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math_formulas

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-21,067
\frac12 = \frac16*3
-1,935
\pi/2 = -7/12 \cdot \pi + 13/12 \cdot \pi
-2,505
\sqrt{63} - \sqrt{28} = \sqrt{9\cdot 7} - \sqrt{4\cdot 7}
-10,770
-\dfrac{6}{20 + 50\cdot y} = 2/2\cdot (-\frac{3}{10 + 25\cdot y})
28,103
\sin(y) = \frac{1}{2*i}*(e^{i*y} - e^{-i*y})*\cos(y) = \left(e^{i*y} + e^{-i*y}\right)/2
49,670
1 * 1 + 1 + 1 = 3
5,686
(c + e) \cdot x = x \cdot c + e \cdot x
-12,369
125^{1 / 2} = 5^{\frac{1}{2}} \cdot 5
53,931
5400 = 1200 + 3600 + 600
15,233
5 + \dfrac{57}{350} = 1807/350
31,391
\cos{y} \sin{y} = \sin{y} \sin(-y + \frac{\pi}{2})
31,100
\dfrac16 \cdot 5 = \frac{5}{6}
18,686
\gamma^2 \coloneqq \gamma \cdot \gamma
43,491
\left(4 + 1\right)/2 = 2.5 = 2
-24,212
(2 + 2) \cdot (2 + 2) = 4^2 = 4^2 = 16
-20,639
\frac{-p + 3\cdot (-1)}{-p\cdot 4 + 12\cdot (-1)} = \frac{1}{-p + 3\cdot \left(-1\right)}\cdot (3\cdot (-1) - p)/4
6,018
\frac{1}{6}\cdot (2 + 1 + 2 + 2 + 1 + 2) = 5/3
-29,240
5 \times 0 + 0 \times (-1) = 0
-20,793
\frac{1}{(-1) + z} \left((-1) + z\right)/8 = \frac{1}{8z + 8\left(-1\right)}((-1) + z)
-20,718
4/4\cdot (9\cdot (-1) - 3\cdot x)/6 = \dfrac{1}{24}\cdot (36\cdot (-1) - x\cdot 12)
42,446
-2 = \left(-1\right)*5 + 3
16,646
(1 - t)^{-d} = (1 + t + t^2 + ...)^d
-6,436
\dfrac{40 \cdot y}{10 \cdot (y + 10 \cdot \left(-1\right)) \cdot (8 + y)} + \frac{(y + 8) \cdot 5}{\left(8 + y\right) \cdot (y + 10 \cdot (-1)) \cdot 10} - \frac{6}{(y + 8) \cdot (y + 10 \cdot (-1)) \cdot 10} \cdot (y + 10 \cdot (-1)) = \frac{1}{10 \cdot \left(8 + y\right) \cdot (10 \cdot (-1) + y)} \cdot \left((y + 8) \cdot 5 - 6 \cdot \left(y + 10 \cdot (-1)\right) + y \cdot 40\right)
16,246
z + 8(-1) = -4(x + 1) = -4x + 4(-1) \implies z + x \cdot 4 + 4(-1) = 0
18,462
4 = (2 \cdot a + g)^2 + 3 \cdot g^2 \geq (2 \cdot a + g) \cdot (2 \cdot a + g) + 12
-10,488
\frac1z*(4*z + 1)*3/3 = (3 + z*12)/(z*3)
31,486
\frac{1}{E \cdot K} = \tfrac{1}{K \cdot E} = K \cdot E = E \cdot K
-14,126
4 + 2\cdot 6 = 4 + 12 = 16
-10,486
-\frac{4\cdot q + 6}{q^2\cdot 5}\cdot \frac{12}{12} = -\dfrac{1}{60\cdot q^2}\cdot (72 + 48\cdot q)
974
\left(y * y = 9 \implies 9^{1/2} = y\right) \implies 3 = y
-22,263
\left(n + 2\cdot (-1)\right)\cdot (10\cdot (-1) + n) = n^2 - n\cdot 12 + 20
38,381
17\cdot 4 + 3 + 2 + 1 = 74
-3,319
6*\sqrt{5} = \sqrt{5}*\left(1 + 2 + 3\right)
15,483
(-1) + 35 + 6*(-1) = 28
-1,496
\frac{18}{45} = \frac{18\cdot \frac{1}{9}}{45\cdot \frac19} = 2/5
