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-4,129 | \dfrac{d^2}{d \cdot d^2} \cdot 72/32 = \frac{d^2}{d^3} \cdot \dfrac{9 \cdot 8}{8 \cdot 4} |
20,381 | -\lim_{x \to 0} (3 + x)^2/x = -6 - \lim_{x \to 0} \dfrac1x9 |
29,952 | 5^{\frac{1}{2}}*45 = (5^3*3^4)^{1 / 2} |
17,792 | 0.3 \frac{1}{16}7 q = q\frac{21}{160} |
16,069 | 2\sin{X} \cos{H} = \sin(X - H) + \sin(X + H) |
-26,468 | 5z^2 - 20 z + 20 = 5\left(z^2 - z*4 + 4\right) |
1,824 | (2 + l) \cdot 4^2 - l \cdot 3^2 = 32 + 7 \cdot l |
-10,266 | 3/3*(-\dfrac{4}{x*5 + 10}) = -\frac{12}{30 + 15*x} |
33,831 | -x + g = g - x |
24,482 | \sin\left(\pi + x\right) = \cos{x} \cdot \sin{\pi} + \cos{\pi} \cdot \sin{x} |
14,743 | -\left(k + \left(-1\right)\right)*(1 + k) + x*k = -(1 + k)*(2*\left(-1\right) + k + 1) + x*(k + 1 + (-1)) |
9,784 | \cos(2 \times u) = 1 - 2 \times \sin^2(u) = 2 \times \cos^2(u) + (-1) |
5,923 | -\frac{2}{y^2 + 1} + 2 = \frac{2 \cdot y^2}{1 + y^2} |
13,537 | n \cdot 4 = (-1) + 2 \cdot n + 1 + 2 \cdot n |
-4,613 | \frac{1}{20 + x^2 + 9\cdot x}\cdot (-x\cdot 2 + 7\cdot (-1)) = \frac{1}{4 + x} - \frac{1}{5 + x}\cdot 3 |
-6,699 | 0/10 + \frac{9}{100} = \tfrac{9}{100} + \frac{1}{100}\cdot 0 |
393 | \operatorname{Var}[N - X] = \mathbb{E}[(N - X)^2] - \mathbb{E}[N - X] \cdot \mathbb{E}[N - X] = \mathbb{E}[N^2] - 2\cdot \mathbb{E}[N\cdot X] + \mathbb{E}[X^2] - (\mathbb{E}[N] - \mathbb{E}[X])^2 |
-20,419 | \frac{x \cdot 9 + 90 (-1)}{10 x + 100 \left(-1\right)} = 9/10 \frac{x + 10 (-1)}{x + 10 \left(-1\right)} |
17,583 | \overline{y \cdot w} = \overline{y} \cdot \overline{w} |
36,373 | 1^2 + 4 \cdot 4 = 17 |
14,876 | g^2 - d^2 = (-d + g) (g + d) |
7,542 | (x \cdot a) \cdot (x \cdot a) = (a \cdot x)^2 |
48,782 | 7 \cdot 7 \cdot 19 = 931 |
13,663 | \cos{\pi/4} = \sin{\dfrac{1}{4}\pi} = 1/\left(\sqrt{2}\right) |
33,262 | 3^6 = 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3 |
5,376 | \left(\sqrt{2}\right)^{(\sqrt{2})^{(\sqrt{2})^{\left(\sqrt{2}\right)^{\sqrt{2} \ldots}}}} = 2 |
-20,283 | \frac{7}{r + 4}\cdot 9/9 = \frac{63}{36 + r\cdot 9} |
13,346 | t\cdot (-A\cdot B + B\cdot A)^2\cdot s = 2\cdot t\cdot \left(B\cdot A\right)^2\cdot s - 2\cdot t\cdot s\cdot A^2\cdot B \cdot B |
35,606 | \tan(\beta) = \sin(\beta)/\cos\left(\beta\right) rightarrow \tan\left(\beta\right) |
-20,918 | 3/3 \cdot \frac12 \cdot (8 + 6 \cdot k) = \frac16 \cdot (k \cdot 18 + 24) |
11,523 | y'*4 + z*2 + 2y' y + 6(-1) = 0 \Rightarrow y' = \frac{1}{2y + 4}(6 - 2z) = \dfrac{3 - z}{y + 2} |
