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math_formulas

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int64
-30,985
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28,656
z^2 + z + 1 = (1/2 + z)^2 + 3/4
19,436
( a'^2*4 + b'^2*8 + 10, 20) = ( 5 + 2 a'^2 + 4 b'^2, 10)*2
-6,020
\frac{2}{2 \cdot \left(y + 8 \cdot (-1)\right)} = \frac{2}{y \cdot 2 + 16 \cdot (-1)}
31,477
(2*n)^2 + (2 + n*2)^2 + \left(n*2 + 4\right)^2 = (n^2*3 + n*6 + 5)*4
7,715
A \cdot t^{A + (-1)} = \frac{\partial}{\partial t} t^A
-23,475
\frac{5}{14} = 5\cdot 1/7/2
5,135
\frac{1}{3}\times 392 + 1120/3 = \tfrac13\times 1512 = 504
10,881
\frac{60.0}{5} = 12.0
-3,188
\sqrt{16*5} - \sqrt{9*5} = -\sqrt{45} + \sqrt{80}
22,109
\frac1b\cdot c = \frac{c}{b}
26,413
153 = \frac{17*18}{2}
2,301
(8\cdot l)^2/2 = 32\cdot l \cdot l
23,245
5278 = 13\cdot \frac{29}{2}\cdot 28
-1,581
\pi/6 + \pi*\frac{23}{12} = \frac{1}{12}*25*\pi
18,042
(1 + \sqrt{-5})\cdot (1 - \sqrt{-5}) = 6
-20,458
-9/2*\frac{-l + 1}{-l + 1} = \frac{9*(-1) + 9*l}{2 - 2*l}
13,945
b^y = \left(\frac{1}{b}\right)^{-y} = (\frac{1}{b})^{-y}
8,724
\sin(2\cdot q) = 2\cdot \sin(q)\cdot \cos\left(q\right)
1,584
n = 316^2 - 3^6 \cdot 17 = 316^2 - 3^4 \cdot 3^2 \cdot 17 = 316 \cdot 316 - 3^4 \cdot (296^2 - n)
26,938
(-1) + y\cdot 2/z = \dfrac1z (-z + y\cdot 2)
-20,911
\left(10\cdot p + 10\right)/(p\cdot \left(-60\right)) = (1 + p)/(p\cdot (-6))\cdot 10/10
4,767
n + 4 \cdot (-1) = 1\Longrightarrow 5 = n
-716
-\pi \cdot 24 + \pi \cdot 25 = \pi
-4,336
\frac{1}{2s * s} = \dfrac{1}{2s^2}
-25,784
\dfrac{11}{4}\frac{1}{12} = 11/48
19,418
1/(1/(1/25)) = 1/25*1^{-1}/1 = 1/25
3,739
-\frac{1}{100} + \frac{1}{10} + \frac{1}{10} = \frac{19}{100}
6,934
t^{(-1) + a}*t = t^a
11,325
\frac15 = 1/(6*\frac{5}{6})
-1,884
-π \dfrac74 + π\cdot 3/2 = -π/4
3,037
\frac{\sin x^5}{x} = x^4 \frac{\sin x^5}{x^5} \to 0 \cdot 1 = 0
-29,556
\dfrac{1}{x}\cdot (6\cdot x^2 - x\cdot 4 + 3\cdot \left(-1\right)) = -3/x + \dfrac{x^2\cdot 6}{x} - \dfrac{4\cdot x}{x}\cdot 1
14,959
|-x \cdot I + X \cdot B| = |-I \cdot x + B \cdot X|
-25,809
5\cdot 1/4/10 = \frac{5}{40}
9,042
9 = -4\times p \Rightarrow -\dfrac{9}{4} = p
-13,445
\frac{6}{10 + 4 \cdot (-1)} = \frac{1}{6} \cdot 6 = \dfrac16 \cdot 6 = 1
8,066
3^2 + 4^2 + 5^2 = 5^2 + 5^2 = 2 \cdot 5^2
-1,162
\frac{1}{6 \cdot \dfrac15} \cdot (\tfrac19 \cdot \left(-5\right)) = 5/6 \cdot (-\tfrac{5}{9})
12,342
2*y'*z + x*2 = (-x + 2*x * x + 2*z * z)*2*((-1) + 4*x + 4*y'*z)
10,935
\cot(\frac{1}{2}*\pi + x) = -\tan\left(x\right)
29,697
13 = -3 \cdot 6 + 31
31,879
2^{2^2} =16
10,912
2*135689^2 = 39^5 + 75^5 + 128^5
15,835
\pi + \tan^{-1}{-1} = \pi - \frac{\pi}{4} = \frac{3}{4} \cdot \pi
28,045
0.5441 = \left(1 - 0.01\right)*0.51 + 0.08*0.49
-30,556
-200/(-100) = -\dfrac{100}{-50} = -\frac{50}{-25} = 2
18,033
N = \sqrt{(-N)^2} = \sqrt{-N}*\sqrt{-N}
20,276
x\cdot y^2\cdot y = x\cdot y^3
1,978
\cos\left(\tfrac32\pi\right) = 0
4,860
(120 + 20)*(x + 3*\left(-1\right)) = 140*(x + 3*(-1)) = 140*x + 420*\left(-1\right)
4,000
x^3 + 8\left(-1\right) = (x^2 + 2x + 4) (x + 2(-1))
