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int64 -30,985
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11,153 | 2 \cdot 2^2 + 4 \cdot (-1) = 8 + 4 \cdot (-1) = 4 |
4,250 | 4^1 + x^4 = (1 + (1 + x)^2) \cdot ((x + (-1))^2 + 1) |
11,321 | \frac{\dfrac{1}{\sqrt{5} + 2}\cdot (\sqrt{5} + 2)}{\sqrt{5} + 2\cdot (-1)} = \dfrac{1}{\sqrt{5} + 2\cdot (-1)} |
18,980 | 1 + \sqrt{5} \cdot i = 1 + \sqrt{-5} |
27,503 | 0\le-x<1\implies \tan(\arcsin(x))=-\tan(-\arcsin(x))=-\tan(\arcsin(-x))=-\frac{-x}{\sqrt{1-x^2}} |
43,839 | x^2 = x x |
-7,392 | 1/4\cdot 3/2 = \frac38 |
1,779 | f^{\frac{3}{2}} = (f^{1/2})^3 |
35,959 | 240 = 3 \cdot (-1) + 3^5 |
44,652 | \left(-5\right) * \left(-5\right) = 25 \geq 0 |
18,432 | \frac{1}{gx} = 1/(gx) |
-6,466 | \tfrac{1}{\left(x + 7(-1)\right)*2}4 = \frac{1}{14 (-1) + 2x}4 |
-18,318 | \frac{56\cdot (-1) + s^2 - s}{s \cdot s - s\cdot 9 + 8} = \frac{(8\cdot (-1) + s)\cdot (s + 7)}{(s + (-1))\cdot \left(8\cdot \left(-1\right) + s\right)} |
15,879 | \frac{\mathrm{d}}{\mathrm{d}x} (\cos(x) + \sin(x)) = -\sin\left(x\right) + \cos(x) = u \Rightarrow u^2 = -\sin\left(2x\right) + 1 |
34,134 | \sin(90) = 1 = 2\cdot \sin(30) = 2\cdot 0.5 = 1 |
14,692 | \|v\|^2 = \sqrt{v_1^2 + v_2 \cdot v_2 + v_3^2} \cdot \sqrt{v_1^2 + v_2 \cdot v_2 + v_3^2} = v_1^2 + v_2^2 + v_3^2 |
44,752 | \left(\frac{1}{27}\cdot (c_1^3 + c_2 \cdot c_2 \cdot c_2 + g^3 + 24)\right)^{1/3} = \frac13\cdot (c_1 + c_2 + g) \leq (\frac{1}{27}\cdot (c_1^3 + c_2^3 + g \cdot g \cdot g))^{1/27} |
4,171 | \frac{1}{n + 1} = \frac{1}{(1 + n)!}*n! |
-3,354 | 13^{1/2}\cdot 9 = 13^{1/2}\cdot (4 + 3 + 2) |
13,819 | 2^{1 / 2} = \frac{1}{2^{\dfrac{1}{2}}}\cdot 2 |
218 | 1/x - 1/b = \dfrac{b}{x b} - x/(x b) = (x - b)/\left(x b\right) |
-8,922 | -1^5 = (-1) \cdot (-1) \cdot \left(-1\right) \cdot (-1) \cdot \left(-1\right) |
11,209 | \left(b + 1\right)\cdot (b^{\left(-1\right) + x} - b^{2\cdot \left(-1\right) + x}\cdot ...\cdot ... + 1) = b^x + 1 |
35,329 | 10/8991 + \frac{1}{333} = 1/243 |
15,226 | 2\times \frac{100}{2}\times (100 + 1) + 100 = 100 + 10100 |
89 | {8 \choose 3}\cdot (5/3 + \frac14\cdot 5)\cdot {7 \choose 2} = 3430 |
-19,213 | \tfrac{4}{15} = \tfrac{Y_q}{100 \cdot \pi} \cdot 100 \cdot \pi = Y_q |
8,928 | \frac{1}{1 + 7 + 6} \cdot 6 \cdot \frac{5}{5 + 4} = \frac{1}{126} \cdot 30 |
7,035 | y x = 1 \implies \frac{1}{x} = y |
39,032 | q*(-q + 1) = q - q^2 |
