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int64 -30,985
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11,871 | t < w + 1,w < 1 + t \implies w = t |
34,186 | 84 = \binom{\left(-1\right) + 6 + 3}{3 + (-1)}*3 |
32,431 | \dfrac{1}{z_1*z_2} = \frac{1}{z_1*z_2} |
9,502 | (-3/2 + 2)^2 = \left(1 - 3/2\right) \times \left(1 - 3/2\right) |
-22,360 | (3 + a) \cdot \left(a + 5\right) = a^2 + a \cdot 8 + 15 |
25,357 | (x + \sqrt{C}*y - \sqrt{R}*z)*(x + y*\sqrt{C} + \sqrt{R}*z) = x^2 + C*y^2 + y*\sqrt{C}*x*2 - R*z^2 |
-18,469 | 4 \cdot n + 4 \cdot (-1) = 5 \cdot \left(5 \cdot n + 8 \cdot (-1)\right) = 25 \cdot n + 40 \cdot \left(-1\right) |
-20,137 | -\dfrac{1}{-9} \cdot 81 = \frac{9}{1} \cdot (-\frac{1}{-9} \cdot 9) |
5,768 | (z + 1)^2 = (z + 1)\cdot (z + 1) = z^2 + 2\cdot z + 1^2 |
38,287 | 105 = (1 + 2 + 3 + 4) \cdot 10 + 5 |
22,323 | n^2 + 2 \cdot n + 3 \cdot (-1) = (n + 3) \cdot \left((-1) + n\right) |
26,234 | (1 + n) ((-1) + n) + 1 = n^2 |
23,361 | 1 + \tfrac12 \cdot (4 + \left(-1\right)) = 1 + \frac{3}{2} = \frac{1}{2} \cdot 2 |
19,799 | z^2 + y y - z y = (-y + z)^2 + y z |
24,127 | \dfrac12 (9999 + 1000 (-1) + 1) = 4500 |
1,769 | \frac12 = (2 \cdot \left(-1\right) + 3)/2 |
-110 | -10 + 3 \cdot (-1) = -13 |
27,076 | (-1) + 100^{1/2} = 9 |
22,989 | s = z + \dfrac{1}{z} \cdot r \implies z = \frac12 \cdot (s ± (s^2 - 4 \cdot r)^{1/2}) |
30,999 | 5^{-n} = 2^n\cdot 10^{-n} |
19,042 | 28 = 4*6 + 3*0 + 4 + 2*0 |
25,451 | (2^3)^A = 8^A |
15,574 | (b + a) \cdot (b + a) = b^2 + a \cdot a + 2\cdot b\cdot a |
30,794 | u = \frac1x \implies x = \frac1u |
15,984 | (c - g) \cdot (c - g) = g^2 + c^2 - 2 \cdot c \cdot g |
12,768 | n^4 + 4\cdot n^3 + 8\cdot n \cdot n + 8\cdot n + 4 = (n^2 + 2\cdot n + 2)^2 = ((n + 1)^2 + 1)^2 |
1,518 | 1 + f^3 = (1 + f)\cdot (1 - f + f^2) = (1 + f)\cdot \sqrt{3}\cdot f |
11,816 | \frac{1}{3 + n*2} = \frac{1}{1 + 2*(n + 1)} |
3,361 | (2^{10} + 2 \cdot (-1)) \cdot 6 = {4 \choose 2} \cdot (2^{10} + 2 \cdot (-1)) |
-1,383 | \dfrac{\tfrac{1}{9} \cdot \left(-2\right)}{1/9 \cdot 8} = \frac{9}{8} \cdot (-2/9) |
-2,335 | -1/16 + \dfrac{2}{16} = 1/16 |
15,162 | \sin(D)\times \cos(G) + \cos(D)\times \sin(G) = \sin\left(D + G\right) |
28,580 | 0 = d_1^2 - 50\cdot d_1 + 225 \Rightarrow (d_1 + 45\cdot (-1))\cdot (d_1 + 5\cdot (-1)) = 0 |
