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int64 -30,985
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-20,847 | ((-48)\cdot n)/(n\cdot 18) = -8/3\cdot n\cdot 6/\left(6\cdot n\right) |
2,844 | z \cdot 10 = 2 \cdot z \cdot 2 + z \cdot 6 |
19,917 | 1 + x^2 + x = 3/4 + (x + \frac12)^2 |
7,652 | r\cdot x\cdot y = y\cdot x\cdot r |
-20,537 | -\frac17 \cdot (-\dfrac{9}{-9}) = 9/\left(-63\right) |
15,453 | \tan{x} = \dfrac{1}{\cos{x}} \cdot \sin{x} = -i \cdot \frac{e^{i \cdot x} - e^{-i \cdot x}}{e^{i \cdot x} + e^{-i \cdot x}} |
10,197 | \sin(A) = 2*\sin(A/2)*\cos(\frac{A}{2}) |
28,816 | 0 - y - z = z - y |
2,167 | 1 + 2\cdot r = (1 + r)^2 - r \cdot r |
-504 | \left(e^{\dfrac{i*\pi*13}{12}}\right)^{16} = e^{16*\frac{13*\pi*i}{12}} |
44,279 | 10^z = 5^z\cdot 2^z |
-11,955 | \frac{13}{15} = \frac{1}{12 \cdot \pi} \cdot x \cdot 12 \cdot \pi = x |
16,943 | \dfrac{6}{100} = \frac{1}{10} \times 2 \times 3/10 |
46,296 | 1 + 5 + 4 + 3 + 2 = 15 |
-18,966 | 7/18 = \dfrac{1}{100*\pi}*Z_t*100*\pi = Z_t |
45,996 | 689 = 13 \cdot 53 |
11,212 | {-1 \choose r} = \frac{1}{r!} \cdot ((-1) \cdot (-2 \cdot \cdots \cdot \left(-1 - r + 1\right))) = \left(-1\right)^r |
-10,269 | 3/3\cdot \frac{1}{4\cdot (-1) + r\cdot 8}\cdot (3\cdot r + 2\cdot (-1)) = \frac{r\cdot 9 + 6\cdot (-1)}{12\cdot (-1) + 24\cdot r} |
15,047 | \cos{s} = -\sin{s} |
-19,718 | \frac{2}{9}\cdot 10 = 20/9 |
-3,417 | (4(-1) + 2 + 3)*11^{1 / 2} = 11^{\frac{1}{2}} |
16,097 | w*\rho^U*z = w*z*\rho^U |
24,028 | \sin^2{\frac12 \cdot x} = \frac{1}{2} \cdot (1 - \cos{x}) = \dfrac12 \cdot (1 - \sqrt{1 - \sin^2{x}}) |
16,993 | \frac{1}{z^2\cdot x}\cdot \sin(x\cdot z^2)\cdot \frac{x\cdot z \cdot z}{x^2 + z \cdot z} = \frac{1}{x^2 + z^2}\cdot \sin(x\cdot z^2) |
-20,543 | \frac{1}{\left(-9\right) \times t} \times t \times 15 = \frac{(-3) \times t}{(-3) \times t} \times (-5/3) |
-2,527 | \sqrt{2} + 5\sqrt{2} = \sqrt{25} \sqrt{2} + \sqrt{2} |
-4,052 | 100*l/(l*40) = 100/40*l/l |
-5,173 | 10^{4 + 1}\cdot 36 = 36\cdot 10^5 |
-19,379 | 2/9\cdot \frac35 = \frac{2\cdot \frac{1}{9}}{5\cdot \frac{1}{3}} |
-4,663 | \frac{5}{x + 5(-1)} + \dfrac{1}{x + 2(-1)}4 = \dfrac{9x + 30 (-1)}{x^2 - 7x + 10} |
26,684 | x\times \frac{36}{\sqrt{1463}} = \frac{1}{2\times \frac{1}{108}\times \sqrt{1463}}\times 2 / 3\times x |
27,130 | 1/(g*h) = 1/(h*g) = \frac{1}{g*h} |
29,204 | 2 + b\cdot a - a + b = 1 + \left((-1) + a\right)\cdot (b + (-1)) |
