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math_formulas

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\frac{1}{\frac{1}{8} \cdot (-1)} \cdot ((-1) \cdot 4 \cdot 1/5) = -\tfrac{1}{5} \cdot 4 \cdot (-8/1)
17,866
12 = 3 3 + 3 = 2^3 + 2^2
-17,172
-8 = -8*5 z - -8 = -40 z + 8 = -40 z + 8
16,006
\frac{c_1}{q}\cdot \frac{c_2}{s} = \frac{c_1\cdot c_2}{s\cdot q}\cdot 1
16,359
\sin(A - B) = \cos(B) \sin(A) - \sin(B) \cos\left(A\right)
5,342
\dfrac{2}{y + 4*\left(-1\right)} - \tfrac{1}{y + (-1)} = \frac{y + 2}{((-1) + y)*(y + 4*(-1))}
7,722
d^T x \leq 0 \Rightarrow -xd^T \geq 0
-6,428
\frac{1}{4\cdot y + 20\cdot (-1)}\cdot 5 = \tfrac{5}{(y + 5\cdot (-1))\cdot 4}
18,918
\frac{2 z^2}{z z + (-1)} = 2 + \frac{1}{z^2 + (-1)} (z + 1 - z + (-1)) = 2 + \frac{1}{z + (-1)} - \frac{1}{z + 1}
18,687
1 - 1/y = \frac{1}{-\frac{1}{1 - y} + 1}
520
8\cdot (-1) + 20 + 6\cdot (-1) = 6
35,532
g' x = g' g x = g g' x
-10,496
3/3 \cdot 9/a = \dfrac{1}{3 \cdot a} \cdot 27
-30,652
5 \cdot \left(-1\right) - z^2 \cdot 5 = -5 \cdot (z^2 + 1)
-6,980
56 = 4*2*7
-20,980
\dfrac{p + 10}{p + 10} (-9/10) = \dfrac{90 (-1) - 9p}{10 p + 100}
21,091
\sin{g} \cdot \cos{g} \cdot 2 = \sin{g \cdot 2}
-3,918
\frac{t^5}{t^2}\cdot 66/24 = \frac{66\cdot t^5}{t \cdot t\cdot 24}\cdot 1
24,497
\frac{1}{(1 + x^2)^{1/2}} = \cos(\operatorname{atan}(x))
4,816
b*a*2 = 2*-a*(-b)
1,065
9/2 - -\dfrac92 = 9/2 + 9/2 = 9 \neq 0
14,451
1 + z - 2 \cdot z^2 = \left(-z + 1\right) \cdot \left(1 + 2 \cdot z\right)
866
1/(A*a) = \frac{1}{a*A}
32,588
5 + 13^2 + 2 \cdot 13 = 5 \cdot 5 \cdot 8
1,551
\sqrt{4-(x-3)^2}=2\sqrt{1-((x-3)/2)^2}
37,387
|Q^Q| = 1 = |Q|
11,905
y\cdot 5 + x\cdot 12 = 1 \Rightarrow x = -2,1 = y
16,987
D I_\epsilon = D I_\epsilon
19,439
m*x + y*k = 1 \Rightarrow m*x = -y*k + 1
25,935
2^6 + 1 = \left(2^2 + 1\right) \cdot \left(1 + 3 \cdot 2^2\right) = 5 \cdot 13
30,870
x^2 = \alpha^2 \Rightarrow \alpha = x
6,094
\mathbb{Var}[X^2] = \mathbb{E}[(X^2)^2] - \mathbb{E}[X^2]^2 = \mathbb{E}[X^4] - \mathbb{E}[X^2]^2
26,097
-k * k + (1 + k)^2 = 1 + k*2
-20,989
-\frac{7}{-63} = \frac19 \cdot (\dfrac{1}{-7} \cdot (-7))
48,275
1234567 = 127 \times 9721
-12,018
19/24 = \dfrac{x}{12*\pi}*12*\pi = x
5,975
(fz)^2 = z^2 = (zf) \cdot (zf)
-20,905
\frac{3(-1) + x}{x + 3\left(-1\right)} (-7/4) = \dfrac{-7x + 21}{12 (-1) + x*4}
-15,825
5\cdot \frac{5}{10} - \frac{5}{10}\cdot 5 = 0
-13,276
6\times \left(9 + 4\right) = 6\times 13 = 78
21,648
g' \cdot g \cdot H := H \cdot g/g'
16,189
\pi\cdot 2 = 3\cdot \pi\cdot 2/3
4,198
\frac{1}{b}\cdot m\cdot b\cdot d/m = d \Rightarrow b\cdot d/m
27,148
11/6 + \dfrac14 = \dfrac{50}{24} = 25/12
-30,243
(4 + x)*(x + 4*(-1)) = x * x + 16*(-1)
17,869
(A * A * A)^T = (AAA)^T = A^T A^T A^T = (A^T)^3
1,723
(x + 2\cdot (-1))\cdot (x + 1) = 2\cdot (-1) + x^2 - x
-5,928
\frac{1}{3 \cdot z + 6} \cdot 3 = \frac{3}{(z + 2) \cdot 3}
-4,567
\frac{13 (-1) - z\cdot 4}{6(-1) + z \cdot z - z} = -\frac{5}{3(-1) + z} + \frac{1}{z + 2}
17,161
