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int64 -30,985
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20,767 | y \cdot x/100 = \frac{x}{100} \cdot y |
-1,695 | \pi*17/12 + \pi*\dfrac{11}{12} = \dfrac{7}{3}*\pi |
21,296 | |b_n a_n - ab| = |b_n a_n - ba + ba_n - a_n b| |
10,767 | x = x - \sum_{j=2}^n e_j*x_j + \sum_{j=2}^n e_j*x_j = \sum_{j=1}^n e_j*x_j |
12,549 | p^2 - p = p*(\left(-1\right) + p) |
-7,737 | \frac{1}{i\cdot 4 + 2}\cdot (-i\cdot 2 + 4)\cdot \tfrac{-i\cdot 4 + 2}{-i\cdot 4 + 2} = \frac{1}{2 + 4\cdot i}\cdot (4 - 2\cdot i) |
36,798 | -\frac{1}{15} \cdot 4 = -4/15 |
30,284 | \{\} = \left( \left(-1\right) + z_1, \alpha\right) \implies \{\} = [z_1, \alpha] |
-7,766 | \frac{1}{3 - i \cdot 3}(-i \cdot 3 + 3) \frac{-3 - 3i}{3 + i \cdot 3} = \frac{-i \cdot 3 - 3}{i \cdot 3 + 3} |
28,461 | 26 = 5^2 + 1^2 = 4^2 + 3^2 + 1^2 = 3^2 + 3 \cdot 3 + 2^2 + 2^2 |
25,964 | 108124016 = \left(2002\cdot (-1) + 15504\right)\cdot (2002 + 6006) |
-22,547 | \tfrac{8}{9}\cdot \frac78 = 8\cdot 7/\left(9\cdot 8\right) = 56/72 = \frac{1}{9}\cdot 7 |
-5,925 | \frac{2*g}{(2 + g)*(g + 6)} = \frac{g*2}{g * g + 8*g + 12} |
-23,599 | \frac{1/3*2}{7} = 2/21 |
11,167 | n^2 + n*3 + 2 - n*3 + 3*(-1) = n^2 + (-1) |
24,533 | \frac{1}{2} 109824 = 54912 |
15,694 | (1 - q)^2 = 1 - 2q + q * q |
-2,877 | -(9*13)^{1/2} + (25*13)^{1/2} = 325^{1/2} - 117^{1/2} |
21,892 | \dfrac{1}{2} \cdot \left(2 + (-1) + 2 \cdot n + (-1)\right) = n |
-25,952 | 0.58 = \tfrac{4.64}{8} |
29,792 | m \cdot (m + \left(-1\right))! = m! |
21,276 | 0 = \frac1x rightarrow 1 = 0x |
22,284 | (3\cdot (-1) + x)\cdot (6\cdot (-1) + x) = 18 + x^2 - 9\cdot x |
-13,838 | \frac{72}{7 + 5} = \frac{72}{12} = \tfrac{72}{12} = 6 |
-20,843 | -\frac{1}{7}\cdot 4\cdot \frac{4\cdot q}{4\cdot q} = ((-16)\cdot q)/(q\cdot 28) |
6,615 | \cos{x} = \sin{x}\Longrightarrow \frac12 \times \left(e^{x \times i} + e^{-i \times x}\right) = \frac{1}{2 \times i} \times (-e^{-i \times x} + e^{x \times i}) |
10,253 | \dfrac{t_i - \frac{1}{t_i}}{t_i + (-1)} = 1 + \dfrac{1 - \dfrac{1}{t_i}}{t_i + (-1)} \geq 1 + \frac{1}{2 \times (t_i + (-1))} |
25,978 | (-1)^n\cdot \binom{-2}{n} = \binom{n + 1}{n} = \binom{n + 1}{1} = n + 1 |
11,006 | 2 = \sin^2{F_2} + \sin^2{F_1} + \sin^2{C} \Rightarrow 1 - \cos^2{F_2} + 1 - -\sin^2{C} + \cos^2{F_1} = 2 |
29,145 | 50 K = \dfrac{1}{20} 1000 K |