22,287 | 3*\left(-1\right) + x = -x - 1 \implies x = 1 |
2,006 | \frac{y^l + \left(-1\right)}{y + \left(-1\right)} = \frac{1}{y + (-1)}*(y + (-1))*(1 + y + \dotsm + y^{l + \left(-1\right)}) = 1 + y + \dotsm + y^{l + (-1)} |
-4,984 | 4.640 \times 10 = {4.640 \times 10} \times 10^{4} = 4.640\times 10^{5} |
12,722 | a^2 + G = a + a + G = (a + G) \cdot (a + G) = (a + G) \cdot (a + G) |
23,603 | -2\cdot \lambda - \lambda\cdot 2 - \frac12\cdot \lambda = 16 \Rightarrow \lambda = -\frac{32}{9} |
33,163 | 4\pi^2 Qr = 2Q\pi \cdot 2\pi r |
-1,823 | \pi \cdot 5/4 = -\pi \cdot 2 + 13/4 \cdot \pi |
-7,958 | (105 - 100\cdot i + 42\cdot i + 40)/29 = \tfrac{1}{29}\cdot (145 - 58\cdot i) = 5 - 2\cdot i |
-16,052 | 7\times 6\times 5 = \frac{7!}{(7 + 3\times (-1))!} = 210 |
-15,069 | \frac{m^5}{\frac{1}{m^3} \cdot s^4} = \frac{\tfrac{1}{\frac{1}{m \cdot m \cdot m}}}{s^4} \cdot m^5 = \frac{1}{s^4} \cdot m^{5 - -3} = \frac{m^8}{s^4} |
694 | 315 = 3 + \frac17\cdot (3^7 + 3\cdot (-1)) |
15,301 | X = \arccos(y) \Rightarrow \cos\left(X\right) = y |
4,462 | \left(m + 1\right)\cdot (m + (-1)) = m^2 + (-1) |
2,689 | 2 \cdot 1/8 \cdot 1/8/8 = 2/512 |
5,171 | (-2^{1/2} + 2)^{1/2} = \frac{2^{1/2}}{(2 + 2^{1/2})^{1/2}} |
12,410 | 1/8 = \tfrac{1}{2\cdot 4} |
-8,795 | 25 \times 4 = 100 |
1,225 | \mathbb{Cov}\left(R,R\right) = VAR\left(R\right) |
9,325 | a^3 - b^3 = (a^2 + b\cdot a + b^2)\cdot (a - b) |
10,923 | X*X = X * X |
-19,538 | 9/2 \cdot \frac{9}{4} = \tfrac{1/2}{4 \cdot \frac{1}{9}} \cdot 9 |
16,117 | \frac{2}{\frac13}\frac{1}{3}*40 = 2*40 = 80 |
3,487 | (-\dfrac{x}{x} + 1) x = 0\Longrightarrow 1 = \frac{x}{x} |
-20,781 | \dfrac{6}{60 \left(-1\right) + 36 z} = \frac{1/6*6}{10 (-1) + z*6} |
19,623 | -1 < 2\times (-1) + \dfrac{x}{2} \implies 2 < x |
5,738 | \sqrt{2} = \frac{\cos(\frac{\pi}{12}) \cdot 4}{-\tan(\pi/12) + 3} |
-10,408 | -\frac{3}{3 + x}*3/3 = -\frac{1}{3*x + 9}*9 |
27,481 | p^3 = 1 + p^2 \times p - p \times p + p^2 - p + p + (-1) |
10,294 | \left(-\dfrac{1}{2}\right)^{k + 1} = \frac{(-1)^{1 + k}}{2^{1 + k}} |
21,876 | 50 + 1 - 2\cdot (-7) + 1^2 - 2\cdot 2\cdot (-1) + 2\cdot (-7) + 2 \cdot 2 + 2\cdot (-1) = 58 |
14,974 | x^3 + 2\cdot x^2 + 2\cdot x + 1 = (x + 1)\cdot (x \cdot x + x + 1) |
18,330 | \mathbb{N}_{l} := \left\{..., 1, l\right\} |
15,923 | (-b + 10) (-b + 10) = b^2 + 100 - b\cdot 20 |
22,325 | \dfrac{3}{2} \cdot y \cdot z - 5/4 = -1/2 + z \cdot y \cdot 3/2 - \dfrac14 \cdot 3 |
36,739 | 16^m = 4^{2 m} |
