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int64 -30,985
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-26,463 | (-3*x + 2)^2 = 2^2 - 3*x*2*2 + (x*3)^2 |
20,023 | m\cdot q + m + (-1) = m\cdot \left(1 + q\right) + (-1) |
14,010 | (x + 1 + I)\cdot (x + 1 + I) = x^2 + 2\cdot x + 1 + I = x + x \cdot x + x + 1 + I = x + I |
20,666 | \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{x} = -\dfrac{1}{x^2} = -\dfrac{1}{x^2} |
29,049 | \left(n + (-1)\right) \cdot 2 + 1 = \left(-1\right) + n \cdot 2 |
4,687 | \operatorname{Var}(V) = \operatorname{Var}(V_1 + \dotsm + V_{10}) = \operatorname{Var}(V_1) + \dotsm + \operatorname{Var}(V_{10}) |
-23,426 | \frac{\dfrac15}{2}*4 = \frac{1}{5}*2 |
11,715 | aE = Ea |
39,663 | 1 + \tan(x)/x = \frac{1}{x}*(x + \tan(x)) |
-22,319 | 12 + n * n - n*8 = (n + 2*(-1))*(n + 6*(-1)) |
24,213 | -45 \cdot 5 + 1140 + 120 \cdot (-1) = 795 |
29,425 | 10 \cdot (-1) + (-1) = -11 |
-1,304 | 7*\frac16/((-7)*1/4) = 7/6 (-\dfrac47) |
-27,850 | \frac{\mathrm{d}}{\mathrm{d}y} \csc(y) = -\cot(y)\cdot \csc\left(y\right) |
9,905 | (-2^k + 2)/\theta = -2^k/\theta + 1/\theta + \frac{1}{\theta} |
-5,618 | \frac{2}{2 h + 16 \left(-1\right)} = \frac{1}{\left(h + 8 (-1)\right)\cdot 2} 2 |
21,613 | \frac{1}{4\cdot 2}(-4 + \sqrt{16 + 64 (-1)}) = \frac12(-1 + \sqrt{-3}) |
14,537 | \overline{v \times x} = \overline{x} \times \overline{v} |
9,339 | \beta \lt -\alpha\Longrightarrow -\beta \gt \alpha |
27,266 | rrx = r^2 x |
5,240 | 1 = \frac{1}{4} + 3/4 |
3,566 | 12\cdot \frac{\dfrac{1}{\sqrt{3}}\cdot 2}{\sqrt{2}} = 24/(\sqrt{6}) |
3,036 | 0 + x^3 + x \cdot x + x \cdot 0 = (x + 0)^2 \cdot (x + 1) |
-6,695 | 50/100 + 3/100 = \frac{5}{10} + \dfrac{1}{100} \cdot 3 |
31,920 | \frac{6}{(2 + 1)*2} = 1 |
-30,853 | \frac{x^3 - 9\cdot x}{-3\cdot x + x^2} = 3 + x |
3,144 | \sin^2{x} = \left(-\cos{2*x} + 1\right)/2 |
16,733 | (n*2 + n * n) \frac{5}{6} = \tfrac{1}{6}5 ((1 + n)^2 + (-1)) |
-15,234 | \frac{1}{\dfrac{1}{x^5}\cdot a \cdot a\cdot \frac{1}{x^8}} = \frac{x^8}{a^2\cdot \frac{1}{x^5}} |
8,151 | S^2 - 2\cdot S + 3\cdot \left(-1\right) = (S + 3\cdot (-1))\cdot (1 + S) |
-17,243 | -29/3 = -\dfrac{29}{3} |
14,648 | -\frac{x}{x + 1} + 1 = \frac{1}{x + 1} |
9,708 | -1*\left(23 - 7*3\right) + 3 = 3 - 23 - 21 |
