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int64 -30,985
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-4,417 | 16 \cdot (-1) + x^2 = (x + 4) \cdot (x + 4 \cdot (-1)) |
-13,935 | \dfrac{96}{8 + 4} = 96/12 = \dfrac{1}{12}96 = 8 |
-17,678 | 8 = 39\cdot (-1) + 47 |
-29,318 | -7\cdot i + 4 + 2 = -7\cdot i + 6 |
3,282 | (\sum_{k=1}^\infty b_k)\cdot |x|^{-\alpha} = \sum_{k=1}^\infty b_k\cdot |x|^{-\alpha} |
3,214 | 100 = 2 + (51 + 2 \times (-1)) \times 2 |
28,492 | b_{1 + n}^2 = b_n \cdot b_n + \frac{1}{b_n^2} + 2 rightarrow b_{n + 1}^2 > b_n \cdot b_n + 2 |
19,824 | \dfrac{2a}{1 - a^2} = -\frac{1}{1 + a} + \frac{1}{-a + 1} |
-19,547 | 9/7 \cdot 4/5 = \frac{\frac{1}{5} \cdot 4}{7 \cdot 1/9} |
-12,311 | \sqrt{40} = 2 \sqrt{10} |
22,098 | i^{-1} = i^{-1} = \dfrac{1}{ii}i = \frac{1}{-1}i = -i |
-11,942 | 9.801 \times 10^{-1} = 9.801 \times 0.1 |
31,352 | a\cos^2(c) = b-\cos(c) \implies a\cos^2(c)+\cos(c)-b=0 |
32,386 | 37 = (7 + 2 \sqrt{3})(7 - 2 \sqrt{3}) |
6,978 | c \cdot h = (\left(h + c\right)^2 - (-h + c)^2)/4 |
-20,667 | -1/10 \cdot \frac{1}{3} \cdot 3 = -\frac{3}{30} |
-20,887 | \dfrac{1}{25}\cdot (-r\cdot 20 + 30) = \frac15\cdot \left(-r\cdot 4 + 6\right)\cdot \frac55 |
-485 | e^{\frac{11}{12}i\pi*10} = (e^{\frac{\pi i*11}{12}1})^{10} |
13,809 | -\dfrac{1}{12} 16 = -\frac43 |
8,003 | \sum_{k=0}^6 (-1)^k\cdot 6!/k! = \sum_{k=0}^6 (-k + 6)!\cdot {6 \choose k}\cdot \left(-1\right)^k |
9,111 | h_1 + \left(h_2 + y\right)^2 = h_2^2 + h_1 + y^2 + h_2 \cdot y \cdot 2 |
19,655 | r! = r \cdot ((-1) + r) \cdot (2 \cdot (-1) + r)! |
-10,589 | 9 = 8 p + 12 + 28 \left(-1\right) = 8 p + 16 (-1) |
27,736 | \cos(\pi \cdot x \cdot 2.4) = \cos(x \cdot \pi \cdot 2 + 0.4 \cdot x \cdot \pi) |
14,719 | \binom{8}{3}\cdot \binom{7}{3} + \binom{7}{2}\cdot \binom{8}{4} = 3430 |
12,940 | \left(g + i\right)^3 - g^3 = (g + 1 - g) \times ((g + 1)^2 + (g + 1) \times g + g \times g) = 3 \times g^2 + 3 \times g + 1 |
-21,007 | 2/2 \cdot \frac{1}{3 \cdot (-1) + s} \cdot (-4 \cdot s + 9 \cdot \left(-1\right)) = \frac{-s \cdot 8 + 18 \cdot (-1)}{6 \cdot (-1) + s \cdot 2} |
-7,225 | 3/10*2/11 = \frac{1}{55}*3 |
-11,549 | -i*4 + 0 + 8*(-1) = -8 - i*4 |
10,889 | 1 + k \cdot 2 = {2 \cdot k + 1 \choose 1} |
6,700 | 3 \cdot (-1) + n \cdot 2 = n + \left(-1\right) + n + 2 \cdot (-1) |
11,107 | 1 - 5\cdot x^4 = -(5\cdot x^4 + (-1)) = -(\sqrt{5}\cdot x^2 + (-1))\cdot (\sqrt{5}\cdot x \cdot x + 1) |
11,889 | \tfrac{1}{l \cdot l - l + 5\cdot (-1)}\cdot l \cdot l = \frac{1}{1 - 1/l - \dfrac{5}{l^2}} |
21,633 | \dfrac{2*\frac15}{4} = 1/10 |
