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int64 -30,985
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6,401 | (q - p)^2 = (p - q) * (p - q) |
27,273 | \frac12\cdot (1 + 5^{1/2}) = 5^{1/2}/2 + 1/2 |
12,339 | n = \left\{1, ..., n\right\} |
19,120 | m*2 + 3(-1) = m + \left(-1\right) + m + 2(-1) |
26,694 | \frac{1}{-10}\cdot 48 = -24/5 |
8,589 | n^5 + (-1) = (n + (-1)) \cdot \left(n^4 + n^3 + n^2 + n + 1\right) |
17,594 | \frac{1}{12} = 7/z rightarrow 84 = z |
2,765 | kv + wk = k \cdot (w + v) |
40,916 | 121^2 - 17*54 54 = 14641 + 49572 (-1) = -34931 |
-20,889 | \tfrac{1}{-2 \cdot k + 20} \cdot (-k \cdot 10 + 4) = \frac{1}{-k + 10} \cdot (-5 \cdot k + 2) \cdot \frac12 \cdot 2 |
109 | \frac12\left(-\cos(2x) + 1\right) = \sin^2(x) |
4,902 | \varepsilon/F = X/H \implies \frac{1}{H}\cdot X = \varepsilon/F = \frac{X - \varepsilon}{H - F} |
-15,058 | \frac{1}{\frac{1}{y^4 x^6} y^5} = \frac{(\frac1y)^5}{\frac{1}{y^4 x^6}} |
-22,719 | \frac{5 \cdot 8}{7 \cdot 8} = 40/56 |
16,260 | \left(z - y_2\right)\cdot (z - y_1) = y_2\cdot y_1 + z \cdot z - (y_1 + y_2)\cdot z |
-10,643 | 3/(t*12) = \frac{1}{4*t}*1 |
-23,921 | \dfrac{15}{1 + 4} = \frac15\cdot 15 = \frac{15}{5} = 3 |
711 | \sqrt{\frac{1 + t}{1 - t}} = \frac{1}{\sqrt{1 - t^2}} \cdot (1 + t) = (1 + t) \cdot \mathbb{E}[t] |
-2,585 | ((-1) + 4 + 5)\cdot \sqrt{13} = 8\cdot \sqrt{13} |
14,759 | (-y + x)\cdot \left(y + x\right) = x \cdot x - y^2 |
9,718 | 0 = u \cdot (-\lambda \cdot I + B \cdot A)\Longrightarrow u \cdot B \cdot (B \cdot A - \lambda \cdot I) = 0 |
-10,488 | \dfrac{1}{x}(4x + 1)*3/3 = (x*12 + 3)/(3x) |
10,034 | (b_z + \left(-1\right))*(b_z + 1) = b_z^2 + \left(-1\right) |
-536 | \pi\cdot 3/2 = \pi\cdot \frac{1}{2}\cdot 35 - \pi\cdot 16 |
24,092 | N^{x_0} = Nk \Rightarrow N^{x_0 + (-1)} = k |
5,836 | \frac{4}{51}\cdot \frac{48}{52} = \dfrac{16}{221} |
-22,178 | 80\cdot (-1) + z^2 - 2\cdot z = (10\cdot \left(-1\right) + z)\cdot (8 + z) |
13,823 | b^4 - a^4 = (b^2 - a \cdot a)\cdot (b^2 + a^2) = (b - a)\cdot (b + a)\cdot (b \cdot b + a^2) |
-797 | 491/10000 = 1/10000 + 0 + \frac{0}{10} + \frac{4}{100} + 9/1000 |
21,645 | \cos\left(x + z\right) = -\sin(x)\cdot \sin\left(z\right) + \cos\left(z\right)\cdot \cos\left(x\right) |
21,777 | y\cdot 4\cdot \left(1 + l\right) = (l\cdot 4 + 4)\cdot y |