-18,425 | \frac{1}{(k + 6(-1)) \left(k + 5(-1)\right)}k\cdot (5(-1) + k) = \frac{1}{k^2 - k\cdot 11 + 30}(k^2 - 5k) |
-2,097 | 2 \cdot \pi - \pi/3 = \pi \cdot 5/3 |
17,835 | 1 + k*x + x = 1 + (k + 1)*x \leq \left(1 + x\right)^k + x |
12,804 | h\cdot x\cdot x\cdot h\cdot h\cdot x = h^3\cdot x^3 rightarrow h^2\cdot x^2 = x\cdot h\cdot x\cdot h = (x\cdot h) \cdot (x\cdot h) |
20,421 | (-y + z)\cdot (y^2 + z \cdot z + y\cdot z) = -y^3 + z \cdot z^2 |
1,324 | 9\cdot z\cdot 2\cdot z = 18\cdot z^2 |
-4,981 | 10^2\cdot 2.4 = 10^{4 - 2}\cdot 2.4 |
38,255 | \frac12\cdot 8\cdot 9 = \dfrac{72}{2} = 36 |
-1,484 | 36/20 = 36\cdot \dfrac{1}{4}/\left(20\cdot 1/4\right) = \frac{9}{5} |
-30,298 | \frac53 \times \pi = 2 \times \pi - \pi/3 |
-17,918 | 23\cdot \left(-1\right) + 33 = 10 |
306 | \left(b + a\right)^2 = a^2 + 2ab + b^2 |
22,516 | \arcsin\left(\frac{\sqrt{3}-1}{2\sqrt{2}}\right) = \pi/12 |
23,942 | y_2 + y_1 = 4\cdot y_2 + y_1 + y_1\cdot 4 + y_2 |
-20,927 | \frac{x + 2(-1)}{x + 2(-1)} \left(-\frac{3}{7}\right) = \tfrac{-3x + 6}{14 (-1) + x*7} |
23,659 | 2400/l\cdot 2 = 4800/l |
52,456 | U = U^+ |
28,706 | x^6 + (-1) = (x^3 + (-1)) \cdot \left(x^3 + 1\right) = (x^2 + (-1)) \cdot (x^2 + x + 1) \cdot (x \cdot x - x + 1) |
31,477 | (2n)^2 + (n*2 + 2)^2 + \left(2n + 4\right) * \left(2n + 4\right) = (3n^2 + 6n + 5)*4 |
42,887 | 4\cdot 3 + 3\cdot 3 = 21 |
13,601 | 0 = h^3 + a_1 \cdot a_1 \cdot a_1 + a_2^3 - 3\cdot h\cdot a_1\cdot a_2 = (h + a_1 + a_2)\cdot (h^2 + a_1^2 + a_2 \cdot a_2 - h\cdot a_1 - a_1\cdot a_2 - a_2\cdot h) |
8,379 | \frac{1}{10} = \frac19 \cdot \frac{9}{10} |
-4,429 | -\frac{1}{(-1) + x} - \frac{3}{x + 1} = \frac{2 - 4*x}{(-1) + x^2} |
-22,292 | d^2 - 3 d + 70 (-1) = (d + 7) (d + 10 (-1)) |
-4,585 | x^2 - x*8 + 15 = \left(x + 3(-1)\right) (x + 5\left(-1\right)) |
258 | {r + n + (-1) \choose r} = {n + r + \left(-1\right) \choose r} |
25,805 | 1 + x^4 = (1 + x^2) \cdot (1 + x^2) - (x\cdot \sqrt{2}) \cdot (x\cdot \sqrt{2}) |
22,763 | 4 = z * z - x^2 = (z - x)*(z + x) |
27,604 | 64 + 8(-1) + 7(-1) + 7(-1) + 6(-1) = 36 |
14,530 | c^3 + c^2 \cdot g \cdot 3 + g^2 \cdot c \cdot 3 + g^3 = (c + g) \cdot (c + g)^2 |
15,074 | k \times n = y - f \Rightarrow y = k \times n + f |
