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int64 -30,985
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-4,931 | 10^{0 + 5}*29.4 = 29.4*10^5 |
17,819 | 3 - 2*f = f + b + c - 2*f = -f + b + c |
26,129 | \frac1y (-z + c) = 1 \Rightarrow y + z = c |
15,290 | \left(h + 6 = 25 + b\cdot 2 \Leftrightarrow 13\cdot \left(h + 6\right) = 13\cdot (2\cdot b + 25)\right) \Rightarrow 2\cdot b + 19 = h |
9,959 | -\frac{1}{25}\times 216 + 400/25 = \frac{1}{25}\times 184 |
-11,099 | (x + 3\left(-1\right))^2 + b = (x + 3\left(-1\right)) (x + 3(-1)) + b = x^2 - 6x + 9 + b |
28,877 | 3^{1/2}*(c + 2^{1/2}*d) + a + 2^{1/2}*x = a + 2^{1/2}*x + 3^{1/2}*c + 6^{1/2}*d |
1,956 | (y + x)*(y^2 + x^2 - x*y) = y^2 * y + x^3 |
-20,373 | y*3/\left(y*24\right) = 3*y*1/(3*y)/8 |
6,717 | 1 - \cos(4\cdot z) = 2\cdot \sin^{22}(z) = 8\cdot \sin^2\left(z\right)\cdot \cos^2(z) = 8\cdot (1 - \cos\left(z\right))\cdot (1 + \cos\left(z\right))\cdot \cos^2(z) |
28,559 | 0.250 \cdot 2 = 0.50 \rightarrow 0 |
-4,933 | 3.78 \cdot 10 = \frac{10}{10^6} \cdot 3.78 = \tfrac{3.78}{10^5} |
-22,226 | (z + (-1))\cdot (z + 3\cdot (-1)) = z^2 - 4\cdot z + 3 |
22,812 | -\frac12 + \frac{10}{4} + x = 0 \Rightarrow -2 = x |
25,064 | 3!/4! = \dfrac{6}{24} = 1/4 |
-1,863 | 11/12 \cdot \pi = -\pi \cdot 0 + \frac{1}{12} \cdot 11 \cdot \pi |
-18,285 | \dfrac{y^2 - y - 2}{y^2 + 2y - 8} = \dfrac{(y + 1)(y - 2)}{(y + 4)(y - 2)} |
15,913 | G\cdot i\cdot y^g = i\cdot G\cdot y^g |
10,409 | \dfrac{1}{2\cdot (-1) + (-1)^2\cdot 12 + \left(-1\right)}\cdot \left(\left(-1\right)^2 + 3\right) = \dfrac{4}{9} |
-1,831 | 13/4*π = 11/6*π + \tfrac{17}{12}*π |
-22,217 | (5 + y)*(y + 7) = 35 + y^2 + y*12 |
-24,904 | 8\cdot 7\cdot 6\cdot 5\cdot 4 = \tfrac{8!}{\left(8 + 5(-1)\right)!} = 6720 |
-20,590 | 8/8*\dfrac{9*t}{t + 7}*1 = \tfrac{72}{t*8 + 56}*t |
3,316 | h\cdot b = h^1\cdot b^1 |
22,806 | \sin{\frac{π}{3}} = \sin{\frac{2}{3} \cdot π} |
4,670 | A^B*A^B = (A*A)^B = A^B |
24,566 | (-1) + 2 \cdot n = n^2 - (n + (-1))^2 |
14,498 | -\frac{1}{2} = \frac11\cdot ((-1)\cdot 2\cdot 1/4) |
20,662 | m \cdot 2 + 2(-1) = \left(m + (-1)\right) \cdot 2 |
-1,451 | 1/5*6/(1/8*\left(-1\right)) = -\frac{8}{1}*\frac15*6 |
-9,484 | k\cdot 84 + 36\cdot (-1) = k\cdot 2\cdot 2\cdot 3\cdot 7 - 2\cdot 2\cdot 3\cdot 3 |
-1,977 | \pi\cdot \dfrac76 + 7/4\cdot \pi = 35/12\cdot \pi |
22,363 | (m + 1)! \cdot \left(m + 1 + 1\right) = (1 + m + 1) \cdot \left(m + 1\right)! |
