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int64 -30,985
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8,084 | \sin(π/2 + y) = \cos(y) |
-15,234 | \dfrac{1}{\frac{b^2}{z^5} \cdot \frac{1}{z^8}} = \frac{1}{b \cdot b \cdot \frac{1}{z^5}} \cdot z^8 |
-20,468 | -\frac{5}{2}*\frac{-k*5 + 2}{2 - 5*k} = \dfrac{25*k + 10*\left(-1\right)}{-k*10 + 4} |
18,303 | -1 = 4! - 5*3! + 2!*5 - 5*1! + 1 + \left(-1\right) |
42,513 | 3 \cdot 3 - 1^1 \cdot 8 = 1 |
19,101 | \frac83 1 = 8/3 |
29,558 | G\cdot z = z\cdot G |
22,576 | 72 = 2^3\times 3 \times 3 |
30,368 | -1 = (t + (-1))\cdot (1 + t + t^2 + \ldots) = t + \left(-1\right) + \left(t + (-1)\right)\cdot t + (t + (-1))\cdot t \cdot t + \ldots |
-4,491 | \frac{1}{3 + x} - \frac{3}{1 + x} = \frac{-x \cdot 2 + 8 \cdot (-1)}{x^2 + 4 \cdot x + 3} |
16,849 | \int \frac{y^4}{1 + y^2}\,\text{d}y = \int \frac{1}{y^2 + 1}\cdot (y^4 + \left(-1\right) + 1)\,\text{d}y |
-2,262 | 3/11 = -\frac{2}{11} + 5/11 |
-5,859 | \frac{4}{(7\cdot (-1) + q)\cdot (2 + q)} = \tfrac{4}{14\cdot (-1) + q^2 - 5\cdot q} |
-483 | (e^{\frac{19}{12}\cdot i\cdot \pi})^3 = e^{3\cdot 19\cdot i\cdot \pi/12} |
-6,218 | \frac{1}{12 + z^2 - z \cdot 8} = \dfrac{1}{\left(z + 2 \cdot (-1)\right) \cdot (z + 6 \cdot (-1))} |
-6,135 | \frac{1}{(10 + t)*(7*(-1) + t)}*3 = \frac{3}{t^2 + 3*t + 70*(-1)} |
27,584 | \dfrac14 + \tfrac{1}{5} = 9/20 |
5,321 | 16\cdot g^2 = x^2 + x^2 - g\cdot x\cdot 2 + g^2 \Rightarrow 0 = x^2\cdot 2 - g\cdot x\cdot 2 - 15\cdot g^2 |
4,962 | \dfrac{a^2}{a}\cdot 1 = a |
21,300 | \left(a + (-1)\right) \cdot (1 + a) = \left(-1\right) + a^2 |
8,467 | -\pi/8 = -\frac{\pi}{8} + \pi*0 |
37,209 | 0.999 \dotsm = \frac{9 / 10}{1 - 1/10}1 = 1 |
45,535 | 5\times 17 = 85 |
6,378 | 1/2 + \tfrac{1}{3} + \frac17 + 1/84 = \frac{1}{84} \cdot 83 |
26,814 | 2017 - (2027 + 2011 \cdot \left(-1\right))^{1/2} = 2013 |
29,229 | x*0 + 0*x = 0*x + x*0 + x*0 |
-26,247 | 4 = C \times e^{\left(-5\right) \times 0} = C |
18,811 | s = \frac1x*x^3 \Rightarrow x * x = s |
13,245 | 1/2 = \sin\left(\frac{1}{6}\times \pi\right) |
12,483 | \dfrac{1}{8} \cdot 5/2 = 5/16 |
17,956 | e^{l\cdot z} - \binom{l}{1} = ((-1) + e^z)^l |
2,051 | r*(a*b - b*a) = a*b*r - r*b*a |
-26,621 | 2 \cdot x^2 + 50 \cdot (-1) = 2 \cdot (x \cdot x + 25 \cdot \left(-1\right)) = 2 \cdot (x + 5) \cdot \left(x + 5 \cdot (-1)\right) |
30,994 | b^{301}\cdot a^{301} = (b\cdot a)^{301} |
17,552 | {n \choose q} = {n + (-1) \choose q + (-1)} + {(-1) + n \choose q} |
22,407 | 2^{\frac{1}{2}} = \tfrac{1}{2^{\dfrac{1}{2}}}\cdot 2 |
11,148 | \frac{x^2}{x + 1} = \frac{1}{x + 1} - -x + 1 |
-7,028 | \frac{1}{13} \cdot 3 \cdot 2/12 = \frac{1}{26} |
17,303 | \dfrac{1}{m} + 1 = (m + 1)/m |
7,590 | 0 = y\cdot x = z\cdot x^{m + 1} \Rightarrow 0 = z\cdot x^m = y |
6,682 | z^2 + z \times 4 + 5 \times (-1) = 0\Longrightarrow \left((-1) + z\right) \times (z + 5) = 0 |