52 + y y*4 - y*40 = 0 \implies y = 5 \pm 2 \sqrt{3}
34,324
2^{200} - 2^{192}\cdot 31 + 2^{198} = (2^{96}\cdot 17) \cdot (2^{96}\cdot 17)
53,994
\ln\left(1\right) = 0
-4,052
100/40\cdot m/m = 100\cdot m/\left(m\cdot 40\right)
48,873
105 = \binom{7}{3}*3
37,399
m + 1 = {m \choose 1} + 1
20,884
1 \cdot 2 + (-1) = 1 \cdot 1
-9,381
2*7 - 2*2*3*z = 14 - z*12
20,734
\frac{9}{8} = \frac123*\frac143
-22,282
z^2 - 8 \cdot z + 7 = (7 \cdot \left(-1\right) + z) \cdot \left(z + (-1)\right)
31,069
10 = {3 + 3 + (-1) \choose 3 + (-1)}
3,106
\frac{1}{\left(x^2 + 1\right)^2} = \frac{1}{x^2 + 1} - \frac{1}{\left(x^2 + 1\right)^2} \cdot x \cdot x
7,847
37 = 7(-100) + 11*67
-18,439
\frac{30 + x^2 - 13 x}{-10 x + x * x} = \dfrac{1}{x*(x + 10 (-1))}\left(x + 3(-1)\right) (x + 10 (-1))
8,405
f + \left(g - f\right)/2 = \frac{1}{2}\left(2f + g - f\right) = \dfrac12(f + g)
30,694
x^{l + (-1)}\cdot l = \frac{\partial}{\partial x} x^l
-3,995
k*\frac{7}{6} = k*7/6
36,178
\cos(y) \times (1 - \sin^2(y)) = \cos^3(y)
-18,517
4 = \dfrac{1}{2}8
20,641
c\cdot x = 0 = x\cdot c
19,989
\frac{C}{b} \cdot b/b = \frac{1}{b} \cdot C
-24,669
52*i + 8 = 9 + 52*i + (-1)
5,265
1 + d + d^2 + d^3 + \dotsm + d^n = \frac{1}{1 - d} \cdot (-d^{n + 1} + 1)
19,779
64 + 16\times (-1) = 48
13,840
x^4 + \left(-1\right) = (x^2 + 1) \left(x^2 + (-1)\right) = (x + i) \left(x - i\right) \left(x + 1\right) \left(x + (-1)\right)
3,087
(-4 + 4\cdot (-1))/2 = -4
42,644
7!\cdot 7!\cdot 8 = 8!\cdot 7!
2,644
\dfrac{1}{2^4}\cdot {4 \choose 2} = \frac{1}{16}\cdot 6 = 3/8
-12,862
10/25 = \dfrac{2}{5}
-6,524
\frac{4}{4(9\left(-1\right) + y) (5(-1) + y)} = \frac{\frac{1}{4}}{(y + 9(-1)) \left(y + 5(-1)\right)}4
23,378
100 = 10 \cdot (15 + 5 \cdot (-1))
-20,330
\frac{1}{24*(-1) - t*9}*(-30*t + 80*(-1)) = 10/3*\frac{-3*t + 8*(-1)}{-3*t + 8*\left(-1\right)}
29,193
\left(-kb * b + h^2\right)*4 = -(2b)^2 k + (2h)^2
15,126
c^n/b*b = (\frac1b*c*b)^n
27,177
\frac{(2\cdot n)!}{(2\cdot n + 2)!} = \frac{1}{(2\cdot n + 2)\cdot (1 + 2\cdot n)}
511
x\cdot 0.5832 = 0.72\cdot x\cdot 0.81
-9,571
\tfrac44 = 1
6,600
2^{n + 1} + \left(-1\right) + 2^{n + 1} = 2\cdot 2^{n + 1} + (-1) = 2^{n + 1 + 1} + (-1)
19,432
84 = 4*3*(2*2 + 3)
2,538
G^2 = G_x^2 + G_z^2 \implies G = \sqrt{G_x^2 + G_z^2}
28,972
B^{m + 1} = B\cdot B^m
9,838
2 \cdot q = y + 4 \Rightarrow 2 \cdot q + 4 \cdot (-1) = y
28,765
(-1) + 2 \cos^2(t) = \cos(2 t)
4,807
x^2 + z*x*4 + z^2 = \left(2*z + 7*x\right)^2 - 3*(4*x + z)^2
-9,482
3\cdot (-1) + e\cdot 12 = e\cdot 2\cdot 2\cdot 3 + 3\cdot (-1)
17,064
y = \frac{1}{6}\cdot (-1 \pm \sqrt{12 + 1}) \Rightarrow y = (-1 + \sqrt{13})/6
1,190
\cos(\theta + \alpha) = -\sin\left(\alpha\right) \cdot \sin\left(\theta\right) + \cos(\alpha) \cdot \cos(\theta)
639
y^2 - 10\cdot y + 25 = (5\cdot \left(-1\right) + y)^2
25,644
y\times (-z) = -y\times z
8,870
1 \leq b \cdot b + d^2 \leq 2^2 rightarrow 1 \leq b^2 + d^2 \leq 4
33,686
3^2\cdot 2\cdot 5\cdot 2\cdot 5 \cdot 5\cdot 2^4\cdot 3 = 60^3