1f*(g + h) = \frac{g}{f} + h/f
12,929
\arccos(\frac{(-1) + z^2}{1 + z \cdot z}) = q \cdot 2 \Rightarrow \cos(2 \cdot q) = \dfrac{z^2 + (-1)}{1 + z \cdot z}
5,883
r\cdot (x_1 + x_2) = r\cdot x_1 + r\cdot x_2
27,029
6^2 + 6*36 + 36^2 = 36*(1^2 + 6 + 6 * 6) = 36*43
2,368
\left(-1\right) + 2\cdot x = 2\cdot \left(-\frac12 + x\right)
22,920
F \cdot F^x = F^x \cdot F
-11,517
-20 i + 10 + 10 \left(-1\right) = -20 i
25,665
-7 * 7 + 1^2 - 3^2 + 5 * 5 = -2*4^2
12,792
-(-z' + x')^2 + \left(z' + x'\right)^2 = z'\cdot x'\cdot 4
-19,467
\frac{\dfrac12*3}{8*1/3} = \tfrac18*3*3/2
-4,902
10^{2 \cdot (-1) + 3} \cdot 0.18 = 0.18 \cdot 10^1
21,556
\frac12 + \frac14 \cdot (l + (-1)) = \frac{1}{4} \cdot (1 + l)
20,997
5 = \sqrt{9 + p} \Rightarrow 25 + 9 \cdot \left(-1\right) = p
39,804
|55 + 50 \times (-1)| = 5
-5,902
\frac{1}{q^2 + 4\cdot q + 32\cdot (-1)}\cdot 4 = \frac{1}{(8 + q)\cdot (q + 4\cdot (-1))}\cdot 4
-11,641
-4 + 6 \cdot (-1) + 10 \cdot i = 10 \cdot i - 10
31,034
2^3 - \dfrac42 = 6
11,503
5 - 5 \times p^2 - 24 \times p = -(5 \times p^2 + 24 \times p + 5 \times (-1)) = -(p + 5) \times (5 \times p + \left(-1\right))
-14,110
5 + \dfrac{28}{7} = 5 + 4 = 9
-16,340
6\sqrt{80} = 6\sqrt{16 \cdot 5}
24,502
l^2 - k^2 = \left(l - k\right)*\left(l + k\right)
18,955
(\frac35)^3 + \dfrac{1}{5} 2 (\frac{3}{5})^2 \cdot 3 = 81/125
14,370
n^2*2 = n*2 + k*4 \implies n^2*2 = (n + 2*k)*2
-20,423
\frac{y + 5}{y + 5}\cdot (-\frac{1}{5}\cdot 2) = \frac{-2\cdot y + 10\cdot (-1)}{5\cdot y + 25}
21,735
h\cdot a^{1 + i} = h\cdot a^{i + 1}
37,964
\frac{1}{2}*24 = 12
-3,985
16/32 \cdot \frac{m^3}{m^5} = \frac{16 \cdot m^3}{m^5 \cdot 32}
14,718
0 > 144 - 12\cdot a \Rightarrow a > 12
10,404
\frac12\cdot (3 + \sqrt{5}) = ((1 + \sqrt{5})/2)^2
30,606
y^2 + y + 8 = y^2 - 9 \cdot y + 8 = \left(y + (-1)\right) \cdot (y + 8 \cdot (-1)) = (y + 9) \cdot (y + 2)