-7,164 | \frac{1}{24}\cdot 7 = \dfrac19\cdot 6\cdot \dfrac{7}{10}\cdot 5/8 |
14,817 | \left(\cos{z} = i\cdot \sin{z} \Rightarrow 0 = -i\cdot \sin{z} + \cos{z}\right) \Rightarrow e^{-z\cdot i} = 0 |
-7,293 | 3/9\cdot \frac{2}{10} = \frac{1}{15} |
7,939 | 20 \pi/8 = \frac{\pi\cdot 5}{2} |
-8,978 | 104.7\% = \frac{1}{100} \cdot 104.7 |
-20,878 | \dfrac{-10y - 3}{y - 1} \times \dfrac{7}{7} = \dfrac{-70y - 21}{7y - 7} |
-20,466 | -9/4*\frac{1}{t + 10}*\left(t + 10\right) = \dfrac{1}{t*4 + 40}*(-t*9 + 90*(-1)) |
11,995 | 4 + x^2 = 4 \cdot \left(1 + x^2/4\right) |
240 | \frac14 = -\frac23 + 11/12 |
-11,637 | 16*i - 16 + 3 = i*16 - 13 |
1,061 | 0 = b + 2 \cdot (-1) \Rightarrow 2 = b |
5,848 | 1/(g\cdot f) = 1/\left(f\cdot g\right) |
-5,827 | \dfrac{5}{4 \cdot (p + 5)} = \frac{1}{4 \cdot p + 20} \cdot 5 |
18,149 | 1 = \frac{z}{z} rightarrow \frac1z = 1/z |
18,959 | \cos^2(x) - \sin^2\left(x\right) = 2 \cdot \cos^2(x) + \left(-1\right) = 1 - 2 \cdot \sin^2(x) |
38,378 | 0^{2^{k + 1 + 1}} = 0^{2^k*2*2} |
-17,470 | 19 = 32\cdot \left(-1\right) + 51 |
18,586 | \frac{15}{45} + \frac{24}{45}*\frac{1}{2} = \frac{1}{3} + \frac{4}{15} = \frac15 3 |
35,108 | (n + 1)/n! = 1/n! + \frac{1}{\left(n + (-1)\right)!} |
-7,426 | \frac{9}{91} = \dfrac{3}{13}*6/14 |
17,790 | \frac{x^2 + y^2}{x \cdot y} = \frac{1}{x \cdot y} \cdot (\left(x + y\right)^2 - 2 \cdot x \cdot y) = \frac{(x + y)^2}{x \cdot y} + 2 \cdot (-1) |
-4,455 | -\frac{1}{(-1) + x} - \frac{1}{4 \cdot (-1) + x} \cdot 4 = \dfrac{1}{x \cdot x - 5 \cdot x + 4} \cdot \left(-5 \cdot x + 8\right) |
16,393 | \frac{y}{y + h} = 1 - \frac{h}{y + h} |
-25,312 | \dfrac{d}{dx}\left(\dfrac1x\cos(x)\right)=\dfrac{-\cos(x)-x\sin(x)}{x^2} |
10,305 | \left(b + a = b*a \Rightarrow a*b - a - b = 0\right) \Rightarrow 1 = (a + (-1))*((-1) + b) |
21,168 | 3/8 = 3/4\cdot \dfrac14\cdot 2 |
15,310 | A_1 B_0 + B_1 A_0 = -A_1 B_1 + (A_0 + A_1) (B_1 + B_0) - A_0 B_0 |
-9,177 | x \cdot 54 + 18 \cdot (-1) = x \cdot 2 \cdot 3 \cdot 3 \cdot 3 - 2 \cdot 3 \cdot 3 |
6,448 | 3^x \cdot 2 + 3 \cdot 3^x \cdot c_{k+1} = c_{k+1} \cdot 3^{1 + x} + 2 \cdot 3^x |
23,421 | \frac12 = \frac{1}{4}*2 |
37,475 | 3^{11} = 3^2 \cdot 3\cdot 3^8 = 10\cdot (-1) = 7 |
28,603 | (x + q)*(-q + x) = -q^2 + x^2 |
3,172 | x*261 + 1073 = 29*9 x + 1073 |
33,915 | \frac{1 + n}{\sqrt{n + 1}} = \sqrt{n + 1} |
