id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
33,004 |
6^2 + 8 \cdot 8 = 36 + 64 = 100 = 10^2
|
1,762 |
\dfrac{2}{9} = 2/9
|
27,246 |
5 + \cos^2{z}\cdot 4 - 8\cdot \cos{z} = 1 + 4\cdot \left(-\cos{z} + 1\right)^2
|
-17,910 |
75 + 44\cdot (-1) = 31
|
3,948 |
3\cdot \rho^2 + 24\cdot (-1) = 3\cdot (\rho^2 + 8\cdot (-1)) = 3\cdot (\rho + 2\cdot \sqrt{2})\cdot (\rho - 2\cdot \sqrt{2})
|
20,761 |
m \cdot 2 + 1 + 3 \cdot (-1) + 1 = 2 \cdot m + (-1)
|
-20,174 |
\left(63 + p*7\right)/(p*(-56)) = \frac{1}{(-8)*p}*(9 + p)*7/7
|
16,356 |
100-95 = 5
|
8,354 |
8^{x \cdot 2} + 8^{1 + x \cdot 2} = (8^x \cdot 3)^2
|
8,589 |
(l^4 + l^2 \cdot l + l^2 + l + 1) \cdot (l + (-1)) = l^5 + \left(-1\right)
|
28,851 |
\tan^4\left(x\right)\cdot 3 = \frac{\text{d}}{\text{d}x} \tan^3(x) - \tan(x)\cdot 3 + 3\cdot x
|
35,074 |
-4 \cdot (p + 3) + p^2 \cdot 9 = \left(p \cdot 3 + \left(-1\right)\right) \cdot \left(p \cdot 3 + \left(-1\right)\right) + 2 \cdot p + 13 \cdot \left(-1\right)
|
18,333 |
\frac{1}{x x} = \frac{1}{x^2}
|
8,062 |
\sin{3\cdot J}\cdot \cos{J\cdot 3} = \dfrac{\sin{6\cdot J}}{2}
|
10,698 |
\psi + 5 = 2*k + 1 \Rightarrow \psi = 2*k + 1 + 5*(-1) = 2*k + 4*(-1)
|
21,529 |
k = g_k*b_k = g_k*b_k \Rightarrow \dfrac{1}{g_k}*g_k = b_k/(b_k)
|
-20,284 |
\dfrac{1}{10 \cdot y + 80 \cdot (-1)} \cdot \left(10 \cdot y + 60\right) = \dfrac{1}{10} \cdot 10 \cdot \frac{1}{y + 8 \cdot \left(-1\right)} \cdot (y + 6)
|
42,181 |
2 = 2 \cdot 6 + 10 \cdot \left(-1\right)
|
3,122 |
\sqrt{17} \cdot 11 = \dfrac{\sqrt{17}}{2} \cdot (10 + 12)
|
35,378 |
1/(f\times 1/c) = c/f
|
34,269 |
-z = (-4\cdot z)^2 + z^2 = 17\cdot z \cdot z
|
16,095 |
1 + 2^3 + 3^2 = 3\times 2\times 3
|
24,242 |
\tfrac{1}{2}\cdot (2013 + 1) = 1007
|
-9,242 |
-3*3*13 + 3*3*5*q = 45*q + 117*\left(-1\right)
|
12,867 |
2^x*2^l = 2^{l + x}
|
14,254 |
\sqrt{x + 2} + 2 \cdot (-1) = y\Longrightarrow 2 \cdot (-1) + (y + 2)^2 = x
|
-15,234 |
\frac{z^8}{\frac{1}{z^5}\cdot x \cdot x} = \frac{1}{\frac{1}{z^5}\cdot x^2\cdot \frac{1}{z^8}}
|
7,831 |
(2 + 2 \cdot x)! = \left(2 \cdot x + 1\right)! \cdot (2 + x \cdot 2)
|
26,575 |
4/2 = \dfrac{1}{1} \cdot 2 = \frac{6}{3} = \ldots
|
33,503 |
i^4 = e^{4*\left(\pi/2 + 2*m*\pi\right)*i} = e^{(2*\pi + 8*m*\pi)*i}
|
4,559 |
\sin(z + y) = \sin(z) \cdot \cos(y) + \cos(z) \cdot \sin(y)
|
-2,807 |
-\sqrt{2} \sqrt{16} + \sqrt{2} \sqrt{25} = -4 \sqrt{2} + \sqrt{2} \cdot 5
|
-24,087 |
5 + \frac{1}{1} \cdot 5 = 5 + 5 = 10
|
7,788 |
