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int64 -30,985
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8,824 | \sin{2\cdot y} = \sin^2{y} |
-3,850 | 72/132\cdot \frac{1}{x^3}\cdot x^5 = \frac{72}{x^3\cdot 132}\cdot x^5 |
10,322 | -d = d + h \cdot h = d \cdot h |
-24,209 | 10 + 7 * 7 = 10 + 7*7 = 10 + 49 = 59 |
11,764 | \frac{dy}{dx} = \dfrac{1}{3*y^2}*3*x * x = \frac{1}{y^2}*x^2 |
-9,274 | 3*7 p p + 3p p p = p^3*3 + p^2*21 |
311 | \dfrac{3}{5}*14/33 = 14/55 |
3,576 | \int \frac{1}{\sqrt{9 + y^2}}\,dy = \int \tfrac{1}{\sqrt{y^2 + 3^2}}\,dy |
39,504 | m = l + (-1) \implies 1 + m = l |
632 | \frac{\partial}{\partial t} \left(y\cdot x\right) = y\cdot \frac{dx}{dt} + x\cdot \frac{dy}{dt} |
12,326 | \frac{C*\dfrac{1}{\sqrt{G}}}{G^{1/2}}*1 = \tfrac{C^{\frac{1}{2}}}{G^{1/2}}*\frac{C^{1/2}}{G^{\tfrac12}} |
-11,790 | 125^{-\frac13} = \left(1/125\right)^{\frac13} |
-20,353 | -27/(-36) = \frac{3}{4}*(-\frac{9}{-9}) |
17,289 | (-|D \times D \times u| + |D^2 \times u_i|) \times (|D^2 \times u| + |D^2 \times u_i|) = -|u \times D^2|^2 + |D^2 \times u_i|^2 |
-6,389 | \frac{2}{(n + 9) \cdot 5} = \frac{2}{5 \cdot n + 45} |
10,085 | \left((-1) + x\right) \cdot (x^2 + x + 1) = x^3 + (-1) |
30,906 | (-1) + 2 \cdot x = x \Rightarrow x = 1 |
14,541 | (-1) + 10^{2\times x + 2} = (-1) + 10^2\times ((-1) + 10^{2\times x}) + 10^2 |
-1,504 | 36/72 = \frac{36 \cdot \frac{1}{36}}{72 \cdot 1/36} = 1/2 |
34,787 | {(-1) + x \choose p + (-1)} = {(-1) + x \choose x - p} |
26,760 | c_1\cdot \dfrac1x/c_3\cdot \dots^{-1}/c_n = c_1\cdot |x\cdot |c_3|\cdot \dots|\cdot c_n |
31,956 | (1 + 3^{\frac12}\cdot x + x^2)\cdot (1 - x\cdot 3^{1/2} + x^2)\cdot (1 + x^2) = x^6 + 1 |
21,684 | (m + 1)^2 - m^2 = 2*m + 1 = m + 1 + m |
-16,940 | 5 = 5 \cdot 2 \cdot c + 5 \cdot (-4) = 10 \cdot c - 20 = 10 \cdot c + 20 \cdot (-1) |
37,113 | 3 + 6 = 9 = 9 + 2 (-1) = 2 |
11,128 | \frac{1}{27} = \frac{1}{3}\cdot \frac{1}{3}\cdot \frac{1/2}{3}\cdot 1\cdot 2 |
-2,332 | 5/16 = -4/16 + 9/16 |
8,388 | 24 = a a + d^2 + f^2 + 12 \geq 4 a + 4 d + 4 f |
20,239 | \frac{1}{\tan{y}*(1 + \cos{2*y})} = \csc{2*y} = \frac{1}{\sin{2*y}} |
30,363 | 5/3 = \frac13\times 5 |
24,624 | -\frac12\cdot (-7! + 8!) + 9!/(3!\cdot 2!) = 12600 |
809 | y! = 10! \cdot 11 \cdot 12 \cdot \cdots \cdot y > 10! \cdot 11^{y + 10 \cdot (-1)} |