-3,243 | \sqrt{10} = \sqrt{10}\cdot \left(3 + 2\cdot (-1)\right) |
-26,356 | -1/4 \left(-1/4\right) = 1/16 |
25,371 | \pi*20 = 8*\pi + 8*\pi + 4*\pi |
36,502 | \frac{1}{2} + 1/3 + 1/9 + 1/18 = 1 |
-22,192 | 54*(-1) + p^2 - p*3 = (p + 6)*(p + 9*(-1)) |
21,360 | (z^2 + y * y) * (z^2 + y * y) = (z * z - y^2)^2 + (2zy) * (2zy) = 5^2 + 12^2 = 13 * 13 \Rightarrow z^2 + y^2 = 13 |
-19,420 | 1/2 \cdot 3/(1/6) = 3/2 \cdot 6/1 |
-4,115 | \frac{y \cdot y\cdot 18}{90\cdot y \cdot y}\cdot 1 = \frac{1}{y \cdot y}\cdot y^2\cdot 18/90 |
11,111 | 15 = (1^2 + 1^2 + 1^2)\cdot (2^2 + 1^2 + 0^2) |
24,261 | g + f := f + g |
18,821 | \int (p^2 + \frac{2}{p^2})\,\mathrm{d}p = \int \frac{1}{p^2}\cdot \left(p^4 + 2\right)\,\mathrm{d}p |
40,816 | 2^2\cdot 239 = 956 |
-2,688 | 4 \cdot \sqrt{3} = \sqrt{3} \cdot (3 + (-1) + 2) |
19,311 | \arctan{y} = c + x \Rightarrow \tan(x + c) = y |
40,725 | n^2=\frac{\frac{(2n)(2n)}{2}}{2}=\frac{\frac{(2n+1)(2n)}{2}-n}{2}=\frac{\binom{2n+1}{2}-n}{2} |
16,332 | -2^3 + x^3 = (2\left(-1\right) + x) \left(x^2 + x\cdot 2 + 2^2\right) |
831 | \tan{C\cdot E\cdot M} = M\cdot E/(E\cdot C) \implies M\cdot E\cdot C = \operatorname{atan}\left(M\cdot E/(C\cdot E)\right) |
33,045 | |(f,g)|=|(g,f)|\le \|f\|_2\|g\|_2 |
723 | x^3 - b^2 \cdot b = (-b + x) \cdot \left(b^2 + x^2 + x \cdot b\right) |
28,589 | 112 = 4\cdot \binom{8}{2} |
-23,580 | 1/7 = \frac{5}{5} \cdot \frac{1}{7} |
2,091 | z + \alpha/2 + \frac{\alpha}{2} = z + \alpha |
9,106 | 3/8 \cdot \frac12 + \dfrac12 \cdot \tfrac26 = \dfrac{1}{48} \cdot 17 |
21,919 | 2 + 3*(1 + x) = 5 + x*3 |
-30,245 | z^2 - z\cdot 2 + 1 = (z + (-1))\cdot (z + (-1)) |
-10,441 | -\frac{1}{6*x + 18*(-1)}*20 = -\tfrac{10}{3*x + 9*(-1)}*\frac22 |
9,062 | 13 = 2 + 3 + c_3 \Rightarrow c_3 = 8 |
19,731 | \sum_{i=1}^a x = \sum_{i=1}^x a |
21,703 | 3 + 3\cdot ((-1) + y) + 3\cdot (\left(-1\right) + y)^2 + (y + (-1))^3 = y \cdot y \cdot y + 2 |
12,716 | x * x^2 - x*2 + 2*(-1) = -x*2 + \left(-1\right) + \left(1 + x^2 + x\right)*\left((-1) + x\right) |
18,362 | c + 3*\left(-1\right) = -(3 - c) |
26,570 | -(17 - 3 \cdot 34^{1 / 2}) \cdot (17 + 34^{\frac{1}{2}} \cdot 3) = 17 |
10,212 | (a + c)^2 = a^2 + 2*a*c + c^2 |
-5,253 | 0.61*10^{0 - -3} = 0.61*10 10 10 |
11,280 | \frac{1}{\frac{1}{b\cdot \frac{1}{\frac{1}{h}}}}\cdot a = \frac{a}{1/h}\cdot \frac{1}{\dfrac1b} |
-7,778 | \left(a - b\right) \cdot (a + b) = -b^2 + a^2 |
