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ddrg
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math_formulas

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int64
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\frac{1}{y^2} + y \cdot y = 2 \cdot (-1) + \left(y + \dfrac{1}{y}\right)^2
-6,100
\tfrac{3 \cdot r}{r^2 + r \cdot 18 + 80} = \dfrac{1}{(r + 8) \cdot \left(r + 10\right)} \cdot r \cdot 3
22,389
A\cdot \delta\cdot 2 + \delta \cdot \delta = \left(A + \delta\right)^2 - A \cdot A
8,873
{i + k + 1 \choose i} - {i + k \choose (-1) + i} = {i + k \choose i}
31,620
u = \sqrt{\frac{x + 1}{x + (-1)}} \Rightarrow x = \frac{1}{u^2 + (-1)} \cdot \left(u^2 + 1\right) = 1 + \frac{1}{u^2 + (-1)} \cdot 2
26,368
k \cdot k + (-1) = ((-1) + k) \cdot (1 + k)
3,244
-3/2*l + l^2/2 = -l + {l \choose 2}
-20,215
\frac{35*y + 30}{-28*y + 24*(-1)} = -\frac{1}{4}*5*\dfrac{-7*y + 6*(-1)}{-y*7 + 6*(-1)}
-26,008
\frac{1}{1 - 4i}(9 - i*2) = \frac{1}{-4i + 1}(9 - 2i) \frac{1 + 4i}{4i + 1}
-20,012
\frac{l*15 + 25}{40 + 24*l} = \dfrac{l*3 + 5}{l*3 + 5}*5/8
41,813
\frac{-\tan^2(\frac{y}{2}) + 1}{\tan^2(\frac{y}{2}) + 1} = \cos(y)
5,439
144 + b^2 - 24\cdot b = \left(b + 12\cdot (-1)\right)^2
-29,702
d/dx x^\theta = \theta\cdot x^{\theta + (-1)}
-22,266
g * g - 7*g + 8*(-1) = (g + 8*(-1))*(1 + g)
32,465
\sin\left(2*x\right) = \sin(x)*\cos(x)*2
30,198
y*a = a*y
42,091
(x-y)+2y = x - y + y + y = x+y
-21,021
\frac{1}{10*n}*(-n + 5*(-1))*\frac55 = (-5*n + 25*\left(-1\right))/(50*n)
6,615
\sin{z} = \cos{z} \implies (e^{i\cdot z} - e^{-z\cdot i})/\left(i\cdot 2\right) = (e^{i\cdot z} + e^{-z\cdot i})/2
192
y_0^2 = (1 - y_0)^2 + (2 - y_0)^2\Longrightarrow y_0^2 - y_0 \cdot 6 + 5 = 0
38,387
-0.2*0.9*0.5 + 1 = 0.91
2,070
8881 = (95 + 12)\cdot \left(12\cdot (-1) + 95\right)
-11,867
0.007585 = 7.585 \cdot 0.001
10,632
1 + 3 + 3^2 + \ldots + 3^{(-1) + x} = ((-1) + 3^x)/2
13,123
y^{f + c} = y^c y^f
21,315
T + 10*\left(-1\right) + 3*(T + 30*\left(-1\right)) = 0\Longrightarrow T*3 + 90*(-1) + T + 10*\left(-1\right) = 0
37,402
s^2 + (-1) = 1 + s^2 + 2(-1) = 2s
26,005
v*r*u + u*s*v = \left(r + s\right)*u*v
12,631
\frac{1}{7} \cdot 5 = \frac{5}{7}
-20,636
10/10 \cdot \frac{1}{3 + r} \cdot \left(8 \cdot (-1) - r \cdot 6\right) = \dfrac{1}{r \cdot 10 + 30} \cdot (-r \cdot 60 + 80 \cdot (-1))