-29,016 | 0.48\times23.9=11.472 |
31,956 | \left(x^2 + 1 + x \cdot 3^{1/2}\right) \cdot (x^2 + 1 - 3^{1/2} \cdot x) \cdot (1 + x^2) = x^6 + 1 |
29,181 | \sqrt{(-1)\times (-1)} = \sqrt{(-1)^2} = -1 |
10,350 | \dfrac{3^{120}}{12} = \frac{1}{4}\cdot 3^{119} |
5,552 | -\dfrac{7}{7 + T^l} + 1 = \frac{1}{T^l + 7} \cdot T^l |
-18,431 | \frac{1}{y^2 - y\cdot 7}\cdot \left(y^2 - y\cdot 4 + 21\cdot \left(-1\right)\right) = \frac{(y + 3)\cdot (y + 7\cdot (-1))}{(7\cdot \left(-1\right) + y)\cdot y} |
17,704 | z_{k + 1} = 2 \cdot z_k - z_k \cdot z_k \leq 2 \cdot z_{k + 1} - z_k^2 |
2,471 | \frac{\partial}{\partial x} \operatorname{atan}\left(a + b\cdot x\right) = \dfrac{1}{(a + b\cdot x)^2 + 1}\cdot b |
10,597 | |f| \times |g| = |g \times f| |
3,377 | \cos{b} \times \sin{e} + \cos{e} \times \sin{b} = \sin\left(e + b\right) |
7,258 | agx = gxa |
7,407 | -\frac1h\cdot f + \frac{x}{v} = (x\cdot h - f\cdot v)/(h\cdot v) |
-1,655 | -\pi \cdot 3/2 + 2 \cdot \pi = \frac{\pi}{2} |
18,807 | \frac{d \cdot A \cdot x}{x \cdot d} = \frac{d \cdot A \cdot x}{x \cdot d} |
-20,252 | \frac{1}{q \cdot (-24)} \cdot (12 + 4 \cdot q) = \dfrac{q + 3}{q \cdot \left(-6\right)} \cdot \frac44 |
21,963 | \frac{11}{12} = 1/2 + 1/3 + \dfrac{1}{12} |
-2,692 | (1 + 5) \cdot \sqrt{3} = 6 \cdot \sqrt{3} |
-634 | -10 \cdot \pi + 11 \cdot \pi = \pi |
-26,389 | \left(-3\right)*(-3)*(-3)*(-3) = 81 |
11,598 | 16 \cdot \left(-\tan^{-1}(2) + \pi/2\right) + 4 \cdot \tan^{-1}(2) - 4 \cdot 2 = 8 \cdot \left(-1\right) + 8 \cdot \pi - \tan^{-1}(2) \cdot 12 |
24,927 | 5\cdot y^2 = 247^3 + 273\cdot (-1) + 9 \implies 3013797 = y^2 |
4,736 | -2^2 \frac{120*119}{2} + 13^4 = 1 |
17,572 | \delta^2 + z^2 + \delta \cdot z = -z \cdot \delta + (\delta + z)^2 |
37,320 | b + h + a = h + a + b |
38,371 | -{12 \choose 2} + {17 \choose 2} = 70 |
6,528 | D*(z^2 + (-1)) + D = D*(z^2 + \left(-1\right) + 1) |
-17,667 | 9 \cdot (-1) + 10 = 1 |
4,963 | \frac{q}{2} \cdot 2f = fq |
29,442 | x - r + 2 \cdot r = -(-x - r) |
-18,287 | \frac{x\cdot 8 + x^2}{x^2 + x\cdot 13 + 40} = \frac{x\cdot (8 + x)}{(5 + x)\cdot (x + 8)} |
11,782 | 30/4 = \frac{120}{16} = \frac{(1 + 7)*15}{1 + 15} |
-7,232 | 3/10 = 3/4 \cdot 2/5 |
13,557 | a \cdot x + c \cdot x = x \cdot (a + c) |
19,287 | h\cdot f = \dfrac{f}{f}\cdot h\cdot f |