30,142 | \left(z + 9 \cdot (-1)\right) \cdot (z + 2 \cdot (-1)) = z^2 - 11 \cdot z + 18 |
-20,080 | \frac{6}{6} \cdot (-\frac{9}{9 \cdot (-1) + m}) = -\frac{54}{6 \cdot m + 54 \cdot (-1)} |
30,105 | z^3 = w^2 \times w \Rightarrow w = z |
-2,701 | -\sqrt{3}*\sqrt{9} + \sqrt{3}*\sqrt{16} = -3*\sqrt{3} + \sqrt{3}*4 |
27,639 | \left(y^{k_1}\right)^{k_2} = (y^{k_2})^{k_1} = y^{k_1 k_2} |
36,941 | 1 = 7 - 2\cdot 3 |
-1,244 | -\dfrac{2}{5} \times \left(-6/1\right) = \frac{(-2) \times 1/5}{\frac16 \times (-1)} |
5,154 | w + w + x + x = (w + x)\cdot (1 + 1) = w + x + w + x |
28,095 | 225*\left(-1\right) - x^4 + x^2*34 = -(9*\left(-1\right) + x^2)*(25*\left(-1\right) + x * x) |
18,918 | \tfrac{2*x * x}{x^2 + \left(-1\right)} = 2 + \frac{x + 1 - x + \left(-1\right)}{x * x + (-1)} = 2 + \frac{1}{x + (-1)} - \dfrac{1}{x + 1} |
2,044 | c \cdot G_1 = G_1 \cdot c |
-1,509 | \frac16*5*9/2 = 9*1/2/(\frac{1}{5}*6) |
8,422 | \frac{1}{3}\cdot 2\cdot 2/3 = \dfrac49 |
3,749 | d^2 - d \cdot x + x \cdot h = x^2 - x \cdot h + h \cdot d = h^2 - h \cdot d + d \cdot x |
17,194 | 2 x*2 = 4 x |
6,485 | a \cdot 0 - 0 \cdot a = 0 \cdot a |
12,039 | r\cdot b = \mathbb{E}\left[b\cdot r\right] |
-4,120 | \frac{72}{108 \cdot x^5} \cdot x \cdot x = \dfrac{1}{x^5} \cdot x \cdot x \cdot \frac{72}{108} |
2,373 | \frac{459}{400} = 1 + \frac{1}{2 \cdot 2} - \frac{1}{4^2} - \frac{1}{5^2} |
21,647 | \sin(x - s) = \sin\left(x\right)\cdot \cos(s) - \cos(x)\cdot \sin(s) |
-3,285 | \sqrt{7}\cdot \sqrt{9} + \sqrt{16}\cdot \sqrt{7} = 3\cdot \sqrt{7} + \sqrt{7}\cdot 4 |
50,841 | 21 \cdot 41 = 861 |
15,479 | 3\cdot (\left(-1\right) + 3) = 6 |
10,332 | \dfrac{1}{dt} \cdot \frac{\mathrm{d}E}{\mathrm{d}K} = \left(\frac{\mathrm{d}E}{\mathrm{d}P} \cdot \left(-1\right)\right)/dt |
-22,480 | 81^{-\frac{1}{2}} = (\dfrac{1}{81})^{\frac{1}{2}} |
20,767 | y\cdot x/100 = \dfrac{x}{100}\cdot y |
13,823 | b^4 - a^4 = (b \cdot b - a^2) \cdot \left(b^2 + a^2\right) = (b - a) \cdot (b + a) \cdot (b^2 + a^2) |
-5,036 | 18.0*10^{5 + 2} = 10^7*18.0 |
-3,326 | -\left(4\cdot 6\right)^{1 / 2} + \left(25\cdot 6\right)^{1 / 2} + 6^{1 / 2} = -24^{\frac{1}{2}} + 150^{\dfrac{1}{2}} + 6^{\dfrac{1}{2}} |
-22,435 | (4^{\frac{1}{2}})^3 = 4^{\frac32} |
11,641 | 31 + 21\cdot \left(-1\right) + 19\cdot \left(-1\right) + 17 + 13 + 11\cdot (-1) + 7 + 5\cdot \left(-1\right) + 3\cdot (-1) = 9 |
27,198 | x^{k+2} = x^{k+1}+x^{k+1} = 2x^{k+1} |
-26,385 | \frac{1}{65536} \cdot 4^{11} = 4^{11 - 8} = 4^{11 + 8 \cdot \left(-1\right)} = 4^3 |
-424 | -20\times \pi + 247/12\times \pi = 7/12\times \pi |
18,863 | 2*\cos\left(x\right)*\sin\left(x\right) = \sin(x*2) |