35,992
19 = 3^0 + 3 \cdot 3 \cdot 3 - 3 \cdot 3
-20,040
\frac{1}{-x\cdot 6 + 2\cdot \left(-1\right)}\cdot (4 - x\cdot 3)\cdot \tfrac33 = \frac{12 - 9\cdot x}{6\cdot (-1) - 18\cdot x}
32,864
\cosh(R) = \frac{\mathrm{d}}{\mathrm{d}R} \sinh(R)
7,031
\left(x^{45} = \dfrac{x^{46}}{x} = \frac{1}{x}\Longrightarrow 1/x = 8\right)\Longrightarrow x = \dfrac{1}{8} = 6
17,601
z^{\frac{1}{q}\cdot \mu} = (z^\mu)^{1/q} = (z^\mu)^{\frac{1}{q}}
-23,129
-1/2\cdot \dfrac14\cdot 3 = -\dfrac38
16,670
\left(x - r\right) \left(-r + x\right) = \left(-r + x\right)^2
23,095
5 = \sqrt{4^2 + \left(-3\right)^2}
12,589
\frac{2}{6} = \frac16 + 1/6
10,686
d/dy \csc^2\left(y\times 4\right) = d/dy \csc^2(y\times 4)
3,942
|y_1 + y + y_2| = |y_1 + y + y_2|
17,103
\left(C'\cdot j/j\right) \cdot \left(C'\cdot j/j\right) \cdot \left(C'\cdot j/j\right) = \frac{C'^3\cdot j}{j}
-4,602
-\tfrac{1}{3 \cdot (-1) + x} + \frac{1}{x + 5} \cdot 3 = \frac{1}{15 \cdot (-1) + x^2 + 2 \cdot x} \cdot (14 \cdot \left(-1\right) + 2 \cdot x)
-20,674
\frac{1}{z*10 + 60*\left(-1\right)}*(54*(-1) + 9*z) = \frac{6*(-1) + z}{z + 6*\left(-1\right)}*\frac{9}{10}
-4,180
8x^2/11 = x^2*8/11
-3,586
2*2*2*2*2*2 = 64
15,046
\frac{z^2}{z-2} = z^2 \frac{1}{z-2}
24,821
C*B*A = A*B*C
-448
(e^{\dfrac{\pi*i}{4}*1})^{12} = e^{12*i*\pi/4}
24,127
4500 = (1 + 9999 + 1000\cdot (-1))/2
28,146
\left(x\cdot y\right)^2 = x \cdot x\cdot y \cdot y
16,241
\binom{r}{i} = \dfrac1i\binom{r + (-1)}{i + \left(-1\right)} r
3,586
0.0625\cdot 0.8888 = 0.0625\cdot \left(0.0001 + \dotsm + 0.1111\right)
38,634
\dfrac{W\pi}{\pi} = W
15,301
\arccos\left(x\right) = X \Rightarrow x = \cos\left(X\right)
1,890
\frac{1}{2\cdot \sqrt{\pi}} = \frac{1}{(4\cdot \pi)^{1/2}}
39,661
y^2 = l \Rightarrow y = \sqrt{l}
-22,930
5\cdot 8/(5\cdot 9) = 40/45
-30,573
\frac{1}{t + 5*(-1)}*(t^2 - 3*t + 10*(-1)) = \frac{1}{t + 5*(-1)}*(t + 2)*(t + 5*(-1)) = t + 2
28,674
\left(h^3 = b\cdot b\cdot h \Rightarrow (b\cdot h\cdot b)^k = b\cdot h^k\cdot b = h^{3\cdot k}\right) \Rightarrow h^k\cdot b = b\cdot h^{3\cdot k}
-18,984
5/8 = A_p/\left(100\cdot \pi\right)\cdot 100\cdot \pi = A_p
1,269
det\left(A \cdot F\right) = det\left(F \cdot A\right)
5,565
\binom{7}{2}*\binom{5}{2}*3! = 7!/\left(2!*2!\right)
21,066
\left(-1\right) + l + m = l + (-1) + m
9,430