8,659
v = h + x\Longrightarrow v - h = x
-5,252
\frac{1}{1000} \cdot 0.3 = 0.3/1000
33,168
\frac{1}{-z + 1} = 1 + z + z^2 + z * z^2 + \cdots
5,076
(1 - z)^{n + 3\cdot (-1)} = \left(-1\right)^{n + 3\cdot (-1)}\cdot (z + (-1))^{n + 3\cdot (-1)} = \left(-1\right)^{n + \left(-1\right)}\cdot (z + (-1))^{n + 3\cdot (-1)}
15,999
(y^2 - \sqrt{3} \cdot y + 1) \cdot (1 + y^2 + y \cdot \sqrt{3}) = y^4 - y^2 + 1
6,520
5/83 = \frac{\binom{13}{4}}{39\cdot \binom{13}{3} + \binom{13}{4}}
405
\left(1 + t^2\right) * \left(1 + t^2\right) - 2*t^2 = t^4 + 1
18,893
2\sin{\frac{1}{2}(M + y)} \cos{\left(M + y\right)/2} = \sin(M + y)
18,807
y*G*c/(c*y) = c*y*G/\left(c*y\right)
-22,047
\dfrac{35}{10} = \tfrac72
-11,482
-15 + 2 + 13 \cdot i = -13 + 13 \cdot i
10,001
-3\cdot (y + 2\cdot (-1))^2 = -3\cdot (2\cdot (-1) + y)\cdot (2\cdot (-1) + y)
14,892
0 = -((-1) + x) + (2 + x) \cdot (x + (-1)) \Rightarrow \left(x + 1\right) \cdot (x + (-1)) = 0
1,059
\frac1p = \frac{-\dfrac1p + 1}{(-1) + p}
29,046
\frac{0.054}{0.3 \cdot 0.6} \cdot 1 = 0.3
19,568
\left(3 + x = x^2 \Leftrightarrow 3\cdot (-1) + x^2 - x = 0\right)\Longrightarrow x = \frac{1}{2}\cdot \left(1 ± \sqrt{13}\right)
2,655
x^4 + a^4 = -x^3 a \cdot 4 + (a + x)^4 - 4 x a^3 - 6 x^2 a^2
24,633
4^n*4^n = 4^{2n} = 16^n
12,606
p = \frac{q}{q}\cdot p = q\cdot p\cdot q^2\cdot p\cdot q\cdot p
-3,823
\frac{r^4 \cdot 40}{70 \cdot r^3} = \frac{r^4}{r \cdot r \cdot r} \cdot 40/70
31,582
\cos(A + A) = \cos(A)*\cos\left(A\right) - \sin\left(A\right)*\sin\left(A\right) = \cos^2(A) - \sin^2(A)
-2,766
7^{\dfrac{1}{2}}*9^{1 / 2} + 7^{\dfrac{1}{2}} = 7^{1 / 2}*3 + 7^{\frac{1}{2}}
-10,599
\frac{1}{9 \cdot \left(-1\right) + 3 \cdot q} \cdot 3 = \frac{3 \cdot 1/3}{3 \cdot \left(-1\right) + q}
-18,538
42/30 = \dfrac{1}{5}7
13,959
\sin{z} = z \cdot (1 - \frac{1}{3!} \cdot z^2 + z^4/5! - ...)
