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int64 -30,985
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-20,000 | 9/8 \cdot \frac{-7 \cdot z + 5 \cdot (-1)}{-7 \cdot z + 5 \cdot (-1)} = \dfrac{-63 \cdot z + 45 \cdot (-1)}{-56 \cdot z + 40 \cdot \left(-1\right)} |
21,381 | a - x - c = a - x - c |
22,380 | \|-z_1 + V\| = \|V - z + z - z_1\| |
-19,461 | \frac{\tfrac12 \times 7}{9 \times 1/8} = 7/2 \times \frac89 |
11,927 | -xy + x * x + y^2 = ((x - y) * (x - y) + x^2 + y^2)/2 |
35,440 | \frac{1}{100}\cdot 20 = 1/5 |
696 | (w^2 + 27 \cdot x^2) \cdot 4 = (2 \cdot x)^2 \cdot 27 + (w \cdot 2) \cdot (w \cdot 2) |
6,723 | \left(k + 1\right)\cdot (k + 1)\cdot (1 + k) = (k + 1) \cdot (k + 1) \cdot (k + 1) |
18,333 | \frac{1}{z\cdot z} = \frac{1}{z \cdot z} |
40,849 | |b| = |z - b - z| \leq |z - b| + |z| |
11,413 | 2^{\dfrac{1}{2}}\cdot 11 + 9\cdot 3^{1 / 2} = (3^{1 / 2} + 2^{\frac{1}{2}}) \cdot (3^{1 / 2} + 2^{\frac{1}{2}}) \cdot (3^{1 / 2} + 2^{\frac{1}{2}}) |
12,399 | z^4 + 5*z + 1 = \left(z^2 + 1\right)*(z^2 + (-1)) + 5*z + 5*(-1) = (z + (-1))*(z^3 + z^2 + z + 6) |
-28,531 | -y^2 - 4\cdot y + 21 = 21 - y^2 + 4\cdot y = 21 + 4 - y^2 + 4\cdot y + 4 = 25 - \left(y + 2\right)^2 = 5^2 - (y + 2)^2 |
2,583 | x = z = \dfrac{1}{x} + 1/z |
19,053 | -27 = (-4) \cdot 12 + (-3) - 2 \cdot (-6) - (-2) \cdot 6 |
-19,649 | 7\times 6/\left(9\right) = \frac{42}{9} |
7,071 | 15 + 5*100*a + 10*b*5 = a*100 + b*10 + 1 + 100*a + 10*b + 2 + ... + a*100 + b*10 + 5 |
-23,912 | \frac{60}{4 + 8} = 60/12 = \frac{1}{12}*60 = 5 |
29,140 | A\cdot Z = A\cdot Z |
13,341 | d \cdot h \cdot d \cdot b/d = b \cdot h \cdot d |
12,817 | (\left(-1\right) + y_2)^2 = \left((-1) + y_1\right)^2 \Rightarrow |\left(-1\right) + y_2| = |\left(-1\right) + y_1| |
19,074 | z\cdot e = e\cdot z |
34,269 | -y = \left(-4 \cdot y\right)^2 + y^2 = 17 \cdot y \cdot y |
7,967 | 2 = x^{x^{x^x*\dotsm}} rightarrow x^2 = 2 |
29,894 | 2 \cdot r \cdot r \cdot \pi \cdot 2 = 4 \cdot \pi \cdot r^2 |
28,581 | \frac{1}{n + 1} \cdot \left(n + (-1)\right) = \dfrac{1}{n + 1} \cdot (n + 1 + 2 \cdot (-1)) = 1 - \tfrac{1}{n + 1} \cdot 2 |
11,811 | 1 + x = \dfrac{(-1) + x^2}{(-1) + x} |
-26,736 | \sum_{l=1}^∞ \frac{1}{(l + 1)*\left(-2\right)^l}*(0 + 2)^l = \sum_{l=1}^∞ 1*\dfrac{2^l}{(l + 1)*(-2)^l} = \sum_{l=1}^∞ \frac{(-1)^l*2^l}{(l + 1)*2^l} = \sum_{l=1}^∞ \dfrac{(-1)^l}{l + 1} |
4,081 | x^3 + 24 \cdot (-1) = x \implies x^3 - x + 24 \cdot (-1) = (x + 3 \cdot (-1)) \cdot (x \cdot x + 3 \cdot x + 8) = 0 |
-4,753 | y \cdot y + y \cdot 8 + 15 = (y + 3) \cdot (5 + y) |
5,556 | {6 + 4 + (-1) \choose \left(-1\right) + 4} = 84 |
-4,554 | 3*(-1) + x^2 - 2*x = \left(x + 1\right)*(3*\left(-1\right) + x) |