\left(10 + 5\cdot (-1)\right)\cdot (3 + 3) - \frac{76}{3} = \frac{14}{3}
|
5,154 |
x + x + w + w = (x + w) \cdot (1 + 1) = x + w + x + w
|
29,510 |
2^{40} = 17\cdot (2\cdot l + 1) + 1 = 34\cdot l + 18
|
8,899 |
r^4 + r^2 + r^2 + r^2 + r^2 - r^3 - r^2 \cdot r - r^3 - r^3 = r^4 + 4 \cdot r \cdot r - 4 \cdot r^3
|
27,526 |
\sin(a + b) = \sin{b}\times \cos{a} + \sin{a}\times \cos{b}
|
6,966 |
A - B\cdot A\cdot B = A\cdot B^2 - B\cdot A\cdot B = (A,B)
|
24,355 |
{4 \choose 1}*\left(3*z^2\right)^3*y = 4*3^3*z^6*y = 108*z^6*y
|
21,475 |
\frac{1}{120} \cdot (60 + 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40) = 2
|
17,080 |
\frac{\mathrm{d}}{\mathrm{d}y} (y^2 \cdot e^y) = 2 \cdot e^y \cdot y + e^y \cdot y^2
|
7,955 |
\left(f\times g\right)^k = (f\times g)^k
|
10,603 |
\frac{1}{x + 3\left(-1\right)}x = \frac{x + 3\left(-1\right) + 3}{x + 3\left(-1\right)} = 1 + \frac{1}{x + 3(-1)}3
|
23,008 |
z + z^2 + z \times z \times z = \frac{1}{z + (-1)}\times ((-1) + z \times z^2)\times z
|
6,883 |
\dfrac{3}{4}*3/4 = \frac{9}{16}
|
27,951 |
24 = 512 - 22\cdot 8 - 16\cdot 8 - 13\cdot 8 - 10\cdot 8
|
33,777 |
\frac{8}{3} = 2 \cdot 2/3 \cdot 2
|
-7,033 |
2/21 = 2/6\cdot \dfrac17 2
|
21,361 |
\frac{1}{x + (-1)}\cdot (x \cdot x + (-1)) = \frac{1}{x + (-1)}\cdot (x + 1)\cdot (x + (-1)) = x + 1
|
8,327 |
\left(e^{4 - E \cdot 4} = e \Rightarrow 1 = 4 - 4 \cdot E\right) \Rightarrow E = \frac34
|
937 |
\pi \cdot \sigma \cdot S = \pi \cdot S \cdot \sigma
|
33,364 |
n = 3 \Rightarrow 14 \cdot n^2 + 19 \cdot n + 6 = 189
|
8,402 |
20.17 = \frac{1}{10 * 10}*2017
|
2,008 |
\frac1A \cdot \frac1A = \dfrac{1}{A^2}
|
-7,042 |
\frac{1}{33}\cdot 2 = 4/11\cdot 2/12
|
23,993 |
(x + g) \cdot (x + b) = x^2 + g \cdot x + b \cdot x + g \cdot b = x^2 + (g + b) \cdot x + g \cdot b
|
9,099 |
\sin{t} \cdot \cos{t} = \dfrac{1}{2} \cdot \sin{2 \cdot t}
|
-7,746 |
\frac{-6 + i\cdot 8}{-i\cdot 3 - 4} = \dfrac{1}{-3\cdot i - 4}\cdot (-6 + 8\cdot i)\cdot \dfrac{-4 + 3\cdot i}{3\cdot i - 4}
|
26,861 |
2 \cdot (-1) + (-y + 4)^2 + y \cdot y - (4 - y) \cdot 2 - 2 \cdot y = 0 \implies y^2 - 4 \cdot y + 3 = \left(y + (-1)\right) \cdot (y + 3 \cdot \left(-1\right)) = 0
|
26,413 |
153 = \frac{306}{2} \cdot 1
|
16,013 |
1 + a*4 - b*2 = a*4 - 2*b + 1
|
37,359 |
\frac{g}{2} + \frac{g}{2} = g
|
11,225 |
{(-1) + n + 2\cdot \left(-1\right) + r + 2\cdot (-1) \choose r + 2\cdot (-1)} = {n + r + 5\cdot (-1) \choose r + 2\cdot (-1)}
|
-1,590 |
3/4\cdot \pi = 3/4\cdot \pi + 0
|
20,767 |
z\cdot S/100 = \frac{S}{100}\cdot z