9,650
(x + y*y')^2 = \left(-y + x\right)^2*\left(1 + y' * y'\right)
9,662
\dfrac{1}{k^3} = \dfrac{1}{k^3}
20,543
((-1) + p)/2\cdot (1 + p)\cdot 2 = \left(-1\right) + p^2
19,678
-10 \times 11/2! + 12 \times 11 + \frac{1}{2!} \times 1320 + 9 \times 12 \times 11 \times 10/4! - \frac{110}{2!} \times 1 + 11 \times (-1) + 11 \times \left(-1\right) = 1155
28,777
3^{3^{(-1) + x}\cdot 3} = 3^{3^x}
12,535
x^{-k_2 + k_1} = \dfrac{x^{k_1}}{x^{k_2}}
-18,984
5/8 = X_s/(100\cdot \pi)\cdot 100\cdot \pi = X_s
22,060
\arctan\left(\frac{\sqrt{3}}{3}\right) = \arctan\left(\frac{1}{\sqrt{3}}\right) = \dfrac{\pi}{6}
38,255
\dfrac12*8*9 = \frac{72}{2} = 36
8,858
1 + x_0\cdot 2 = -x_0^2 + (x_0 + 1) \cdot (x_0 + 1)
17,552
{n \choose t} = {n + \left(-1\right) \choose t} + {n + \left(-1\right) \choose t + (-1)}
27,021
\dfrac{\pi^{1/2}}{2} = \int\limits_0^\infty e^{x^2}\,\mathrm{d}x \gt \int_0^1 e^{x \cdot x}\,\mathrm{d}x
19,841
-0.5 = 7 - \frac{15}{2} \neq \sqrt{(7 - \frac{15}{2})^2} = |7 - \frac12 \cdot 15| = 0.5
-22,266
(a + 1) (a + 8 (-1)) = a^2 - 7 a + 8 (-1)
8,578
\sin\left(3 \times y\right) = \sin(2 \times y + y) = \sin(2 \times y) \times \cos(y) + \cos(2 \times y) \times \sin(y)
1,188
m^3 + 3 \cdot (-1) = m^3/2 + m \cdot m \cdot m/2 + 3 \cdot \left(-1\right) > \frac{1}{2} \cdot m \cdot m \cdot m
29,741
4 \cdot l \cdot l + 4 \cdot \left(-1\right) = 4 \cdot \left(l^2 + (-1)\right) = 4 \cdot \left(l + 1\right) \cdot \left(l + (-1)\right)
-1,848
-2\pi + \pi\cdot 41/12 = 17/12 \pi
22,160
\sin(z) = \sin(\frac{z}{2})\cdot \cos(\tfrac{z}{2})\cdot 2
1,658
(2\cdot \left(5 t + 3\right))^2 + 2\cdot (5 t + 3) = 100 t^2 + 120 t + 36 + 10 t + 6 = 10\cdot (10 t t + 13 t + 40) + 2
19,257
d/dy (p \cdot \sqrt{p}) = \dfrac{1}{2 \cdot \sqrt{p}} \cdot p + \sqrt{p} = 3/2 \cdot \sqrt{p}
-19,079
\frac{1}{15} \cdot 2 = \dfrac{D_r}{100 \cdot \pi} \cdot 100 \cdot \pi = D_r
34,386
\frac{1}{y^2} y + \dfrac{x}{2 y} = \frac{1}{y} + \dfrac{1}{2 y} x = \frac{2 + x}{2 y}
14,487
\frac{1}{(r + (-1))^2} = -\frac{d}{dr} \frac{1}{r + (-1)}
-10,754
10 = -6 + 5f + 7(-1) = 5f + 13 \left(-1\right)
36,254
\sqrt{7 + 4*\sqrt{3}} = \sqrt{7 + 2*2*\sqrt{3}} = \sqrt{(\sqrt{3})^2 + 2^2 + 4*\sqrt{3}} = \sqrt{\left(\sqrt{3} + 2\right)^2} = \sqrt{3} + 2
31,903
-\cos^2(A) + 1 = \sin^2\left(A\right)
55,090
4\arctan\frac15 = \arctan\frac{(4/5)-(4/5^3)}{1-(6/5^2)+ (1/5^4)} = \arctan\frac{480}{476} = \arctan\frac{120}{119}
-20,011
\frac{-l\times 10 + 9\times \left(-1\right)}{3\times l + 5}\times \frac18\times 8 = \frac{-80\times l + 72\times (-1)}{40 + 24\times l}