24,255 | \ln\left(r\right) + r = \int (r + 1)/r\,dr |
15,584 | \frac{1}{c*b} = \dfrac{1}{b*c} |
18,935 | \frac{1}{4}*5*t = 15 + t\Longrightarrow t = 60 |
30,197 | x \cdot x \cdot x + (-1) = ((-1) + x) \cdot (1 + x^2 + x) |
6,017 | y = e^h + \left(-1\right) \implies \ln(1 + y) = h |
32,390 | k\cdot k! + k! = (k + 1)! |
-15,682 | \frac{1}{\frac{1}{\dfrac{1}{r^2} x^4}}x^4 = \frac{x^4}{r^2 \frac{1}{x^4}} |
-23,721 | \frac37 \cdot 3/4 = \tfrac{9}{28} |
-6,094 | \frac{3}{z^2 + 8*z + 9*(-1)} = \frac{3}{\left(z + 9\right)*(z + (-1))} |
21,647 | -\sin{s} \cos{x} + \cos{s} \sin{x} = \sin(-s + x) |
15,102 | w^9 = \left(w^3\right)^3 |
6,876 | x^2 - 2\cdot x\cdot a + a^2 + b^2 = b^2 + (-a + x)^2 |
9,446 | 1 = x \cdot 12 + 5 \cdot y\Longrightarrow x = -2\wedge y = 5 |
12,908 | \dfrac{v^2}{x^2} = (\frac{1}{x}\times v)^2 |
-26,582 | \left(7x + 4\right) (-7x + 4) = 16 - 49 x^2 |
26,732 | \frac{1}{4}\cdot π + \dfrac{π\cdot \left(-1\right)}{4} - q = -q |
47,755 | 120^2\cdot 25\cdot 4 = 1440000 |
-1,856 | 7/12 \cdot π + \frac{π}{4} = 5/6 \cdot π |
33,138 | G_x\cdot G_\rho = G_\rho\cdot G_x |
32,354 | (x + z)^3 = (x + z) \cdot (x + z) \cdot (x + z) = (x + z) \cdot \left(x^2 + 2 \cdot x \cdot z + z \cdot z\right) |
17,757 | \left(3\cdot (-1) + y\right)\cdot (4\cdot (-1) + y)\cdot (y + 5\cdot (-1)) = 60\cdot (-1) + y^3 - 12\cdot y^2 + 47\cdot y |
17,463 | y^{\frac73} = y^{4/3 + \dfrac33} = y^{\dfrac43}*y^{\frac{3}{3}} = y^{\frac13*4}*y |
28,283 | \frac16 \cdot (-i + 6) = -\frac16 \cdot i + 1 |
6,470 | \tan(y \cdot 3) = \tan\left(y \cdot 3\right) |
19,282 | z*H*x = H*z*x |
32,066 | 4004001 = 2001 * 2001 |
45,117 | x\cdot v = v\cdot x |
31,602 | \cos(-2 \cdot 2 + 2^2) = \cos\left(-2 \cdot 0 + 0^2\right) |
33,181 | L_k + L_l = L_l + L_k |
40,019 | 25 = 68 + 43\times (-1) |
14,631 | 1/7 + \dfrac{1}{42} = \frac{1}{6} |
26,324 | (g\cdot f)^2 \cdot (f\cdot g) = f \cdot f^2\cdot g^3 |
35,910 | \frac{1}{24}7 = 91/24 + 2(-1) - 1^{-1} - 1/2 |
16,989 | (x\times 3)^2 = 9\times x^2 |
498 | 6\cdot 252 = 1512 |
7,092 | g^2 - b^2 = (g + b)*\left(-b + g\right) |
12,926 | 0 = (c \cdot 2 + \left(-1\right)) \cdot 2 \Rightarrow \frac12 = c |
8,009 | \tfrac32\cdot 1/2\cdot 3 = \tfrac{9}{4} |
974 | \left(9 = y \times y \Rightarrow 9^{1/2} = y\right) \Rightarrow 3 = y |
32,782 | Z \cup Y \setminus Z = Z \cup \left(Y \cap Z^c\right) = (Y \cup Z) \cap (Z \cup Z^c) = Y \cup Z |
