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int64 -30,985
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1,813 | 0\cdot V + V\cdot 0 = V\cdot 0 |
-8,154 | 28 = \frac72 8 |
-2,331 | \frac{6}{20} = \dfrac{3}{10} |
-222 | 5!/(3!\times 2!) = \binom{5}{3} |
-22,299 | (n + 10 \left(-1\right)) (n + 7(-1)) = 70 + n^2 - 17 n |
31,203 | \left(5 - 0.5\right) \times (12 - 0.5) \times ((-1) \times 0.5 + 10) = 491.625 |
4,714 | \left( f, f*2, ...\right) = f |
-23,119 | 63/16\cdot \tfrac34 = 189/64 |
-11,966 | \frac{1}{20} = x/(20\cdot π)\cdot 20\cdot π = x |
3,562 | z \cdot z \cdot z + 8 \cdot (-1) = (4 + z^2 + 2 \cdot z) \cdot (z + 2 \cdot \left(-1\right)) |
27,031 | c^{1 + l} \coloneqq c \cdot c^l |
-4,408 | \frac{x\cdot 4 + 18\cdot (-1)}{x^2 - x\cdot 6 + 8} = \frac{1}{x + 2\cdot \left(-1\right)}\cdot 5 - \dfrac{1}{4\cdot (-1) + x} |
27,479 | \frac{1/6*5}{6} = 5/36 |
-1,633 | \tfrac{13}{12}\cdot π - 0\cdot π = \dfrac{13}{12}\cdot π |
-20,715 | 3/3*(2 + 9*n)/(8*n) = \frac{1}{24*n}*\left(6 + n*27\right) |
4,104 | -1 = 4 \times \left(-1\right) + n\Longrightarrow n = 3 |
24,990 | (t - 1/2)^{r/2}*2^{\dfrac12*r} = (t*2 + (-1))^{r/2} |
16,409 | \beta = 7 + \frac{1}{2 + \dfrac{1}{\beta}} = \frac{15 \cdot \beta + 7}{2 \cdot \beta + 1} |
26,426 | 1/2 + (-1) = -\frac{1}{2} |
22,485 | 100 = (1 + 2 \cdot (-1) + 3 + 4 \cdot \left(-1\right) + 5) \cdot 6 + 7 \cdot (-1) + 89 |
-22,964 | \dfrac{1}{120} \cdot 36 = \dfrac{12 \cdot 3}{10 \cdot 12} |
18,085 | (a + b)^3 = a^3 + 3\cdot a \cdot a\cdot b + 3\cdot a\cdot b^2 + b^3 |
-19,000 | \frac78 = A_q/(64 \pi)*64 \pi = A_q |
5,498 | -\frac13*s + s = s*2/3 |
30,573 | -G \leq -E \Rightarrow E \leq G |
19,502 | \tan x={\sin x}/{\cos x} |
26,470 | x = \sqrt{-24\cdot i + 7} rightarrow x^2 = 7 - i\cdot 24 |
-22,300 | q^2 - 15\cdot q + 50 = (5\cdot \left(-1\right) + q)\cdot (q + 10\cdot (-1)) |
18,792 | E\left(QY\right) = E\left(Q\right) E\left(Y\right) |
-9,491 | -2\cdot 2\cdot 2\cdot 2\cdot y + 2\cdot 2\cdot 11 = -y\cdot 16 + 44 |
77 | a^4 + 4 g^4 = (g^2*2 + a^2 - g a*2) (2 g^2 + a^2 + g a*2) |
19,287 | \frac{1}{d_1} d_1 d_1 d_2 = d_1 d_2 |
-20,298 | \frac{3}{9\cdot (-1) - k\cdot 10}\cdot 8/8 = \dfrac{1}{72\cdot (-1) - 80\cdot k}\cdot 24 |
35,084 | 2\sin(\alpha) \cos(\alpha) = \sin(\alpha*2) |
10,863 | 8 \cdot \frac{\mathrm{d}}{\mathrm{d}x} \arctan(x) = \frac{8}{x^2 + 1} |
37,784 | 2 \cdot m + (-1) + 2 = 2 \cdot m + 1 = 2 \cdot (m + 1) + (-1) |