-26,516 | (5 x)^2 = 25 x^2 |
27,409 | b_1\times s_1 + ... + b_q\times s_q = s_1\times b_1 + ... + b_q\times s_q |
7,078 | \sin(y) = \cos(-y + \tfrac12 \cdot \pi) |
17,409 | z \cdot 2 = \operatorname{acos}(x) \implies x = \cos{2 \cdot z},0 \leq 2 \cdot z \leq \pi |
21,298 | b^z*b^y = b^{z + y} |
9,498 | \left|{A \times A^T}\right| = \left|{A^T \times A}\right| |
1,991 | x \cdot a = a^T \cdot x = x^T \cdot a |
-1,650 | \pi \cdot 4/3 + \pi \frac{11}{12} = \pi \frac{9}{4} |
-22,179 | \dfrac{24}{32} = \frac{3}{4} |
1,445 | 1 + i^2 + i = 0 \implies 1 + i^2 = -i |
16,860 | \int\limits_{-\infty}^\infty ...\,\text{d}x = 2 \int_0^\infty ...\,\text{d}x |
38,236 | \left\{z, g\right\} = \left\{z, g\right\} |
32,955 | \frac{1}{8!\cdot 4!}\cdot 12! = 495 |
6,054 | (x + 0)\times (2 + x^2 + x) = x^3 + x^2 + 2\times x + 0 |
25,121 | 2 - 9\cdot z^7 + 7\cdot z^9 = (1 - z)^2\cdot \left(2 + 4\cdot z + 6\cdot z \cdot z + 8\cdot z^3 + 10\cdot z^4 + 12\cdot z^5 + 14\cdot z^6 + 7\cdot z^7\right) \approx 63\cdot \left(1 - z\right) \cdot \left(1 - z\right) |
23,193 | \cos^2\left(x\right) - \sin^2(x) = 2 \cdot \cos^2\left(x\right) + (-1) |
12,041 | 2/27 = \frac{\frac{1}{3}}{3}\cdot 2\cdot \frac13 |
-16,891 | 5 = 5 \cdot 4 \cdot x + 5 \cdot \left(-5\right) = 20 \cdot x - 25 = 20 \cdot x + 25 \cdot (-1) |
-6,024 | \frac{3*q}{q * q + q*6 + 40*(-1)} = \frac{3}{(10 + q)*(4*(-1) + q)}*q |
22,611 | 2\times ((-1) + 2\times 7)^2 + 5\times (2 + (-1)) \times (2 + (-1)) = 7\times (2\times 4 + (-1)) \times (2\times 4 + (-1)) |
5,700 | x \cdot \alpha \lt \alpha \cdot x \Rightarrow x^2 \cdot \alpha \cdot \alpha < \alpha^2 \cdot x \cdot x |
23,929 | h d = \dfrac{1}{h d} = 1/(d h) = d h |
11,645 | (y^Z \cdot \theta^Z \cdot z)^Z = \left(\theta^Z \cdot z\right)^Z \cdot y = z^Z \cdot \theta \cdot y |
36,037 | \frac{2}{3}\cdot \pi = \frac{1}{3}\cdot 2\cdot \pi |
12,750 | |\overline{h_j}| = |h_j| |
28,184 | (\dfrac{1}{4})^4\cdot 3/4 = \frac{3}{1024} |
28,091 | \cos{B} \sin{C} + \sin{B} \cos{C} = \sin\left(B + C\right) |
35,214 | -\frac18\cdot \pi = \tfrac{(-1)\cdot \pi}{8} |
8,200 | a/(c\cdot b) = a/(c\cdot b) |
15,985 | -2^n + 2^x = 2^n\cdot (2^{x - n} + (-1)) |
6,473 | \frac{1 + 2 \cdot z}{2 + 2 \cdot n} = \dfrac12 \cdot (\tfrac{z + 1}{n + 1} + \frac{z}{n + 1}) |
-4,113 | \dfrac{1}{r \cdot 4} = \tfrac{1}{4 \cdot r} |
9,747 | Z^R*Z = Z*Z^R |
12,402 | \tfrac12(2 + 0) = 1 |
1,040 | z^7 = z^4\cdot z \cdot z^2 |