|
7,493 |
x = p*0 + (1 - p) \left(1 + x\right) = (1 - p) (1 + x)
|
-4,292 |
\frac{10}{k*9} = \frac1k10 / 9
|
-20,034 |
5/5\cdot \frac19\cdot (3\cdot (-1) - 2\cdot r) = (15\cdot \left(-1\right) - 10\cdot r)/45
|
8,356 |
-b + a = -(b - a)
|
-15,891 |
5\cdot 5/10 - 5/10\cdot 7 = -10/10
|
40,312 |
2*(-1) + x^2 + x = (x + 2)*(\left(-1\right) + x)
|
-676 |
(e^{\frac{17}{12}\cdot \pi\cdot i})^7 = e^{7\cdot 17\cdot \pi\cdot i/12}
|
460 |
(z + (-1))\cdot (1 + z^2 + z) = \left(-1\right) + z \cdot z \cdot z
|
36,799 |
35 = (4 + 4) \cdot 4 + 4 - \dfrac{1}{4} \cdot 4
|
-19,344 |
\tfrac{8}{7}*\frac{5}{7} = \frac{8*5}{7*7} = 40/49
|
30,651 |
\tfrac14 = 1/2\times 1/2
|
-10,739 |
-(y\cdot 5 + 6\cdot (-1))/(9\cdot y)\cdot \dfrac44 = -(20\cdot y + 24\cdot (-1))/(y\cdot 36)
|
13,274 |
\frac{1}{2^2} = \frac{1}{2 \cdot 2} \cdot 2^0 = \dfrac14
|
1,578 |
\dfrac{1}{9634471581445544690955000} \cdot 242753155112819 = 2.519631233 \cdot \frac{\dots}{e^{11}}
|
-29,609 |
d/dy (2 \cdot y^4) = 2 \cdot d/dy y^4 = 2 \cdot 4 \cdot y \cdot y \cdot y = 8 \cdot y^3
|
958 |
9^8 + 4^8 + 6^8 = -6^8 + (9^4 + 4^4)^2
|
9,990 |
\cos(a - h) = \cos(h) \cdot \cos(a) + \sin(a) \cdot \sin(h)
|
24,259 |
\left(u + v\right) g = gv + ug
|
12,638 |
\frac{\partial}{\partial x} \left(u*w\right) = \frac{\mathrm{d}u}{\mathrm{d}x}*w + u*\frac{\mathrm{d}w}{\mathrm{d}x}
|
-4,860 |
63.0 \cdot 10^5 = 63 \cdot 10^{2 + 3}
|
20,636 |
36^2 + 24^2 + 14^2 + 6^2 = 2104
|
-4,015 |
\frac{r^5}{r^4}*120/36 = \tfrac{1}{r^4*36} 120 r^5
|
23,461 |
D \times A = A \times D
|
2,156 |
\sqrt{64}/(\sqrt{8}) = \sqrt{\frac{1}{8}64} = \sqrt{8} = 2\sqrt{2}
|
10,408 |
\gamma\cdot A\cdot m = \gamma\cdot m\cdot A
|
-15,073 |
\dfrac{1}{\frac{y^6}{x^9} \cdot \frac{1}{y^5 \cdot \frac{1}{x^5}}} = \tfrac{\frac{1}{y^6} \cdot x^9}{\dfrac{1}{y^5} \cdot x^5}
|
9,088 |
5.021*3.3942037 = \tfrac{5021}{1000}*33942037/10000000
|
7,648 |
\sqrt{(f + c)^2} = |f + c| = \sqrt{f \times f} + \sqrt{c^2}
|
23,793 |
h \cdot H \cdot a \cdot H = h \cdot a \cdot H = a \cdot H = a \cdot h \cdot H = a \cdot H \cdot h \cdot H
|
-6,351 |
\dfrac{1}{5*\left(10 + p\right)} = \frac{1}{5*p + 50}
|
17,748 |
12/35 = 3/5 \cdot 4/7
|
19,322 |
\frac{\sin(5\cdot y)}{y \cdot y} = 5\cdot \tfrac{1}{5\cdot y}\cdot \sin(5\cdot y)/y
|
16,647 |
6/27 = \frac{4*2^2*3}{6 * 6 * 6}
|
16,980 |
\left(3 \cdot (-1) + y \cdot 3 = 3^n \Rightarrow 3^{(-1) + n} = (-1) + y\right) \Rightarrow 1 + 3^{n + \left(-1\right)} = y
|
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