-4,882 | 7.0 \times 10^{4\,+\,3} = 7.0 \times 10^{7} |
25,295 | \left(2\cdot k + 1\right)^2 = 4\cdot k^2 + 4\cdot k + 1 = 4\cdot (k \cdot k + k) + 1 |
-16,369 | 9*4^{1/2}*13^{1/2} = 9*2*13^{1/2} = 18*13^{1/2} |
11,322 | m^2 = m + 2\cdot {m \choose 2} |
-5,395 | 2.8\cdot 10 = \frac{2.8}{10^6}\cdot 10 = \dfrac{2.8}{10^5} |
392 | \dfrac{1}{4} = -\frac{11}{16} + \dfrac{1}{16}*5*3 |
6,341 | \dfrac{2}{3 - \dfrac{2}{-\frac{2}{3 - \frac{1}{3 + 2 \left(-1\right)} 2} + 3}} = 2 |
2,301 | 32 \cdot j \cdot j = (j \cdot 8)^2/2 |
20,378 | 34 \cdot 34\cdot 4 = 48^2 + 4^2 + 48^2 |
443 | \left(m + 1\right)\cdot (1 + x_m) = x_{1 + m} \Rightarrow \frac{1}{1 + x_m}\cdot x_{m + 1} = 1 + m |
-10,343 | -\dfrac{51}{4} = -51/4 |
20,700 | A = A * 1 |
-20,433 | \frac{48*(-1) - 18*k}{k*3 + 8} = -\tfrac61*\frac{8 + 3*k}{8 + k*3} |
1,764 | z + z_1 + z_2 = z_2 + z + z_1 |
6,424 | z\cdot y = \frac{1}{z\cdot y} = \ldots = y\cdot z |
-13,833 | \frac{1}{8 + 5 \left(-1\right)} 9 = 9/3 = \frac{9}{3} = 3 |
1,482 | LF/K = \frac{LF}{F} \frac{1}{K}F \leq L/K F/K |
6,239 | x_2^2 - x_1^2 = \left(-x_1 + x_2\right)\cdot (x_1 + x_2) |
-3,100 | (1 + 4*\left(-1\right) + 5)*\sqrt{7} = \sqrt{7}*2 |
-3,959 | \dfrac{12 \cdot x^2}{21 \cdot x} = x^2/x \cdot \frac{1}{21} \cdot 12 |
8,828 | q = 4/5 \cdot (q^2 + 9)^{1/2} \implies q = 4 |
21,238 | \frac{1 \cdot 2}{3 \cdot 2} = \frac{1}{4 + (-1)} |
-24,108 | (5 + 3)^2 = (8)^2 = 8^2 = 64 |
14,950 | -(1 - B^2) + 1 - B \cdot 2 + B^2 = -2 \cdot B + B^2 \cdot 2 |
-1,213 | \dfrac{42}{20} = 42*\frac{1}{2}/\left(20*\frac{1}{2}\right) = 21/10 |
7,971 | (y^2 + 1) (1 + y) = y^3 + 1 + y + y \cdot y |
10,902 | 4^k + 3^k = \left(1 + (3/4)^k\right) \cdot 4^k |
-26,655 | (7\cdot x^2 + 2)\cdot \left(7\cdot x^2 + 2\cdot (-1)\right) = -2^2 + (x^2\cdot 7) \cdot (x^2\cdot 7) |
-10,383 | -\frac{8}{8\cdot a^2}\cdot 5/5 = -\frac{40}{a^2\cdot 40} |
4,159 | -(n + \left(-1\right))^2 = -n \cdot n + 4 \cdot n - 2 \cdot n + (-1) |
-19,046 | \dfrac{4}{9} = \frac{1}{81 \cdot \pi} \cdot D_s \cdot 81 \cdot \pi = D_s |
26,358 | 10 \sqrt{30}/5 \sqrt{5} = 10 \sqrt{6} |
23,570 | 1 \cdot 1\cdot 3^2 = 9 |
11,518 | 4 \cdot (\frac{4}{3})^{x + (-1)} = 4 \cdot \frac{4^{x + (-1)}}{3^{x + (-1)}} = \dfrac{4^x}{3^{x + \left(-1\right)}} |
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