1,405 | Gu = \mathbb{E}[uG] |
-19,042 | 29/30 = \frac{1}{25*\pi}*X_q*25*\pi = X_q |
-20,176 | \tfrac{1}{24 \cdot (-1) + y \cdot 3} \cdot (-15 \cdot y + 6 \cdot (-1)) = 3/3 \cdot \frac{-y \cdot 5 + 2 \cdot (-1)}{y + 8 \cdot \left(-1\right)} |
26,564 | -3/4*5*\frac16/2 + 1 = \frac{1}{16}*11 |
26,618 | 256*x + 2101*(-1) = \left(x + 8*\left(-1\right)\right)*256 + 53*(-1) |
-1,568 | \frac25 = \tfrac{2}{5} |
2,478 | 1 + \frac{24541}{56660} = 81201/56660 |
-1,632 | \pi/2 + \pi = 3/2\times \pi |
26,168 | x \cdot 2 \gt 3 - x\Longrightarrow 1 < x |
15,609 | \frac{1}{10^2}*(10 - 2*3) * (10 - 2*3) = \tfrac{4^2}{10^2} = 0.16 |
-19,240 | 4/9 = \frac{W_t}{9 \cdot \pi} \cdot 9 \cdot \pi = W_t |
18,857 | \frac{2}{16} + 1/17 = 50/(16\cdot 17) |
21,383 | 6 = (17/21)^2 \times \left(\frac{1}{21}\times 17\right) + (37/21)^3 |
9,054 | \tfrac{\sin\left(z/2\right)}{z} = 1/(z\cdot 1/2)\cdot \sin(\frac12\cdot z)/2 |
12,005 | x \cdot 10 + (-1) = ((-1) + x) \cdot 10 + 9 |
-7,532 | \frac13 \cdot (-i \cdot 12 + 6) = 6/3 - i \cdot 12/3 |
21,102 | e^{A + B} = e^A\times e^B = e^B\times e^A |
-1,080 | 1/\left(6 (-5/9)\right) = ((-9)*1/5)/6 |
10,744 | n/2 + \dfrac13\cdot n + \frac{1}{4}\cdot n = \dfrac{13\cdot n}{12}\cdot 1 \gt n |
-2,289 | 1/18 = 2/18 - \dfrac{1}{18} |
5,961 | (x^3 - x^2 + 1)*(1 + x^2 + x) = x^5 + x + 1 |
15,424 | \left( E * E f, f\right) = ( Ef, Ef) = \|Ef\|^2 |
31,494 | 7^2\cdot 2^2\cdot 3^3\cdot 5 = 26460 |
12,756 | x = k*x/k = \frac{1}{k}*x + x/k |
19,401 | \dfrac{4}{3}*x + x = \dfrac{1}{3}*7*x |
7,695 | 3^2 + 2^2 + 2*2*3 = (3 + 2)^2 |
19,109 | \tan\left(4 \cdot x\right) = \tan\left(π - 3 \cdot x\right) = -\tan(3 \cdot x) |
25,201 | S \cdot M - I = S - L \implies S \cdot (-I + M) = I - L |
18,530 | d^2 * d^2 = d^4 |
9,163 | 1/4 \cdot 0 + \frac14 + \dfrac{1}{2 \cdot 2} = 1/2 |
19,140 | \frac{1}{1 + k}\cdot \left(k + 2\right) = 1 + \frac{1}{k + 1} |
-4,025 | \frac{y^3 \cdot 15}{3 \cdot y^5} \cdot 1 = \frac{15}{3} \cdot \dfrac{y^3}{y^5} |
29,055 | \binom{4}{2}*4*7 \binom{6}{2} = 2520 |
20,217 | 15 = (0.5 \cdot ((-1) \cdot 0.5 + 1) \cdot 900)^{1 / 2} |
8,359 | {S \choose y} = \frac{1}{(-y + S)!\cdot y!}\cdot S! |
-1,715 | 13/6 \cdot π = π \cdot \frac{4}{3} + π \cdot 5/6 |
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