36,311 | a^n\times a^m = a^{m + n} |
-29,004 | \dfrac{1}{2} \cdot (-27 - 44) = -35.5 |
-2,210 | -1/17 + \frac{1}{17} \cdot 5 = 4/17 |
8,050 | 136*(-1) + 504 = 368 |
-17,093 | -3 = -3*2*t - -9 = -6*t + 9 = -6*t + 9 |
-711 | e^{\pi \cdot i/4 \cdot 19} = (e^{\dfrac{\pi}{4} \cdot i})^{19} |
16,386 | -(\sqrt{17} + 1)/4 = -\sqrt{17}/4 - \frac14 |
156 | 2^{1.4} = 2^{\frac{1}{5}7} = (2^7)^{\tfrac15} = 128^{1/5} > 99^{1/5} |
33,640 | 1 - \left(\frac56\right) * \left(\frac56\right) * \left(\frac56\right) (5/6 + \frac164) = 1 - \frac{125}{144} = \frac{19}{144} |
-8,088 | \frac12\cdot (-3 - 7\cdot i + 3\cdot i + 7\cdot (-1)) = \frac12\cdot (-10 - 4\cdot i) = -5 - 2\cdot i |
8,064 | \dfrac{\pi}{5}\cdot 2 + \frac{\pi}{10} = \pi/2 |
16,284 | 4 = {4 \choose 3}\cdot {0 + 4 + (-1) \choose 0} |
479 | -x^2 + 2 - x^2 = 2 - 2*x^2 |
5,057 | i/2 = \frac{1}{2} + i - \frac{1}{2}\cdot (i + 1) |
-20,396 | \frac{t\cdot 5 + 4}{16\cdot (-1) - t\cdot 20} = -\tfrac{1}{4}\cdot \frac{-5\cdot t + 4\cdot \left(-1\right)}{-t\cdot 5 + 4\cdot (-1)} |
12,506 | -g^2 + f^2 = (f - g) \cdot \left(g + f\right) |
-11,080 | (x + 4\cdot (-1))^2 + f = (x + 4\cdot \left(-1\right))\cdot \left(x + 4\cdot (-1)\right) + f = x^2 - 8\cdot x + 16 + f |
19,390 | -k + b^2 \cdot k - b \cdot b + 1 = 0\Longrightarrow 0 = (b^2 + (-1)) \cdot \left(\left(-1\right) + k\right) |
3,952 | 99 = 11\cdot 9 = (3^2 + 2\cdot 1^2)\cdot 3^2 = \left(3^2 + 2\cdot 1 \cdot 1\right)\cdot \left(1^2 + 2\cdot 2^2\right) |
-2,841 | 6^{\frac{1}{2}}*9^{1 / 2} + 6^{1 / 2} = 6^{\frac{1}{2}} + 3*6^{\dfrac{1}{2}} |
26,334 | 52 = 39 \left(-1\right) + 91 |
-598 | \left(e^{i\pi/12}\right)^{15} = e^{15 i\pi/12} |
38,738 | \infty +2=\infty |
9,714 | t \cdot t + 6\cdot t + 10 = 1 + \left(t + 3\right)^2 |
25,040 | l! = l\cdot \left(l + \left(-1\right)\right)! |
38,535 | \frac{1}{\sin{x}} = \csc{x} |
11,578 | \sqrt{k} + q\cdot b = q\cdot b + q\cdot b + \sqrt{k} - q\cdot b = 2\cdot b\cdot q + \tfrac{(\sqrt{k} - q\cdot b)\cdot (\sqrt{k} + q\cdot b)}{\sqrt{k} + q\cdot b} = 2\cdot b\cdot q + \frac{1}{(\sqrt{k} + b\cdot q)\cdot 1/\left(2\cdot q\right)} |
294 | \frac{2 \cdot y}{y + 2 \cdot \left(-1\right)} = \dfrac{1}{y + 2 \cdot \left(-1\right)} \cdot (2 \cdot y + 4 \cdot (-1) + 4) = 2 + \frac{4}{y + 2 \cdot \left(-1\right)} |
41,578 | \cos{0} + i \sin{0} = 1 |
36,494 | \tan^2(\theta) = \sec^2\left(\theta\right) + (-1) |
-157 | -18 + 3 (-1) = -21 |
-28,763 | \frac{y + 5\cdot (-1)}{-2\cdot y + 2} = -1/2 - \frac{1}{2 - y\cdot 2}\cdot 4 |
7,502 | 8/9 = 8\cdot \dfrac{1}{27}/(\frac{1}{3}) |
21,463 | x_k = kx_k/k |
9,884 | \frac{4\cdot n + (-1)}{4\cdot n + 1} = \tfrac{1}{4\cdot n + 1}\cdot (4\cdot n + 1 + 2\cdot (-1)) = 1 - \frac{2}{4\cdot n + 1} |