23,795 | n^6 - n^4\cdot 3 + n n\cdot 3 + (-1) = (n n + (-1))^3 |
28,757 | 3\cdot 12\cdot 11\cdot 4\cdot (10 + 9 + 3) = 34848 |
2,373 | 459/400 = -\dfrac{1}{5^2} + 1 + \frac{1}{2 \cdot 2} - \frac{1}{4 \cdot 4} |
17,756 | 1.414213562373 \cdot \dotsm = 2^{1/2} |
-9,750 | 0.01 \cdot \left(-15\right) = -\frac{1}{100} \cdot 15 = -0.15 |
14,433 | \tan{j} = \sin{j}/\cos{j} |
28,122 | A_i \cdot A_{1 + i} = A_{i + 1} \cdot A_i |
-7,788 | 4\cdot i/2 + 8/2 = \frac{1}{2}\cdot (8 + 4\cdot i) |
13,309 | a^2 - x^2 = \left(a + x\right) \cdot (-x + a) |
-6,750 | \frac{1}{100}6 + \frac{1}{10}8 = 6/100 + \frac{80}{100} |
22,335 | 1 + \frac{z}{-z + 1} = \frac{1}{-z + 1} |
-20,559 | \frac{x\cdot 45}{(-10)\cdot x} = -9/2\cdot ((-5)\cdot x)/\left(x\cdot (-5)\right) |
-24,852 | \frac{u}{3} - \frac{w}{2} = -1/2 \cdot \left(u/3 + w/2\right) + 1 = ((-1) \cdot u)/6 - \frac14 \cdot w + 1 |
1,730 | f_{i_l}\cdot f_{i_k} = f_{i_l}\cdot f_{i_k} |
4,659 | \dfrac{E}{x} = \frac{E}{x} |
19,441 | x\cdot v_2/(v_4) = x\cdot v_2/(v_4) |
13,834 | xx^{n + (-1)} = x^n |
1,961 | \frac{1}{1 - x} = \dfrac{1 + 0 \cdot \left(-1\right)}{1 - x} |
25,405 | 1 + 2^{30} = 5*5*13*41*61*1321 |
49,431 | f = 0 + f |
-3,065 | 7^{\frac{1}{2}} \cdot 4 + 7^{1 / 2} \cdot 5 = 25^{\frac{1}{2}} \cdot 7^{\frac{1}{2}} + 7^{1 / 2} \cdot 16^{1 / 2} |
27,236 | -\frac{\pi}{4} + \frac34*\pi = \frac{\pi}{4}*2 |
-7,117 | \frac{3}{10}*\frac{2}{9} = 1/15 |
14,368 | 2 = \left\{\left( 2, 0\right), \dots, ( 3, 1), ( 4, 2)\right\} |
6,059 | \frac{\left(-1\right) + m \cdot 2}{m \cdot 2 + 3} = 1 - \frac{4}{3 + 2 \cdot m} |
33,048 | 298\cdot (-1) + 1000 + (-1) + 193\cdot (-1) = 508 |
-21,839 | 8/3 + \frac{9}{5} = \frac{8*5}{3*5} + \frac{9*3}{5*3} = 40/15 + \frac{1}{15} 27 = \dfrac{1}{15} (40 + 27) = 67/15 |
37,987 | Z^U\cdot x\cdot Z = Z^U\cdot z \implies \dfrac{Z^U\cdot z}{Z\cdot Z^U}\cdot 1 = x |
27,684 | 9\cdot \left(-1\right) + 10 = \dfrac13\cdot (2 + 1) |
-4,201 | \tfrac{88}{11}\cdot t/t = t\cdot 88/(11\cdot t) |
26,173 | \sum_{i=1}^\infty |-b_i| = \sum_{i=1}^\infty |b_i| |
8,578 | \sin(3\cdot y) = \sin(2\cdot y + y) = \sin(2\cdot y)\cdot \cos(y) + \cos(2\cdot y)\cdot \sin\left(y\right) |
-573 | -4 \cdot \pi + \pi \cdot 14/3 = \pi \cdot \frac23 |
-4,261 | \frac{1}{a^5} \times a^2 \times a \times 132/144 = \frac{132 \times a^3}{a^5 \times 144} |
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