14,894 | \epsilon + \epsilon\cdot (1 + \epsilon) = \epsilon^2 + \epsilon\cdot 2 |
-30,292 | \frac{1}{2}\cdot (-1 + 7) = \tfrac62 = 3 |
7,587 | A \setminus G = A - A \cap G = A \cup G - G |
-486 | \left(e^{\pi i*11/6}\right)^{19} = e^{\frac16 11 i \pi*19} |
40,799 | \binom{9}{6} + 7\cdot (-1) = 77 |
7,387 | \tan^{-1}{w} = G + x \implies \tan(G + x) = w |
43,488 | V\cdot 2 = V + V |
-2,260 | \dfrac{1}{12} = 2/12 - \dfrac{1}{12} |
13,377 | \dfrac{1}{(f^2 + y^2)^2}\cdot y\cdot y = \dfrac{1}{(y^2 + f^2)^2}\cdot y^2 |
27,863 | 7 \cdot i - 1 = \frac14 \cdot (-7 + i \cdot 24 + 3 + i \cdot 4) |
12,409 | {52 \choose 13} = \frac{1}{13}52 {51 \choose 12} = 4{51 \choose 12} |
36,265 | 35 - x^3 = t^3 \implies x = (-t \cdot t \cdot t + 35)^{1/3} |
-24,111 | 2 + 2\cdot \frac{24}{6} = 2 + 2\cdot 4 = 2 + 2\cdot 4 = 2 + 8 = 10 |
30,036 | \frac{1}{b^2} \cdot a \cdot a = p \Rightarrow a^2 = b \cdot b \cdot p |
16,246 | y + 8*(-1) = -4*(x + 1) = -4*x + 4*(-1) \Rightarrow 0 = y + x*4 + 4*(-1) |
35,776 | \frac13\cdot 192 = 64 |
30,964 | \cos{b} \cos{f} + \sin{f} \sin{b} = \cos\left(f - b\right) |
-20,462 | \frac{d + 9}{2 - d\cdot 2}\cdot \dfrac{7}{7} = \frac{63 + d\cdot 7}{14 - 14 d} |
32,500 | \int \tan{x}\,dx = \int \frac{\sin{x}}{\cos{x}}\,dx |
14,644 | \tfrac{m^2}{m + 1} > \frac{m^2 + \left(-1\right)}{m + 1} = \frac{1}{m + 1}\cdot (m + 1)\cdot (m + (-1)) = m + (-1) |
20,841 | x - \dfrac{1}{2} + 5/2 = 0 \Rightarrow x = -2 |
27,985 | |x + (-1)| = |1 - x| \geq |1| - |x| = 1 - |x| \Rightarrow \dfrac{3}{4} \leq |x| |
14,629 | x/y = \frac{2*x}{2*y} |
24,974 | ((-1) + B) \cdot (B + 1) = (-1) + B^2 |
35,151 | A^n\cdot A = A^{1 + n} |
29,789 | 0.99 = -1/100 + 1 |
23,019 | (-1) + \tfrac{1}{g}\cdot (d + f + g) = (f + d)/g |
-30,903 | 50 = 10 + 20\cdot 2 |
2,100 | 1 + z + z \cdot z + ... = \dfrac{1}{1 - z} |
-20,976 | -3/2\cdot (x\cdot (-4))/((-4)\cdot x) = x\cdot 12/\left(x\cdot (-8)\right) |
-12,901 | \dfrac{15}{25} = \frac35 |
27,611 | (y^2 + (-1)) \cdot (y^2 + 1) = (-1) + y^4 |
5,056 | g^2 + 2 \cdot g \cdot a + a^2 = (g + a)^2 |
18,154 | (N + 2 \cdot (-1)) \cdot (N + 2 \cdot (-1)) + (\dfrac{1}{2} \cdot (3 + N)) \cdot (\dfrac{1}{2} \cdot (3 + N)) = N \cdot N + ((5 \cdot (-1) + N)/2)^2 |
15,548 | 43361 = (13*10 + 1) \left(3*11*10 + 1\right) = 131*331 |
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