2,172 | \cos{2} < 1 - \frac{2^2}{2!} + 2^4/4! = -1/3 \lt 0 |
-19,682 | 40/5 = 4*10/(5) |
221 | -1/12 = 1 + 2 + 3 \cdots |
-20,413 | \frac{y\cdot \left(-60\right)}{100\cdot \left(-1\right) + y\cdot 10} = 10/10\cdot \frac{1}{y + 10\cdot (-1)}\cdot \left(y\cdot (-6)\right) |
2,735 | ((-1) + n) \left(2(-1) + n\right)! = (n + \left(-1\right))! |
-3,666 | \frac19 = \frac19 |
-6,765 | 75 = 5*5*3 |
2,661 | E + X = 180 - 180 - X - E |
30,580 | 2! \times 4! = 2! \times 4 \times 3! |
19,226 | 27 + k * k^2 = 3^3 + k^3 = \left(k + 3\right)*(k^2 - 3*k + 9) |
19,409 | |z^n| = (1 + |z| + (-1))^n \gt 1 + (|z| + (-1)) n |
-11,747 | (\frac25)^3 = 8/125 |
23,359 | 2^2 * 2*3*6 = 144 |
7,490 | 2450 = 2\cdot 5 \cdot 5\cdot 7^2 |
-1,165 | \frac{5\cdot 1/9}{(-8)\cdot \frac19} = -\frac{1}{8}\cdot 9\cdot \dfrac{5}{9} |
-3,384 | \sqrt{10}+\sqrt{4} \cdot \sqrt{10}+\sqrt{9} \cdot \sqrt{10} = \sqrt{10}+2\sqrt{10}+3\sqrt{10} |
22,007 | x \times x - x\times 3 + 2 = (x + 2\times \left(-1\right))\times \left(x + (-1)\right) |
30,204 | x^4 + (-1) = (x + (-1))\cdot (x^2 + 1)\cdot (x + 1) |
9,977 | r \cdot \pi = \frac22 \cdot \pi \cdot r |
-20,044 | \frac{1}{8}*8*\dfrac{n + 10}{n*3 + 10} = \dfrac{80 + 8*n}{24*n + 80} |
-6,389 | \frac{2}{45 + m\cdot 5} = \frac{2}{(9 + m)\cdot 5} |
11,787 | \left(n + 1\right)^3/3 \geq 3 \cdot \left(n + 1\right) + 3 \cdot \left(-1\right) = \frac13 \cdot (n + 1)^3 \geq 3 \cdot n |
27,400 | n! \cdot (1 + n) \cdot (n + 2) = (n + 2)! |
-6,681 | 40/100 + \frac{3}{100} = \frac{3}{100} + 4/10 |
26,466 | \tfrac{6!}{3!\cdot 3!} = \frac{720}{6\cdot 6} = 20 |
24,340 | 64 \cdot (-1) + h^2 \cdot 3 - 12 \cdot h = 3 \cdot (16 \cdot (-1) + h^2 - 4 \cdot h) + 16 \cdot (-1) |
-22,991 | \frac{33}{44} = \frac{3}{4\cdot 11}\cdot 11 |
2,548 | \sin{2\cdot (\pi + x)} = \sin{x\cdot 2} |
2,311 | x*y*4 = (x + y)^2 - (-y + x)^2 |
11,100 | \left(0 \leq x \Rightarrow |t| = t\right) \Rightarrow xx/2 = \int_0^x t\,dt |
8,373 | 1 + 2\cdot n\cdot s = s + 2\Longrightarrow (n\cdot 2 + (-1))\cdot s = 1 |
21,254 | 4 = 2 \times (-1) + 5 + 1 |
-29,386 | -3/2*\frac34 = ((-3)*3)/\left(2*4\right) = -\frac{9}{8} = -\frac98 |
7,721 | x*\frac{F}{q}*f = \frac{f*x*F}{q} |
-7,032 | 25/182 = 5/14\cdot \dfrac{5}{13} |
-20,411 | \frac{1}{-9 y + 9 (-1)} ((-1) y) \frac18 8 = \frac{y*(-8)}{72 (-1) - 72 y} |
9,336 | \left(\left(2 = b + 1/b \implies 1 + b^2 - 2 \cdot b = 0\right) \implies (\left(-1\right) + b)^2 = 0\right) \implies b = 1 |
-3,922 | \frac{66*d^2}{d^5*30} = \frac{d^2}{d^5}*\tfrac{66}{30} |
