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ddrg
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math_formulas

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int64
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8,137
x^{10} + \left(-1\right) = \left(x^5 + 1\right) \cdot \left(x^5 + (-1)\right)
11,753
4\cdot \pi/3 = \frac{1}{3}\cdot 4\cdot \pi
18,543
4 + 4 \leq 5 + 1 \implies 6 \geq 8
40,025
100 \cdot 101 + \left(-1\right) = 10099
-175
\frac{1}{(9 + 5\cdot (-1))!}\cdot 9! = 9\cdot 8\cdot 7\cdot 6\cdot 5
-17,420
\dfrac{32.5}{100} = 0.325
-7,392
\frac12*3 / 4 = 3/8
6,624
-1 = \xi^k\Longrightarrow 1 = \xi^{2\cdot k}
11,489
0 = 2i\pi*0
5,636
x^3 + 6 x^2 + 11 x + 6 = (x + 1) (2 + x) (x + 3)
29,088
2 \sin(x) \cos(x) = \sin(2 x)
-17,717
56 + 53 (-1) = 3
22,020
4 + z^2 + 5 \times z = (1 + z) \times \left(z + 4\right)
2,809
-\frac{1}{1 + k} + \frac{k + 1}{k + 1} = 1 - \frac{1}{k + 1}
18,082
\left(-b + h\right) (h^{n + (-1)} + h^{n + 2\left(-1\right)} b + h^{n + 3(-1)} b * b \ldots b^{n + (-1)}) = -b^n + h^n
23,986
\dfrac{z^i}{b} \cdot b = (z/b \cdot b)^i
45,846
2\cdot (-3) = -3 - 3 = -6
37,514
3 \cdot 3 \cdot 3 \cdot 2^4 = 432
-6,213
\frac{3}{5\times x + 10\times (-1)} = \frac{3}{(x + 2\times (-1))\times 5}
-9,396
x*45 + 35 = 3*3*5*x + 5*7
1,541
R\cdot 2 = R - -R
20,435
4 = (-1)\cdot (-4) = \left(-4\right)\cdot (-1)
-30,974
60 \cdot{1} = 60
12,833
(a - b)^2 = b^2 + a^2 - a*b*2
1,998
\frac{58!}{38!} = 3 \cdot 13 \cdot 58!/39!
7,306
\tfrac{s}{\sqrt{s^2 + 1}} = \frac{d}{ds} \sqrt{s^2 + 1}
17,572
x^2 + zx + z^2 = (x + z)^2 - xz
26,241
2^{2 + i} = 2^3*2^{(-1) + i}
17,306
-3\cdot y^3 + y^2\cdot 8 + 5\cdot y + 6\cdot (-1) - 9\cdot y - y^3\cdot 3 + 6\cdot y^2 = y^2\cdot 2 - 4\cdot y + 6\cdot (-1)
26,113
A^{2001} = (A^2 \cdot A)^{667}
-5,019
10^{5 + 0} \times 13.8 = 10^5 \times 13.8
-23,553
\dfrac{4}{15} = \dfrac23 \cdot 2/5
-16,550
7 \cdot (9 \cdot 11)^{1/2} = 99^{1/2} \cdot 7
-6,149
\frac{q\cdot 2}{9 + q^2 + q\cdot 10} = \dfrac{q\cdot 2}{(q + 1)\cdot (q + 9)}\cdot 1
-14,043
9 + \tfrac{27}{9} = 9 + 3 = 9 + 3 = 12
11,423
\tan(\operatorname{atan}(x) + \operatorname{atan}(x \cdot x^2)) = \frac{x + x^3}{1 - x^4} = \frac{1}{1 - x^2}\cdot x
20,315
(z_1 + z_2) \left(z_2 - z_1\right) = z_2^2 - z_1^2
46,755
20 = 4^1 + 4^2
20,769
3g + E = (g + E) (g + E) (g + E) = \left(g + E\right)^2 \cdot (g + E)
-23,426
2/5 = \tfrac{\frac{1}{5}*4}{2}
-22,215
n^2 + n \cdot 7 + 8 \cdot (-1) = \left(n + (-1)\right) \cdot (n + 8)
-11,764
\tfrac{1}{100} = 10^{-1} \cdot 10^{-1}
17,246
\tfrac{1}{3.4^{1/2}} = \dfrac{1}{(4 - 0.6)^{1/2}} = \frac{1}{2\cdot (1 - 0.15)^{1/2}}
18,595
\cos(t + \pi \cdot x) = \cos(t) \cdot \cos(\pi \cdot x) - \sin(t) \cdot \sin(\pi \cdot x) = (-1)^x \cdot \cos(t)
20,940
295 = 5 \times 59
-9,432
-2*2*2*2*x*x - x*2*2 = -4*x - 16*x^2
31,908
\sin\left(z\right) = \sin\left(z + \pi*2\right)
26,413
153 = 18*17/2
2,126
E\left[B/B\right] = E\left[1\right] = 1 = \frac{E\left[B\right]}{E\left[B\right]}
5,479
\frac{4!}{2!}\cdot 3!/2! = 3!\cdot 3! = 36
16,456
{10 \choose 2} \cdot 8! = \frac{10!}{2!}
47,513