5,965 | \sum_{n=1}^\infty (-3)^n\cdot n\cdot c = \sum_{n=1}^\infty n\cdot (2\cdot \left(-1\right) - 1)^n\cdot c |
32,650 | 1 - 2*\sin^2{x} = \cos{x*2} |
3,190 | 3^{2 \cdot 2^2} + (-1) = \left(3^2 + 1\right)\cdot (3^4 + 1)\cdot (3^2 + \left(-1\right)) |
43,232 | 85079 = -2 \cdot 3 + 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 |
-26,599 | 640 - 10*x * x = 10*\left(64 - x^2\right) = 10*(8 + x)*(8 - x) |
-104 | -28 = 5\cdot (-1) - 23 |
-16,459 | 8 \sqrt{75} = 8 \sqrt{25\cdot 3} |
-4,773 | -\frac{1}{y + 2\cdot (-1)}\cdot 3 + \tfrac{5}{1 + y} = \frac{1}{2\cdot (-1) + y^2 - y}\cdot \left(13\cdot (-1) + y\cdot 2\right) |
-10,584 | \frac{4}{x\cdot 12}\cdot 5/5 = \frac{1}{60\cdot x}\cdot 20 |
17,468 | a^g \cdot a^x = a^{x + g} |
-16,439 | 3\sqrt{9\cdot 11} = \sqrt{99}\cdot 3 |
9,429 | \left(z - \dfrac1z\right)^2 + 2 + 1 = z^2 + 1 + \frac{1}{z^2} |
8,044 | 1/(\rho\cdot z) = 1/(z\cdot \rho) |
2,019 | z^{p^k} = e \Rightarrow (1/z)^{p^k} = \frac{1}{z^{p^k}} = 1/e = e |
3,582 | L\cdot 2 = L + L |
32,847 | (1 + x^2 - x*\sqrt{2})*(x^2 + \sqrt{2}*x + 1) = 1 + x^4 |
6,315 | 2^{k + 1} = (1 + 1)^{k + 1} = {k + 1 \choose 0} + {k + 1 \choose 1} + \dotsm + {k + 1 \choose k + 1} |
14,878 | \left((n,1) = \left(m, 1\right) \Rightarrow n = m\right) \Rightarrow m = n |
9,265 | (-20^{1/2} + 6)^{1/2} = (-5^{1/2}*2 + 6)^{1/2} |
26,407 | 2*\cos^2{y} + \left(-1\right) = \cos{2*y} |
32,260 | (x \times z)^2 = x^2 \times z^2 |
1,241 | 1 = |v| \Rightarrow 2 \geq |i - v| |
7,058 | 6x + 6 = 6(x + 1) |
2,318 | 1 + \left((-1) + x\right)\cdot (y + 1) = y\cdot x + x - y |
-29,013 | 0 = (0.01 - 0.01)/2 |
1,328 | y^{1 + 2 + 2}*2*2 = y^2*2 y*2y^2 |
27,551 | \overline{r_1}[x_1]+...+\overline{r_n}[x_n]=[r_1x_1+...+r_nx_n]\in M/NM |
-1,375 | 1/5\cdot 7/\left(1/8 \left(-1\right)\right) = -\dfrac81\cdot 7/5 |
10,518 | \dfrac{1}{-\frac1x + x/x} \cdot (6 \cdot x/x - \frac{1}{x} \cdot 9) = 3 \cdot \tfrac{1}{x + (-1)} \cdot \left(2 \cdot x + 3 \cdot (-1)\right) |
36,024 | \tfrac{1}{\nu} = \frac{1}{\nu} |
6,329 | 1 - x^6 = (x^4 + 1 + x^2)*(1 - x * x) |
160 | 2450448 = \frac{18!}{10! \cdot 5! \cdot 3!} |
11,463 | -\frac{1}{d + k + 1} + \frac{1}{d + k} = \dfrac{1}{(k + d) \cdot (d + k + 1)} |
22,003 | \frac{2}{31} = \frac{30}{31}/30 + \tfrac{1}{31} |
38,416 | 1 + 11 \cdot 9 = 10 \cdot 10 |
-10,279 | -\dfrac{1}{12 (-1) + y\cdot 3}5\cdot 5/5 = -\frac{1}{y\cdot 15 + 60 (-1)}25 |