-22,995
\tfrac{70}{98} = \tfrac{5 \cdot 14}{14 \cdot 7}
35,829
\cos^2(x) = \dfrac12*(1 + \cos(2*x))
5,074
\left(1 = x\cdot z\cdot \frac{1}{z}/x \Rightarrow z\cdot x/z = x\right) \Rightarrow x\cdot z = z\cdot x
-603
e^{11*\frac12*\pi*i} = (e^{\dfrac12*i*\pi})^{11}
8,322
T^p T^q = T^p T^q
1,768
[h, e] = \left[c, d\right] \implies h = e,d = c
-10,412
-\tfrac{1}{k\cdot 4}(k + 6) \frac155 = -\left(30 + 5k\right)/(20 k)
34,313
x + 2 = 0 \Rightarrow x = -2
7,871
\frac{1}{36} = 1/4 - \dfrac{2}{9}
-28,872
(-6^0 + 6^1) \cdot 6^x = 6^x \cdot 5
21,001
x^4 = (1 - x)^2 = x^2 - 2 \times x + 1 = 1 - x - 2 \times x + 1 = 2 - 3 \times x
12,733
900 = 360*(-1) + 1260
-17,226
-44/5 = -\frac1544
-1,719
0 - \pi*7/6 = -\pi*7/6
15,558
2 \cdot (a - g) = g^3 - a \cdot a \cdot a = (g - a) \cdot (g^2 + a \cdot g + a \cdot a)
5,430
b \cdot X \cdot x rightarrow b \cdot X \cdot x
-20,041
\frac{-t\cdot 27 + 18\cdot (-1)}{t\cdot 15 + 10} = \frac{2 + t\cdot 3}{2 + 3\cdot t}\cdot \left(-9/5\right)
-17,369
\frac{1}{100} \cdot 17.1 = 0.171
15,926
-(y + (-1)) (y + 3) = 3 - y^2 - y\cdot 2
-6,018
\dfrac{1}{l*5 + 50} 2 = \dfrac{1}{(10 + l)*5} 2
-10,316
2/2*(-\frac{4}{3*n + 3}) = -\frac{8}{6*n + 6}
-20,087
\frac{1}{4 + o \cdot 3} \cdot (o + 5 \cdot \left(-1\right)) \cdot 7/7 = \frac{1}{28 + o \cdot 21} \cdot (35 \cdot (-1) + o \cdot 7)
2,112
0 = (a - d) \cdot (a - d) + 3 \cdot c^2 \Rightarrow a = d, c = 0
-2,271
\tfrac{1}{3} 2 = 8/12
29,389
\cos{\pi/12} = \cos(\dfrac{1}{3} \cdot \pi - \pi/4) = \cos{\frac{\pi}{3}} \cdot \cos{\frac{\pi}{4}} + \sin{\pi/3} \cdot \sin{\frac14 \cdot \pi} = \frac12 \cdot 1/(\sqrt{2}) + \dfrac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{2}} = \frac{1 + \sqrt{3}}{2 \cdot \sqrt{2}}
2,271
x\cdot c/c\cdot c = c\cdot x
10,039
(l + 1)! = l!*(l + 1) \Rightarrow (1 + l)! - l! = l*l!
10,903
x = a,w = d \implies a\cdot w = d\cdot x
23,542
(r + 1)^3 - r^3 = 1 + r^2*3 + r*3
17,906
U\cdot B = B\cdot U
-24,892
2/15 = q/(12 \pi) \cdot 12 \pi = q
4,337
5^{3*m} + 2*5^{2*m} - 5^m + 2*(-1) = (5^m + 2)*(5^{2*m} + (-1)) = (5^m + 2)*\left(5^m + (-1)\right)*(5^m + 1)
25,238
\tan(x + \frac{1}{4}\times \pi) = \cot(-x + \dfrac{1}{4}\times \pi)
-18,368
\frac{(r + (-1))\cdot r}{(9\cdot (-1) + r)\cdot ((-1) + r)} = \tfrac{-r + r \cdot r}{r^2 - r\cdot 10 + 9}
42,703
2^7 = 2^4*(1 + {7 \choose 1})
-9,125
z \cdot z\cdot 54 = z\cdot 2\cdot 3\cdot 3\cdot 3 z
27,319
q - t + s = -s + q - t
24,279
\left(a^3\right)^n + n = (a^3)^n + n^3 - n^3 + n = (a^n + n)*((a^2)^n - n*a^n + n^2) - n^3 + n
-15,150
\frac{1}{x \cdot (a^4 \cdot x \cdot x)^5} = \frac{1}{a^{20} \cdot x^{10} \cdot x}
-18,364
\frac{x \cdot \left(8 \cdot \left(-1\right) + x\right)}{\left(x + 8 \cdot (-1)\right) \cdot \left(x + 5\right)} = \frac{-8 \cdot x + x \cdot x}{x^2 - 3 \cdot x + 40 \cdot (-1)}