12,848
\sqrt{b^2 - 4\cdot c} = i\cdot \sqrt{4\cdot c - b \cdot b} = i\cdot \sqrt{\|b^2 - 4\cdot c\|}
-7,019
4/35 = \frac{1}{5} \times 2 \times 3/6 \times 4/7
-5,709
\frac{4}{4n + 36} = \dfrac{4}{4(n + 9)}
-4,903
3.65\cdot 10 = \dfrac{3.65\cdot 10}{100} = \dfrac{3.65}{10}
30,049
\cos\left(\operatorname{acos}(t)\right) = t
-6,344
\dfrac{4}{2 (r + 8) (r + 6)} = \dfrac{1}{(6 + r) \left(r + 8\right)} 2*\frac{2}{2}
-16,594
9\sqrt{25*7} = \sqrt{175}*9
10,672
1 - \sin^2\left(\frac{t}{2}\right)\cdot 2 = \cos(t)
20,629
3^2 = 11 + 2*\left(-1\right)
6,852
e^{-i\cdot y} = \cos\left(-y\right) + i\cdot \sin(-y) = \cos(y) - i\cdot \sin\left(y\right)
-5,862
\dfrac{3}{10 + t \cdot 5} = \dfrac{3}{(t + 2) \cdot 5}
24,647
\left(\pi/2\right) \left(\pi/2\right)/2 = \pi \pi/8
17,425
m^2 - m + \frac{1}{1 + m}\cdot m = \frac{m^3}{1 + m}
1,242
l*x + n'*x = \left(l + n'\right)*x
-25,073
\sec^2(4x) \tan(4x)*8 = \frac{\mathrm{d}}{\mathrm{d}x} \sec^2\left(4x\right)
34,010
\int (-a)\,\mathrm{d}z = -\int a\,\mathrm{d}z
5,442
63 = (-1) + 4 \cdot 4 \cdot 4
31,404
\tan(x + π) = \tan\left(x\right)
14,710
(y^T Ay)^T = y^T A^T y = -y^T Ay
7,280
0 = (1 - z)\cdot z = z - z^2
-1,415
\frac{7}{1} \cdot \frac94 = 1/4 \cdot 9/(1/7)
22,503
\cos^2(x) = 1 - \sin^2(x) > 1 - x^2
35,517
(1 + p + (-1))^n = p^n
15,145
(2\cdot (-1) + n)! = (n + 2\cdot (-1))\cdot (3\cdot (-1) + n)\cdot (n + 4\cdot (-1))!
10,944
\left((2 + i)\times \left(i + 1\right)\times (i + 3)\times ...\times (x + 2\times (-1))\times (x + (-1))\times x\right)^{-1} = \frac{1}{x!}\times i!
9,458
\sin(x) = \frac{1}{1 + \frac{1}{2 \cdot 3 - x^2 + \dotsm} \cdot x^2} \cdot x
8,666
\cos(2 p) = 2 \cos^2\left(p\right) + (-1) = 1 - 2 \sin^2(p)
33,921
216 + x^3*125 = 6^3 + (5*x)^3
21,435
KtY = Yt K
42,157
|\varphi - y| = |-\varphi + y|
29,238
\dfrac{1}{l^{2 p}} (1 + l) = \frac{1}{l^{p*2}} + \dfrac{l}{l^{p*2}}
29,022
u^2 + w^2*3 = (-w + u) * (-w + u) + (u - w)*2w + (w*2) * (w*2)
33,856
h = \frac{h\cdot 2}{2}
12,887
-4/(-1) + A + 5 = \frac{(2 + 7)*(2 + 5*(-1))}{1*(2*(-1) + 1)}\Longrightarrow A = 18
14,857
\binom{3}{1} \binom{3}{2} \binom{5}{2} \binom{2}{1} = 180
-22,034
\frac{1}{15}*24 = 8/5
-24,186
7\cdot \left(5 + 7\right) = 7\cdot 12 = 84
-24,261
\frac{126}{9 + 5} = 126/14 = \dfrac{126}{14} = 9
14,931
Y = Z \cdot R \Rightarrow \frac{dY}{dR} = R \cdot \frac{dZ}{dR} + Z
14,282
\sin\left(2 \cdot A\right) = 2 \cdot \sin(A) \cdot \cos(A)
-507
(e^{\frac{3}{4} \cdot \pi \cdot i})^{14} = e^{14 \cdot \frac34 \cdot \pi \cdot i}
25,404
1 + 1 + 1 + \ldots + 1 + 1 = m = m
21,482
\frac{\left(-2\right)^l}{3^{1 + l}} = (-\frac23)^l/3
21,920
1 + (2*1 + 1*2) + (3*1 + 2*2+1*3) + (1*2 + 2*3 + 3*2 + 2*1) + (1*1 + 2*2 + 3*3 + 2*2 + 1*1)+ (1*2 + 2*3 + 3*2 + 2*1) + (3*1 + 2*2+1*3) + (2*1 + 1*2)+1 = 1+4 + (1+0) + (1+6)+ (1+9) + (1+6) +(1+0) + 4 +1 = 36
25,105
\cos(3 \cdot z) = \cos(z + 2 \cdot z) = \cos(z) \cdot \cos(2 \cdot z) - \sin(z) \cdot \sin(2 \cdot z)
4,082
0 = (1 - 1)/2
-3,788
\dfrac{2*\frac13}{s^2} = \tfrac{2}{s^2*3}
22,442
400/375*100/80*120 = 160
14,217
n*(m + 1) = nm + n