6,500 | 1/2 \cdot 2 + \dfrac{1}{2} = 3/2 \neq 5/3 |
-5,039 | 0.73 \cdot 10^5 = 0.73 \cdot 10^{0 \cdot \left(-1\right) + 5} |
31,873 | \cos{y} + \sin{y} = X \cdot \sin(y + y_0) = X \cdot \sin{y} \cdot \cos{y_0} + X \cdot \cos{y} \cdot \sin{y_0} |
1,484 | k^3 - (k + 2 \cdot (-1))^3 = k^3 - k^3 - 6 \cdot k \cdot k + 12 \cdot k + 8 \cdot (-1) = 6 \cdot k^2 - 12 \cdot k + 8 |
26,214 | x \cdot \sum_{n=0}^m x^n = \sum_{n=1}^{m + 1} x^n = \sum_{n=0}^m x^n + x^{m + 1} + (-1) |
-10,437 | 5/5*2/\left(16 t\right) = 10/(t*80) |
8,605 | \dfrac{1}{f_1 \cdot 1/\left(f_2\right)} = f_2/(f_1) |
-20,972 | (-63\cdot q + 14)/70 = \frac{7}{7}\cdot \frac{1}{10}\cdot (-9\cdot q + 2) |
5,178 | (\frac13 2) (\frac13 2)^2 = \frac{8}{27} |
9,792 | A \cdot n = 1 + 7/10 \cdot \left(A \cdot n - A\right) + 3/10 \cdot (A \cdot n + A) = A \cdot n + 1 - \frac25 \cdot A |
27,768 | 4 = 2/x \Rightarrow x = \frac{1}{2} |
35,422 | -\pi + 2 \cdot \pi/3 = (\left(-1\right) \cdot \pi)/3 |
14,052 | \frac{k}{2} + 1 = \dfrac{k}{2} + \frac22 = \frac12 \cdot (k + 2) |
558 | \left(U \cdot U \cdot U + 1 = 0 \implies (-1) + U^3 = -2\right) \implies -2 = ((-1) + U) \cdot (1 + U^2 + U) |
-2,603 | 6*\sqrt{7} = \sqrt{7}*(3*(-1) + 5 + 4) |
-22,349 | 8\cdot \left(-1\right) + l^2 + l\cdot 2 = (4 + l)\cdot (l + 2\cdot \left(-1\right)) |
18,562 | f^5 = b^4 \Rightarrow (\frac{b}{f})^4 = f |
34,314 | -\tfrac{1}{2} + \sqrt{2} = \sqrt{2} - 1/2 |
-20,387 | \frac{30\cdot x + 15}{70\cdot x + 35} = \frac{3}{7}\cdot \dfrac{10\cdot x + 5}{x\cdot 10 + 5} |
18,585 | \cos{1/z} z = z - 1/(z*2!) + \frac{1}{(z^{34})!} - \dotsm |
21,460 | z^4 + 1 = z^4 - 2 z z + 1 - -2 z^2 = \left(z^2 + \left(-1\right)\right)^2 - z^2 = (z^2 + (-1) + z) (z^2 + (-1) - z) |
-18,332 | \frac{x^2 + x\cdot 10}{x x + 13 x + 30} = \dfrac{(10 + x) x}{(x + 3) (10 + x)} |
33,026 | 1 = \frac{1}{(-1)*0.5 + 1}*0.5 |
25,706 | 2\cdot x + (-1) = 2\cdot (-\dfrac{1}{2} + x) |
19,112 | \frac{\frac{1}{6!}\cdot 10!}{10^4} = 63/125 |
23,453 | i^4 = i^{2 + 2} = i^2 i^2 = \left(-1\right) (-1) = 1 |
47,086 | \tanh{i\times z} = \dfrac{\sinh{i\times z}}{\cosh{i\times z}} = \frac{\frac{1}{2}\times (e^{i\times z} - e^{-i\times z})}{\frac12\times \left(e^{i\times z} + e^{-i\times z}\right)} = i\times \sin{z}/\cos{z} = i\times \tan{z} |
-20,565 | \frac{1}{-a\cdot 15 + 30}\cdot (20\cdot a + 45) = \frac55\cdot \dfrac{9 + 4\cdot a}{-3\cdot a + 6} |
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