1,842 | 2/3 = \frac{2}{3}*0 + \frac13 + 1/3 |
-6,329 | \frac{2}{10 \cdot (-1) + m} \cdot \frac{m + 1}{m + 1} = \frac{2}{(10 \cdot (-1) + m) \cdot \left(m + 1\right)} \cdot (m + 1) |
-19,473 | \frac{\dfrac{1}{7}}{3}\cdot 8 = \frac{1}{3\cdot \frac{1}{8}\cdot 7} |
28,291 | -\cos(h) = \cos(h + \pi) |
48,064 | 16\cdot 11 = 176 = 7\cdot 25 + 1 |
412 | \sin(2\cdot q - q) = \sin{q} |
30,740 | \frac{1}{y - x} = \frac{1}{(1 - \frac1y \cdot x) \cdot y} |
6,578 | h_1 n_1 n_2 h_2 = n_1 n_2 h_2 h_1 |
-6,252 | \dfrac{1}{x^2 - x*3 + 18 (-1)}4 = \tfrac{1}{(x + 3) (x + 6(-1))}4 |
14,411 | 3 \leq y \implies e^{y + (-1)} > 2^{y + (-1)} \geq 2^{y + \left(-1\right)} = \left(1 + 1\right)^{y + \left(-1\right)} |
25,467 | \frac{1}{2} \cdot \left(1 - \cos{2 \cdot x}\right) = \sin^2{x} |
11,533 | 3/100\cdot (1 - \frac{3}{100}) = 0.0291 |
16,161 | -\frac16\cdot 3 = -1/2 |
3,168 | I = (I - B) \cdot (C + I) = C + I - B \cdot C - B |
-4,284 | \frac{z^3}{z * z} = z*z*z/(z*z) = z |
23,948 | 123456789=3^2\times3607\times3803 |
-7,600 | \left(12 - 28 i + 12 i + 28\right)/8 = (40 - 16 i)/8 = 5 - 2i |
-29,592 | \frac{d}{dx} (2\cdot x^2) = 2\cdot \frac{d}{dx} x \cdot x = 2\cdot 2\cdot x^1 = 4\cdot x |
22,232 | \frac{11}{50} = 13/26 \cdot 2 \cdot 12/25 \cdot 11/24 |
8,567 | 6 \cdot (m \cdot n \cdot 6 + n + m) + 1 = (6 \cdot m + 1) \cdot (1 + 6 \cdot n) |
18,285 | 1 - \cos\left(u\right) = 2 \sin^2(\dfrac{u}{2}) \leq u^2/2 |
23,855 | \dfrac16 * \left(\dfrac16\right)^2 = 1/216 |
26,520 | -y^4 + x^4 = (x + y) \left(-y + x\right) (x^2 + y * y) |
14,573 | 12^2 = (2^2*3)^2 = 2^4*3^2 |
16,797 | (p-2x)^2 = p^2-4px+4x^2 |
12,712 | (-1) + (k + 1)*k!*\left(2 + k\right) = (2 + k)*k!*(k + 1) + (-1) |
-3,951 | \frac{44 \cdot a^5}{a^5 \cdot 55} \cdot 1 = \frac{1}{55} \cdot 44 \cdot \dfrac{1}{a^5} \cdot a^5 |
-3,125 | 5 \sqrt{2} = \sqrt{2} \cdot ((-1) + 2 + 4) |
2,211 | \dfrac{1}{6} = 0.166666\cdot \ldots |
10,174 | 3^k + (-1) = 2 \cdot 3^0 + 3^1 \cdot 2 + 2 \cdot 3^2 + \cdots + 2 \cdot 3^{k + \left(-1\right)} |
12,587 | 46 = 15 + 5*0 + 4*2 + 3*3 + 2*7 |
3,018 | \dfrac{2}{2}\cdot 20\cdot 4 = 20\cdot 4 = 80 |
25,353 | -7/24 = \cot{\alpha} \implies \tan{\alpha} = -24/7 |
13,547 | 1/(\frac{1}{d_1} d_2) = d_1/(d_2) = 1/(\dfrac{1}{d_2} d_1) |
5,542 | \cot(-\frac{37}{2} \cdot \pi) = 0 |