20,466 | 1/(1/(\dfrac{1}{\frac{1}{25}})) = 5^{-2(-(-1) (-1))} = 5^2 = 25 |
21,428 | \frac{1}{\frac{1}{3^x}} \cdot \sin(\frac{a}{3^x}) = 3^x \cdot \sin(\dfrac{a}{3^x}) |
2,776 | \sin\left(\beta\right) \sin(x) + \cos(\beta) \cos(x) = \cos(x - \beta) |
46,488 | \dfrac{\cos{y}}{\cos{2y} + 1}2 = \dotsm \dotsm \dotsm = 1/\cos{y} = \sec{y} |
18,053 | \operatorname{E}\left(X_G\cdot X_B\right) = \operatorname{E}\left(X_B\right)\cdot \operatorname{E}\left(X_G\right) |
-13,905 | (4 + (2 - 7 \times 6)) \times 1 = (4 + (2 - 42)) \times 1 = (4 + (-40)) \times 1 = (4 - 40) \times 1 = (-36) \times 1 = -36 \times 1 = -36 |
-15,254 | \dfrac{1}{m^6\cdot \dfrac{1}{y^6}}\cdot m^5 = \frac{m^5}{\frac{1}{\frac{1}{m^6}\cdot y^6}} |
-29,869 | \frac{\mathrm{d}}{\mathrm{d}z} (5\cdot z^4 - z^3\cdot 2 - z^2) = z^3\cdot 20 - z^2\cdot 6 - z\cdot 2 |
-3,514 | \frac{1}{100}*6 = 3*2/(2*50) |
19,623 | -1 \lt 2 \cdot (-1) + \frac{s}{2} \implies s \gt 2 |
-6,681 | \frac{4}{10} + 3/100 = \frac{1}{100}*3 + 40/100 |
33,709 | \mathbb{E}[Y]\cdot \mathbb{E}[V] = \mathbb{E}[Y\cdot V] |
11,709 | (-1) + 2 (1 + m) = m*2 + 1 |
15,283 | \int 1\cdot 2\cdot \pi\cdot s\,ds = 2\cdot \dfrac12\cdot s^2\cdot \pi = \pi\cdot s^2 |
10,806 | 20160 = \left(2*(-1) + 2^4\right)*(4*(-1) + 2^4)*(-2^3 + 2^4)*(2^4 + (-1)) |
-718 | \dfrac{1}{12}*19*\pi = \pi*187/12 - 14*\pi |
699 | b^L*b^l = b^{l + L} |
51,869 | \dfrac{1}{x\cdot y} + 1/(y\cdot z) + \frac{1}{z\cdot x} = \frac{1}{(x\cdot y\cdot z)^2}\cdot (y\cdot z\cdot z\cdot x + x\cdot y\cdot z\cdot x + x\cdot y\cdot y\cdot z) = \frac{1}{x\cdot y\cdot z}\cdot \left(x + y + z\right) |
-20,462 | \frac{63 + 7*h}{-14*h + 14} = \frac77*\frac{1}{-h*2 + 2}*(9 + h) |
-4,387 | \frac{8\cdot p^5}{p^2\cdot 14} = \frac{8}{14}\cdot \frac{p^5}{p^2} |
-20,620 | \frac{8z}{z*(-14)} = \left((-1)*2 z\right)/(z*(-2)) (-\dfrac47) |
32,313 | k + (-1) = {k \choose 1} + (-1) |
-18,481 | 5\cdot k = 2\cdot (3\cdot k + (-1)) = 6\cdot k + 2\cdot (-1) |
17,007 | 1 = \frac33 = 3 \cdot 0.333 \cdot ... = 0.999 \cdot ... |
-7,785 | \dfrac{-2\cdot i + 8}{i - 4}\cdot \frac{-i - 4}{-4 - i} = \tfrac{8 - 2\cdot i}{-4 + i} |
-20,498 | -3/2*9/9 = -\dfrac{27}{18} |
38,290 | 2/8 + 10/16 = \frac{1}{8} \cdot 7 \leq 1 |
-8,060 | (-52 - 14 \cdot i + 130 \cdot i + 35 \cdot (-1))/29 = \left(-87 + 116 \cdot i\right)/29 = -3 + 4 \cdot i |
5,910 | \frac{1}{100} \cdot 3 = 3\% |
-23,291 | 0.28^8 = ((-1)\cdot 0.72 + 1)^8 |
25,517 | X_j \cdot X_x = X_j \cdot X_x |
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