-20,400 | -\dfrac{7}{10\cdot (-1) + n}\cdot \frac{9}{9} = -\frac{1}{9\cdot n + 90\cdot (-1)}\cdot 63 |
9,135 | x^2 + 2\cdot x + 4 = x^2 + 2\cdot x + 1 + 3 = \left(x + 1\right)^2 + 3 |
16,082 | 32 \cdot (1 + 1/2 + \tfrac14 + \dots) = 10000 + 1000 + 100 + 10 + 1 |
9,401 | (c \cdot b + 1) \cdot (c \cdot b + \left(-1\right)) = b^2 \cdot c^2 + (-1) |
31,239 | \mathbb{E}(\frac{1}{x^2}) = \dfrac{1}{x x} |
-16,056 | 9\cdot 8\cdot 7\cdot 6 = \frac{9!}{(9 + 4\cdot (-1))!} = 3024 |
27,288 | (N_k + 1) \cdot (N_x + (-1)) = N_k \cdot N_x + N_x - N_k + (-1) \gt N_k \cdot N_x |
25,852 | \frac{1}{8 + z \cdot 5} \cdot 2 = \frac{2 \cdot 1/z}{\frac{1}{z} \cdot 8 + 5} |
-10,289 | (10 \cdot (-1) + k \cdot 5)/k \cdot \frac44 = \frac{1}{4 \cdot k} \cdot \left(20 \cdot k + 40 \cdot (-1)\right) |
-4,278 | \frac{a^4}{a \cdot a \cdot a} \cdot 44/132 = \frac{44}{132 \cdot a^3} \cdot a^4 |
-20,187 | \dfrac88 \cdot \frac{4 - 2 \cdot t}{3 + t} = \frac{32 - 16 \cdot t}{24 + 8 \cdot t} |
3,918 | -2 = 8 + \left(-10\right) |
-10,279 | -\dfrac{5}{3\cdot x + 12\cdot (-1)}\cdot \frac{5}{5} = -\frac{25}{x\cdot 15 + 60\cdot (-1)} |
-18,483 | 4\cdot x + 2 = 10\cdot (3\cdot x + 7\cdot (-1)) = 30\cdot x + 70\cdot (-1) |
36,262 | \frac{1}{4} \sqrt{33} + 3/4 = \left(\sqrt{33} + 3\right)/4 |
3,906 | \dfrac{1}{(t^2 + g^2)^2} \cdot t = \frac{\dfrac{1}{t \cdot t + g^2}}{t^2 + g^2} \cdot t |
10,294 | (-1/2)^{1 + k} = \frac{(-1)^{k + 1}}{2^{1 + k}} |
33,608 | (6^2 + (-1))/12 = \frac{35}{12} |
6,964 | 2/n + 1 = \frac{1}{n} \cdot (2 + n) |
19,551 | -l \cdot 2 + x = 1 \Rightarrow l = \frac{1}{2} \cdot ((-1) + x) |
2,117 | -((-1) + x) + l + 1 = 2 + l - x |
-2,175 | -\pi/6 = -\pi\cdot \frac{1}{12}\cdot 23 + 7/4\cdot \pi |
44,162 | \frac{1}{x^2+4x+3}=\frac{1}{(x+1)(x+3)}=\frac{1}{2}\left(\frac{1}{x+1}-\frac{1}{x+3}\right)=\frac{1}{2}\left(\frac{1}{(x-2)+3}-\frac{1}{(x-2)+5}\right) |
32,723 | (-h + f) \cdot (h + f) = -h^2 + f^2 |
-7,002 | \frac16\cdot 3\cdot \frac{1}{8}\cdot 5\cdot \frac{4}{7} = \frac{5}{28} |
23,805 | 1 + 3 + \cdots + 2\times m + (-1) = m\times (2\times m + \left(-1\right) + 1)/2 = m^2 |
689 | \dfrac{1}{c_1^2}\cdot c_2 \cdot c_2 = 3 \Rightarrow \frac{1}{c_1}\cdot c_2 = \frac{c_1\cdot 3}{c_2} |
15,418 | \tfrac{-v + 1}{(-v + 1)^{3/2}} = \tfrac{1}{\left(-v + 1\right)^{1/2}} |
12,636 | (a + b)^2 = a * a + 2*b*a + b * b |
10,851 | k^{1 / 2} = k^{1/2} = k^{1 - \frac{1}{2}} = \tfrac{1}{k^{1/2}}*k |
31,286 | \left\{..., 2, 3, 1\right\} = \mathbb{N} |
-6,806 | 4 \times 8 \times 8 = 256 |
-15,819 | -6\cdot 9/10 + 9/10 = -\frac{1}{10}\cdot 45 |
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