-9,121 | 63\cdot x - 7\cdot x^2 = -7\cdot x\cdot x + x\cdot 3\cdot 3\cdot 7 |
-21,006 | -\dfrac{2}{3}\cdot \frac{6\cdot (-1) - z}{6\cdot (-1) - z} = \dfrac{12 + 2\cdot z}{-z\cdot 3 + 18\cdot (-1)} |
8,622 | -f'' = f''*i^2 |
-6,687 | \frac{1}{100}4 + 4/10 = 4/100 + \frac{40}{100} |
30,113 | \sqrt{6}\cdot 2 + 5 = \dfrac{1}{-2\cdot \sqrt{6} + 5} |
22,130 | \binom{19}{2}\cdot \binom{1}{1}/(\binom{20}{3}) = \frac{3}{20} |
52,571 | (x^2 - y^2) \times (x^2 - y^2) + \left(2 \times x \times y\right)^2 = x^4 - 2 \times x^2 \times y^2 + y^4 + 4 \times x^2 \times y^2 = x^4 + 2 \times x^2 \times y^2 + y^4 = (x^2 + y^2)^2 |
22,595 | c = 3^0*c |
-7,846 | (-11 - 3 \times i - 22 \times i + 6)/5 = \frac15 \times (-5 - 25 \times i) = -1 - 5 \times i |
6,363 | \sin{2*x} = 2*\sin{x}*\cos{x} = \sin^2{x} |
-10,726 | -(p\cdot 8 + 10)/\left(2\cdot p\right) = \frac{2}{2}\cdot (-(4\cdot p + 5)/p) |
21,560 | (-y^2 + 2 \cdot 2)^{1/2} = h\Longrightarrow h \cdot h + y^2 = 2^2 |
-20,775 | 8/8\cdot \frac{2 - 6\cdot n}{n + 5\cdot (-1)} = \tfrac{-48\cdot n + 16}{n\cdot 8 + 40\cdot \left(-1\right)} |
-12,428 | 58 = \dfrac{116}{2} |
24,675 | x^6 = (3*x^3)^2 + (-x * x*2)^3 |
8,973 | L' - \dfrac{1}{1 + \sin{L'}}(L' - \cos{L'}) = L' |
35,532 | Cy = Cg y = gC y |
2,882 | (-\sqrt{2} + 2)*(5 + \sqrt{2}) = (\sqrt{2} + 2)*(-\sqrt{2}*7 + 11) |
-174 | \binom{9}{5} = \frac{9!}{5! \left(9 + 5 (-1)\right)!} |
-19,013 | 1/2 = \frac{G_q}{16\cdot \pi}\cdot 16\cdot \pi = G_q |
5,146 | \dfrac{1}{q + 1} = 1 - q + q^2 - \frac{q \cdot q^2}{1 + q} |
29,050 | k * k * k + k^2*3 + 3*k + 1 = \left(1 + k\right)^2 * (1 + k) |
-10,569 | \frac{1}{25 \cdot y} \cdot 1 = \frac{3}{y \cdot 75} |
12,162 | \sin(z) = (e^{i*z} - e^{-i*z})/(2*i) = -i*\sinh(i*z) |
25,028 | x + s = (x + s) \cdot (x + s) \Rightarrow x \cdot s + x \cdot s = 0 |
-19,058 | 3/4 = \frac{A_s}{49*π}*49*π = A_s |
-2,605 | (16\cdot 11)^{1 / 2} - (4\cdot 11)^{\frac{1}{2}} = 176^{1 / 2} - 44^{\dfrac{1}{2}} |
13,182 | ( x^2, x \cdot N) = ( x^2, N) \cap ( x \cdot x, x) = x \cap \left( x \cdot x, N\right) |
5,966 | 1 - x \cdot x \cdot x = (x^2 + 1 + x) \cdot (1 - x) |
12,973 | -a + a + z = a + y - a rightarrow y - a + a = -a + a + z |
22,763 | 4 = z^2 - x * x = (z - x)*(z + x) |
3,437 | 400\cdot (1 + 0.25) = 500 |
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