9,691 | \lim_{x \to -\infty} -x + x = \lim_{x \to -\infty} \left(x^2 + x \cdot 5 + 3\right)^{1/2} + x |
7,427 | z^2 = 9 \cdot z \cdot z + 6 \cdot z + 1 = 3 \cdot (z \cdot z + 2 \cdot z) + 1 |
11,272 | i\cdot A = i - 1\Longrightarrow A = i + 1 |
35,351 | 63/125 = \dfrac{7}{10} \cdot 8/10 \cdot 9/10 |
8,405 | a + \left(b - a\right)/2 = \left(2a + b - a\right)/2 = \frac{1}{2}(a + b) |
-10,562 | \frac{4}{r\cdot 5 + 5\cdot \left(-1\right)}\cdot \dfrac{4}{4} = \frac{16}{20\cdot r + 20\cdot \left(-1\right)} |
2,352 | 8\cdot \cos^3(x) = 2\cdot (3\cdot \cos(x) + \cos(3\cdot x)) = 6\cdot \cos(x) + 2\cdot \cos(3\cdot x) |
10,577 | 3 \cdot z \cdot z + 1 + 2 \cdot z = \frac{\mathrm{d}}{\mathrm{d}z} (z^3 + 2 + z + z \cdot z) |
19,448 | h = h c - x c = (h - x) c |
12,935 | 4\cdot y^3 - 7\cdot y + 3\cdot (-1) = (y + 1)\cdot (a\cdot y^2 + b\cdot y + c) = a\cdot y^3 + b\cdot y \cdot y + c\cdot y + a\cdot y^2 + b\cdot y + c |
18,226 | (z^4 + 1) (z^4 + (-1)) = z^8 + (-1) |
9,217 | 0 \lt -q\Longrightarrow q \lt 0 |
3,045 | (1 +- \sqrt{5})/2 = \frac{1}{1 \cdot 2} \cdot (1 +- \sqrt{(-1)^2 - 4 \cdot (-1)}) |
22,806 | \sin(\pi/3) = \sin(\frac{2*\pi}{3}) |
-10,558 | \frac{r \cdot 10 + 50 \cdot (-1)}{r \cdot 20 + 20 \cdot \left(-1\right)} = \frac{1}{2 \cdot r + 2 \cdot (-1)} \cdot (r + 5 \cdot \left(-1\right)) \cdot \frac{10}{10} |
12,380 | \pi = 2 I \implies I = \dfrac{\pi}{2} |
22,150 | \mathbb{E}(1 + T) = 1 + \mathbb{E}(T) |
4,473 | 5/9 = 1/(9/20*4) |
-6,326 | \frac{(9 \cdot \left(-1\right) + x) \cdot 3}{(x + 6) \cdot (x + 9 \cdot (-1)) \cdot 12} = \frac{(9 \cdot (-1) + x) \cdot 3}{4 \cdot (6 + x)} \cdot \frac{1}{3 \cdot (9 \cdot \left(-1\right) + x)} |
8,924 | \frac{1}{(n + 1)^2}(\left(n + 1\right)^2 + \left(-1\right)) = \frac{n^2 + 2n + 1 + \left(-1\right)}{(1 + n) \cdot (1 + n)} |
48,158 | \binom{n}{k} = \dfrac{n\cdot(n-1)\cdot(n-2)\cdots(n-k+1)}{k!} = \dfrac{n!}{(n-k)!k!} |
1,406 | x + x\Delta - x = x\Delta |
3,832 | 1\cdot 2/3/2 = \frac13 |
-20,882 | -\frac{1}{-6}\cdot 6\cdot (-\frac23) = 12/(-18) |
19,469 | (3 + x) \cdot (x + 2 \cdot (-1)) = 6 \cdot (-1) + x \cdot x + x |
15,987 | 16 + 24/41 = \dfrac{680}{41} |
-20,950 | \dfrac{1}{-p \cdot 35 + 7\left(-1\right)}35 = \frac{5}{(-1) - p \cdot 5} \cdot 7/7 |
-22,324 | (y + 9)\cdot (8\cdot (-1) + y) = y \cdot y + y + 72\cdot \left(-1\right) |
-1,580 | \frac{3}{4} \pi - \pi*5/6 = -\frac{\pi}{12} |
29,529 | (\frac{4\cdot 6 + (-1)}{6 + 4\cdot (-1)})^{\frac{1}{2}} = (23/2)^{1 / 2} \lt 4 |
3,755 | \dfrac{1}{2}\cdot 45\cdot (2\cdot 79 + 44\cdot (-4)) = -405 |
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