24,458
(\frac12 + \frac{1}{6})/2 = \frac{1}{3}
2,760
6^{1/2} = (3*2)^{1/2} = 3^{1/2}*2^{1/2}
2,608
\frac{1}{x^2 + \left(-1\right)}\cdot (x^4 - 3\cdot x^2 + 2\cdot x + (-1)) = \frac{1}{(-1) + x^2}\cdot (2\cdot x + 3\cdot (-1)) + x \cdot x + 2\cdot (-1)
2,571
\left(4 4 - 3 3 + 2^2 - 1^2\right)/2 = 5
39,355
f\cdot C = C\cdot f
12,991
2^2 + 2 \cdot 4^2 = 3^2 \cdot 4
20,143
1 + n^2 - 2*n = \left(\left(-1\right) + n\right)^2
13,397
\frac12 \cdot \left(3^{2003} + (-1)\right) \cdot \left(3^{2003} + 1\right) = \left(3^{4006} + (-1)\right)/2
32,364
C^2 = C*C = C
29,603
c^{85*24 + 8} = c^{2048}
11,844
10^2 = R^2 + y^2 \Rightarrow \sqrt{10^2 - R^2} = y
11,415
0 + v + w + 0 = 0 + 0 + w + v rightarrow w + v = w + v
26,892
-34 = (-1)*2*17 = \left(-1\right)*(-2)*(-17)
32,399
2^{n + 2 \cdot \left(-1\right)} \cdot 2^6 = 2^{4 + n}
14,548
154 = 8\times 8 + 7\times 8 + 7\times 8 + 8\times (-1) + 8\times \left(-1\right) + 7\times \left(-1\right) + 1
-160
\frac{10!}{\left(10 + 3\cdot (-1)\right)!} = 10\cdot 9\cdot 8
12,765
(1 + n) \cdot 2 + n = n \cdot 3 + 2
-10,459
\dfrac{8}{16*s + 20*\left(-1\right)}*5/5 = \frac{1}{100*(-1) + 80*s}*40
18,150
1 = 3 \cdot (x \cdot y \cdot z)^{2/3} + 2 \cdot (-1) \leq x \cdot y + y \cdot z + z \cdot x + 2 \cdot \left(-1\right)
17,618
\left(1 + z\right)^m\cdot (1 + z)^m = (1 + z)^{m\cdot 2}
2,749
x = 5 \Rightarrow (-1)^x = -1
19,944
3 \cdot 741 = 2223
11,633
72 + z * z - 18 z = (12 (-1) + z) (z + 6(-1))
14,171
m + m + 1 + ... + m + 10 = 11 m + 55 = 11 (m + 5)
30,478
\left(\sqrt{2} (-z + 1)/2 = z \implies -z + 1 = \sqrt{2} z\right) \implies \sqrt{2} + (-1) = z
-1,835
\frac{π}{6} - 11/12 π = -\frac{1}{4}3 π
22,786
(n + 2*(-1))!*(2*(-1) + n)*(n + (-1)) = (n + (-1))!*(n + 2*(-1))
-5,012
10^{0 + 2} \cdot 3.6 = 10 \cdot 10 \cdot 3.6
12,172
-\cos\left(x\right) + \sin(x \times 0) = -\cos(x)
-5,659
\frac{5}{80 + s^2 - s*18} s = \frac{5 s}{(8 (-1) + s) (10 (-1) + s)} 1
-7,223
10^{-1} = \tfrac{6}{15} \cdot \frac{4}{16}
2,777
x^2 + z^2 = q^2\Longrightarrow -q^2 + x^2 + z \cdot z = 0
18,150
1 = 3 \cdot (x \cdot y \cdot z)^{2/3} + 2 \cdot \left(-1\right) \leq x \cdot y + y \cdot z + z \cdot x + 2 \cdot (-1)
20,303
\mathbb{E}\left(X*Y\right) - \mathbb{E}\left(X\right)*\mathbb{E}\left(Y\right) = \mathbb{E}\left(\left(-\mathbb{E}\left(X\right) + X\right)*(-\mathbb{E}\left(Y\right) + Y)\right)
16,014
f_1 \cdot z \cdot f_2 = z \cdot f_1 \cdot f_2
-13,527
\tfrac{49}{5 + 2} = 49/7 = \frac{49}{7} = 7