-20,347 | (16\cdot (-1) - n\cdot 40)/(-80) = 8/8\cdot \frac{1}{-10}\cdot (-n\cdot 5 + 2\cdot (-1)) |
1,888 | z*y*\Delta = z*\Delta*y |
4,307 | |2 - 2\cdot z| = 2\cdot |z + (-1)| |
39,297 | (10 + 6 \cdot \left(-1\right))^m = 4^m \geq 2^m |
29,006 | \tfrac12 + \frac{1}{2}\cdot \sqrt{5} = \frac12\cdot (\sqrt{5} + 1) |
21,641 | n*2 + (-1) = 1 + 2*(n + (-1)) |
24,137 | \dfrac{1}{2\cdot 2} = \dfrac{1}{4} |
-19,394 | \frac14\cdot 5\cdot 7/6 = \frac{5}{6\cdot 1/7}\cdot \dfrac{1}{4} |
19,638 | \frac{1}{3}(0.5+0.6+0.7)=0.6 |
30,080 | \sin\left(-x + \dfrac{1}{2}\pi\right) = \cos\left(x\right) |
-23,740 | 2/3 \cdot 6/7 = \frac17 \cdot 4 |
41,408 | \left(f\times x + \left(-1\right)\right)/(x\times f)\times \left(-x + f\right) = f + \frac1f - 1/x + x |
7,218 | (-1) + x^7 = \left(x^6 + x^5 + x^4 + x \cdot x \cdot x + x^2 + x + 1\right) (x + (-1)) |
-10,380 | \frac{1}{40 \cdot b \cdot b} \cdot (40 \cdot b + 30 \cdot (-1)) = \frac{1}{4 \cdot b \cdot b} \cdot (b \cdot 4 + 3 \cdot (-1)) \cdot \frac{1}{10} \cdot 10 |
31,241 | h + b - h + b = h + b - h - b = h - h + b - b |
31,299 | \dfrac{1}{c^x} = c^{-x} |
20,551 | \dfrac{3 / 7}{3}\cdot 1 = \frac17 |
-5,016 | 0.84*10^3 = 0.84*10^{\left(-1\right) (-1) + 2} |
25,766 | \frac{1}{2}*1/4 = \frac18 |
-598 | \left(e^{π \cdot i/12}\right)^{15} = e^{15 \cdot i \cdot π/12} |
-8,085 | \frac{-8 \cdot i + 2}{5 \cdot i + 3} \cdot \frac{3 - 5 \cdot i}{-i \cdot 5 + 3} = \dfrac{-i \cdot 8 + 2}{3 + 5 \cdot i} |
4,262 | \left(-a = x \Rightarrow x^m = -a^m\right) \Rightarrow 0 = x^m + a^m |
5,427 | (l + 1)! + \left(l + 1\right)! (l + 1) = (l + 1)! (1 + l + 1) = (l + 2)! |
-4,682 | \frac{4}{x + 2\cdot (-1)} + \frac{5}{x + 3\cdot (-1)} = \dfrac{x\cdot 9 + 22\cdot (-1)}{x^2 - 5\cdot x + 6} |
-16,980 | 5 = 15\cdot m \cdot m + 20\cdot m + 5\cdot (-3\cdot m) + 5\cdot (-4) = 15\cdot m^2 + 20\cdot m - 15\cdot m + 20\cdot (-1) |
-20,273 | \dfrac{4 \cdot (-1) - 20 \cdot j}{j \cdot 45 + 9} = -4/9 \cdot \frac{j \cdot 5 + 1}{1 + j \cdot 5} |
113 | 4({9 \choose 1} \cdot 1! + {9 \choose 2} \cdot 2! + \dots + {9 \choose 9} \cdot 9!) = 3945636 |
35,990 | 2\pi = \pi + \pi |
-11,493 | i\cdot 36 + 16 + 20\cdot (-1) = -4 + 36\cdot i |
24,203 | (-2 \cdot 2^{1 / 2} + 3) \cdot 4 = 12 - 2^{\frac{1}{2}} \cdot 8 |
49,982 | 4\times 1000 = 4000 |
-3,985 | \frac{l^3}{32 \cdot l^5} \cdot 16 = 16/32 \cdot \frac{1}{l^5} \cdot l^2 \cdot l |
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