-4,731 | -\frac{1}{z + 3}\cdot 4 + \frac{2}{5\cdot (-1) + z} = \frac{26 - 2\cdot z}{z^2 - 2\cdot z + 15\cdot \left(-1\right)} |
7,092 | h \cdot h - g \cdot g = (g + h)\cdot (h - g) |
19,131 | (-8/3 + 3)^2*\frac{2}{9} = \frac{2}{81} |
26,575 | \frac124 = \frac21 = \frac{6}{3} = \dots |
32,700 | ((1 + p)/2)^2 - \left(\dfrac{1}{2}\left(p + \left(-1\right)\right)\right)^2 = p |
-24,660 | \frac{12}{30} = \frac{2 \cdot 6}{6 \cdot 5} |
18,102 | N\cdot x\cdot b = b\cdot N\cdot N\cdot x |
12,835 | x^2 + x + 2(-1) + 2\sqrt{x^3 - x^2 - x + 1} = x * x * x \Rightarrow 4(x^3 - x^2 - x + 1) = (x^3 - x * x - x + 2) * (x^3 - x * x - x + 2) |
3,293 | -x^2 + (1 + x) * (1 + x) = 2*x + 1 |
4,106 | (\int_0^1 (-\sigma + b)\,\text{d}\sigma) \cdot 2 = \frac{\partial}{\partial b} \int\limits_0^1 (\sigma - b)^2\,\text{d}\sigma |
-14,041 | 7 + \frac{1}{5}50 = 7 + 10 = 17 |
20,269 | (i + 1)! = i! (i + 1) < 2^i\cdot (i + 1) |
39,323 | 4 \cdot (-1) + 3 + 1 = 0 |
1,404 | 5 \cdot y^3 + y^2 \cdot 20 - y \cdot 195 + 270 = (y + 9) \cdot (2 \cdot (-1) + y) \cdot (y + 3 \cdot (-1)) \cdot 5 |
5,467 | -\tfrac{1}{2 + x} \cdot \left(2 \cdot \left(-1\right) + x\right) = \frac{1}{2 + x} \cdot \left(-x + 2\right) |
17,482 | -\left(a^2 + c \cdot c\right)^2 + (a^2 - c^2)^2 = -a^4 - 2\cdot a^2\cdot c^2 - c^4 + a^4 - 2\cdot a^2\cdot c^2 + c^4 = -4\cdot a^2\cdot c \cdot c |
966 | (2 \cdot (-1) + z) \cdot 5 = 10 \cdot \left(-1\right) + z \cdot 5 |
20,273 | (-\sqrt{x^2 + 1} + t + x) \cdot (t + x + \sqrt{x \cdot x + 1}) = t \cdot t + 2 \cdot x \cdot t + (-1) |
18,968 | zz = z \cdot z = z + 1 |
27,569 | d \cdot x \cdot f = d \cdot x \cdot f = \frac{d}{x \cdot f} |
6,208 | 34658 = 1^3 + 14^3 + 17^3 + 30^2 \times 30 |
34,920 | \sqrt{-4} = \sqrt{4}*\sqrt{-1} = 2i |
5,919 | 258\cdot 4 + 147 \left(-7\right) = 3 |
1,423 | \binom{5}{1} \times 6! \times 5! \times 2 = 864000 |
28,480 | 0 = \frac{z^2 - y^2}{z^2 + y \cdot y} \implies z \cdot z = y \cdot y |
-30,287 | \frac12(0 + 8) = \frac82 = 4 |
-26,654 | 3\times z^2 - z\times 20 + 7\times (-1) = (z\times 3 + 1)\times (z + 7\times (-1)) |
15,878 | (n * n + \frac{n}{2})^2 = n^4 + n^3 + \tfrac{1}{4}n^2 < n^4 + n^3 + n * n + n + 1 |
-20,225 | -\frac72\cdot (-\frac{1}{-9}\cdot 9) = \frac{63}{-18} |
18,049 | \frac{1}{2} \cdot (\frac{10303}{63} + 9 \cdot \left(-1\right)) = \dfrac{1}{63} \cdot 4868 \approx 77.27 |
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