6 \cdot \binom{9}{2} \cdot 7! = 6 \cdot \frac{9!}{2! \cdot 7!} \cdot 7! = 3 \cdot 9! = 1088640
54,059
3 \cdot 3 = 9 = -1
31,080
1 = |9\cdot (-1) + 8|
-4,629
-\frac{1}{y + 4 \cdot (-1)} - \frac{1}{y + 3 \cdot (-1)} = \frac{-2 \cdot y + 7}{12 + y^2 - y \cdot 7}
32,637
0 = a^7 + 1 = \left(a + 1\right) (a^6 - a^5 + a^4 - a^3 + a \cdot a - a + 1)
6,943
\frac{\pi*(-1)}{12} = -\frac{1}{4}*\pi + \pi/6
10,656
(k^2 \cdot 2 + 2 \cdot k) \cdot 2 + 1 = (1 + k \cdot 2)^2
29,864
d^{\eta + z} = d^z\cdot d^\eta
-11,532
-6 + 8 \times i = -3 + 3 \times (-1) + 8 \times i
20,179
a + g + h = a + g + h
24,640
X^2 B = X \cdot X B
17
24 xx_2 x_1 = -(-x_1 + x + x_2) * (-x_1 + x + x_2) * (-x_1 + x + x_2) + (x_1 + x + x_2)^3 - (x_2 + x_1 - x)^3 - (-x_2 + x_1 + x)^2 * (x_1 + x - x_2)
9,078
g^{h + z} = g^z*g^h
2,534
h^{-1}g^rh=(h^{-1}gh)^r
30,864
(n + (-1))^2 + 1^2 = n^2 - n*2 + 2
11,658
\left((-1) + 2^{k + (-1)}*3\right)*2 = 3*2^k + 2*(-1)
5,032
g^m g^l = g^{m + l}
24,210
\frac{1}{2}\pi = \frac{\pi}{2}\left(1 + 0\right)
16,771
2 + 7 + 12 + 17 + \ldots + k \cdot 5 + 3 \cdot (-1) = \frac{k}{2} \cdot (5 \cdot k + (-1))
10,102
\sin(\pi/2 - t) = \cos(t)
16,657
\left((-1)\cdot 35.7 + x = 4.1\cdot (-1.34) \Rightarrow x = 35.7 + 4.1\cdot (-1.34)\right) \Rightarrow 30.206 = x
19,132
z + 3 (-1) \geq 0 \implies 3 \leq z
10,990
\pi\cdot n\cdot 2 + \pi/2 = \left(4\cdot n + 1\right)\cdot \pi/2
27,035
2^8 + 2^{11} + 2^k = (2^{k + 8(-1)} + 9) (2^4)^2
-26,573
16 - 49 \cdot z^2 = -(z \cdot 7)^2 + 4 \cdot 4
7,729
\dfrac{4!}{1!\cdot 3^1\cdot 1^1\cdot 1!} = 8
10,650
R = x \cdot x \cdot x rightarrow R^{\frac{1}{3}} = x
14,082
\frac{2\cdot \frac{1}{17}}{5\cdot \frac{1}{17}} = \frac25
-5,365
10^{2 + 1} \cdot 3.6 = 10^3 \cdot 3.6
-9,459
j \cdot 2 \cdot 2 \cdot 2 - j \cdot 2 \cdot 2 \cdot 7 \cdot j = 8 \cdot j - j^2 \cdot 28
25,929
0 = x^r + \left(-1\right) = (x + (-1))^r
-20,298
\frac{24}{72 (-1) - 80 k} = \frac188 \cdot \dfrac{3}{9(-1) - k \cdot 10}
10,760
x\cdot 2 + 1 + 2\cdot \alpha + 1 = 2\cdot (1 + \alpha + x)
-7,708
(-25 - 125*i - 5*i + 25)/26 = \frac{1}{26}*(0 - 130*i) = -5*i
34,038
\sum_{k=1}^n z_k x_k = \sum_{k=1}^n (z_k x_k + zx_k - zx_k) = \sum_{k=1}^n (z_k - z) x_k + \sum_{k=1}^n zx_k
-23,475
5/14 = \dfrac{1}{2}\cdot 5 / 7
34,527
n = 2^{n_1} \times n_2 = 2^{n_1} \times n_2
14,417
\frac{1}{\ln(y + 1)} = \frac{1}{y\cdot (1 - y/2 - \dfrac13\cdot y \cdot y + y^3/4 + \dotsm)}
14,420
(\sqrt{x} + 2 \cdot (-1)) \cdot (\sqrt{x} + 2) = x + 4 \cdot (-1)
539
-\frac18\cdot (\cos{\pi} - \cos{0}) = -\tfrac{1}{8}\cdot (-1 + (-1)) = \frac14
3,021
\cos(y) \sin\left(z\right) + \cos\left(z\right) \sin\left(y\right) = \sin(y + z)
-10,408
-\dfrac{1}{9 + 3 m} 9 = -\frac{3}{3 + m}\cdot 3/3
15,111
\left( x, C \cdot z \cdot \Phi(g)\right) = ( x, \Phi(g) \cdot z \cdot C)
10,931
\sin(\dfrac{21\cdot x}{2} - 2\cdot x/2) = \sin{\frac{19}{2}\cdot x}
-23,245
4/9*\frac{1}{7}*3 = 4/21
2,208
\dfrac{4 + (-1)}{52 + \left(-1\right)} = \tfrac{1}{51}3 = \frac{1}{17}
4,549
x^2 b^2 = (b x)^2
8,907
1 - 4 \cdot (x + 3 \cdot \left(-1\right)) = 1 - 4 \cdot x + 12 \cdot \left(-1\right) = 1 - 4 \cdot x + 12 = 13 - 4 \cdot x
33,228
2*x^2 = 2*x*x = 2*x*x = x*x = x * x