-7,618 | \dfrac{i*2 - 1}{-1 + 2*i}*\frac{-6 + i*8}{-1 - 2*i} = \frac{8*i - 6}{-1 - 2*i} |
-3,818 | \frac{144 \cdot a^5}{72 \cdot a} = \frac{a^5}{a} \cdot 144/72 |
13,670 | |\left(x - y\right)/(y\cdot x)| = |1/x - 1/y| |
11,259 | \left(0 > z + 5 \cdot (-1) \Rightarrow 1 = 5 - z\right) \Rightarrow 4 = z |
29,333 | \left(11 + 1\right) \cdot (22 + 1) \cdot (10 + 1) = 12 \cdot 23 \cdot 11 = 3036 |
31,459 | \int\limits_c^b \cot{x}\,\mathrm{d}x = \int\limits_c^b \cot{x}\,\mathrm{d}x |
2,813 | (10 + y) \cdot (10 + y) = x^2 + y^2 = (x + 27 \cdot (-1))^2 + (y + 9)^2 |
7,469 | 4/36 = \frac46 \cdot 1/6 |
54,616 | 62 - 56 = 6 |
-8,061 | \dfrac{-2 + i\times 5}{-2 + i\times 5}\times \dfrac{26 + 7\times i}{-5\times i - 2} = \frac{26 + i\times 7}{-5\times i - 2} |
25,456 | 2^{n + 1} = 1 + 2^0 + 2^1 + 2 \cdot 2\cdot \dots\cdot 2^n |
7,695 | (3 + 2)^2 = 2 \cdot 2 + 2\cdot 2\cdot 3 + 3^2 |
19,964 | x^2 + x \cdot x + 1 = x\cdot x + x + x + x\cdot x = x \cdot x + x + x + x \cdot x + 1 |
-30,249 | \frac{1}{z + 4 \cdot (-1)} \cdot (z^2 - 8 \cdot z + 16) = \tfrac{1}{z + 4 \cdot \left(-1\right)} \cdot (z + 4 \cdot \left(-1\right))^2 = z + 4 \cdot (-1) |
1,429 | \|f-g\|_p=\|f-f_n+f_n-g\|_p\le\|f-f_n\|_p+\|f_n-g\|_p<\tfrac\varepsilon2+\tfrac\varepsilon2=\varepsilon |
71 | \{A, H\} \implies A \cup H = H |
3,285 | (\frac{1}{2})^{-2/3} + (-1) = 2^{\tfrac23} + (-1) = 4^{\frac13} + (-1) |
18,357 | (12*\sqrt{2} + 19)*(19 - 12*\sqrt{2}) = 73 |
17,278 | 3 = 1^3 + 1 \cdot 1 + 1^2 |
1,390 | a = b^3 \frac{a}{b^3} = b^2 ba\cdots ba\frac{1}{bb^2}/b |
28,274 | \binom{j + i}{i} = \frac{\left(i + j\right)!}{j!\times i!} |
18,326 | 999 = 10 10^2 + (-1) |
30,882 | (-1) + 2^n = 2*2^{n + (-1)} + 2*\left(-1\right) + 1 |
42,362 | 6/60 = 1/10 |
-7,150 | \frac{1}{28} \cdot 3 = \frac18 \cdot 3 \cdot \frac27 |
16,341 | \frac{d}{dD} \left(\frac{\sin{D}}{1 + \cos{D}}\right) = \frac{1}{1 + \cos{D}} |
19,857 | x^2\times \alpha^2 = x \times x\times \alpha \times \alpha |
6,802 | \frac{\pi}{10} = \operatorname{asin}(\frac14 \cdot (\left(-1\right) + \sqrt{5})) |
32,256 | 2^n - 2^{n-1} = 2^{n-1}(2 -1) = 2^{n-1} |
9,922 | \left(-\lambda + x\right)\cdot \left(-c + x\right) = x \cdot x - (\lambda + c)\cdot x + c\cdot \lambda |
23,056 | 4/k = b^2 - c^2 = (b - c)*\left(b + c\right) \Rightarrow \dfrac{1}{k*(-c + b)}*4 = b + c |
24,602 | \left(1/2\right)^2 + (\frac12) * (\frac12) = \frac12 |
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