6*(-1) + 9 = 3 \implies 15 = 6*\left(-5\right) + 9*5
22,793
x \cdot q + (-1) - x + q + 2 \cdot \left(-1\right) = x \cdot q - x - q + 1 = (x + (-1)) \cdot (q + (-1))
8,583
\frac{(-1)^n}{(-1)^{n*2}} = \frac{1}{(-1)^n}
27,288
(x_i + 1) \cdot (x_k + \left(-1\right)) = x_i \cdot x_k + x_k - x_i + (-1) > x_i \cdot x_k
3,626
a^2 = h^3 = g^3 = a \cdot h \cdot g
-18,252
\tfrac{1}{(4\cdot (-1) + a)\cdot a}\cdot (a + 4\cdot (-1))\cdot \left(3 + a\right) = \dfrac{1}{-a\cdot 4 + a^2}\cdot (a^2 - a + 12\cdot (-1))
13,821
-\frac{1}{\xi^2} = \frac{\text{d}}{\text{d}\xi} \frac{1}{\xi}
26,810
0 = \left(0 + 1\right)\cdot \frac12\cdot 0
32,027
x \cdot y \cdot r = r \cdot x \cdot y
3,276
T^{x + k} = T^x\cdot T^k
522
5 - 0 \cdot 3 + 9/3 = 5 + 0(-1) + 9/3 = 5 + 0\left(-1\right) + 3 = 5 + 3 = 8
33,747
2^{\frac13 \cdot 2} = 2^{2/3}
13,668
\cos(\lambda) = \frac{1}{\cos(\lambda)} \times \left(1 - \sin^2(\lambda)\right)
5,020
|x| = \sqrt{x \cdot x} < \sqrt{x^2 + 1}
-20,076
\dfrac{9 - n}{n \cdot 6 + 54 \cdot (-1)} = \frac{9 \cdot (-1) + n}{n + 9 \cdot (-1)} \cdot (-1/6)
30,597
\frac{20}{20}\times 2 = 2
-13,086
2 \cdot (-2) = 2 \cdot (-2)/(1) = -4/1
448
n^2 + m^2 = a^2 + b^2 = (n - a)^2 + (m - b)^2
17,255
\binom{m + 2}{1 + m} = \binom{m}{m} + \binom{1 + m}{m}
32,511
(1 + n)! - n! = nn!
1,611
\dfrac{1}{10} = \dfrac{1}{8} \cdot \frac{4}{5}
19,524
3*3/4/1 = 9/4
-4,565
(2 + y) \cdot (y + 3) = y^2 + y \cdot 5 + 6
12,500
a^{∞} \cdot a = a^{∞}
29,527
i + (-1) + k - i = (-1) + k
31,925
A - E \cup Y = A \cap E \cup Y^\complement = Y^\complement \cap (A \cap E^\complement) = E^\complement \cap \left(A \cap Y^\complement\right) = A - Y - E
31,525
b_J = \overline{\overline{b_J}}
30,471
\frac14 \cdot (\sqrt{5} - 1) = \cos(2 \cdot π/5)
17,900
(d^T Ub)^T = b^T U^T d = b^T Ud
7,531
\mu*g + x^2 + (\mu + g)*x = \left(\mu + x\right)*(g + x)
13,333
0 = (-52)^2 + 52 \cdot \left(-52\right)
-22,265
(5 (-1) + t) (t + 10 (-1)) = t^2 - t\cdot 15 + 50
9,651
\lim_{h \to 0} \mathbb{E}\left(y\right) \cdot (\mathbb{E}\left(h\right) + (-1)) \cdot \cdots = \lim_{h \to 0} \mathbb{E}\left(h + y\right) - \mathbb{E}\left(y\right)
-29,935
\frac{\mathrm{d}}{\mathrm{d}z} \left(-z^3\right) = -\frac{\mathrm{d}}{\mathrm{d}z} z^3 = -3z^2 = -3z^2
37,413
(z + 3)\cdot (3\cdot (-1) + z) = z \cdot z + 9\cdot (-1)
41,369
111 = 258 + 147*\left(-1\right)