22,945 | E_k\cdot x_k = E_k\cdot x_k |
-7,706 | \frac{1}{5 - i} \cdot (-5 - 25 \cdot i) = \tfrac{1}{i + 5} \cdot (5 + i) \cdot \frac{1}{5 - i} \cdot (-i \cdot 25 - 5) |
-10,634 | \frac{6 + t \cdot 12}{120 + t \cdot 90} = \dfrac{t \cdot 2 + 1}{20 + t \cdot 15} \cdot 6/6 |
7,255 | x^4 + x^2 + 1 = (1 + x^2 + x) (1 + x^2 - x) |
22,791 | F^{m + l} = F^m F^l |
-2,886 | 7\cdot \sqrt{2} = (4 + 2\cdot (-1) + 5)\cdot \sqrt{2} |
14,661 | \sin^2{t} = x \implies \cos{2*t} = 1 - 2*\sin^2{t} = 1 - 2*x |
9,027 | 2^{n \cdot 2} = \frac{2^{-n^2}}{2^{-n \cdot 2 - n^2}} |
12,530 | a \times b = \frac{1}{a \times b} = \frac{1}{b \times a} = b \times a |
10,773 | 7/100 + \dfrac{171}{200} = 185/200 = 0.925 |
-3,985 | 16/32\cdot \frac{n^3}{n^5} = \frac{16\cdot n^3}{32\cdot n^5} |
804 | (1 + M*2 - x*2)/2 \delta = \delta*(M - x) + \frac{\delta}{2} |
9,508 | \frac{1}{\frac{2}{k^3}\cdot k} = k^2/2 |
-22,926 | 72/54 = 4\cdot 18/(18\cdot 3) |
-2,453 | (5 + 4(-1)) \sqrt{10} = \sqrt{10} |
10,778 | 1 = 7 - 167 - 7*23 = 7*24 + 167 (-1) |
8,228 | -x^2 \cdot \cos(\pi - \phi) \cdot 2 + x \cdot x = x \cdot x \cdot \cos^2\left(\phi\right) + x \cdot x \cdot \sin^2(\phi) + \cos(\phi) \cdot x^2 \cdot 2 |
-20,395 | \tfrac{45 k + 9}{81 (-1) + 9 k} = 9/9 \dfrac{1 + k*5}{k + 9 (-1)} |
-5,113 | \dfrac{1}{1000}\cdot 36 = \frac{1}{1000}\cdot 36 |
23,263 | 1/12 = \frac{1}{3\cdot 4} |
13,279 | 27/216 = \dfrac36\cdot \frac16\cdot 3\cdot 3/6 |
9,773 | 0 = (a + g + f) * (a + g + f) = 1 + 2\left(ag + gf + fa\right) |
-233 | \frac{1}{(5\cdot \left(-1\right) + 7)!\cdot 5!}\cdot 7! = {7 \choose 5} |
20,802 | \dfrac{15}{34} = \dfrac{9 + 6}{20 + 14} |
4,247 | \left(l + 1 - s\right)*\binom{l}{s + (-1)} = s*\binom{l}{s} |
-17,078 | 6 = 6*(-t) + 6*\left(-4\right) = -6*t - 24 = -6*t + 24*(-1) |
-5,618 | \frac{2}{2*(h + 8*(-1))} = \frac{2}{h*2 + 16*(-1)} |
7,366 | \mathbb{E}\left[Y'\cdot x\right] = \sqrt{\mathbb{E}\left[Y'^2\right]\cdot \mathbb{E}\left[x^2\right]} |
7,493 | x = t*0 + (1 - t)*(1 + x) = (1 - t)*(1 + x) |
-19,044 | 5/8 = F_s/(4\pi)*4\pi = F_s |
39,116 | 1/(x*y) = \dfrac{1}{x*y} |
36,555 | 0 + \frac{1}{3} + 1/2 = \frac56 |
4,913 | q = r^{a\cdot m}\cdot q^{b\cdot m} = (r^a\cdot q^b)^m |
28,099 | 63 = 3\cdot (4 + 4 + 4 + 4 + 4) + 3 |
33,391 | (x^{1250} + x^{625} \cdot 10 + 50) \left(50 + x^{1250} - x^{625} \cdot 10\right) = x^{2500} + 2500 |
-12,854 | 11 + 7 + 6 = 24 |
23,070 | 9^l + 4^{l + 1} = (5 + 4)^l + 4^{l + 1} = 5 \times h + 4^l + 4^{l + 1} = 5 \times h + 5 \times 4^l |
29,894 | (2 \pi r) (2r)=4\pi r^2 |
15,572 | \left(x + 3 \times (-1)\right) \times (x + 2 \times (-1)) = x^2 - 5 \times x + 6 |
-22,715 | \tfrac{30}{18} = 6\cdot 5/(3\cdot 6) |
-26,628 | (m \cdot 3 + n \cdot 5)^2 = 9 \cdot m^2 + m \cdot n \cdot 30 + 25 \cdot n^2 |
32,240 | \frac{\mathrm{d}w}{\mathrm{d}x} = \frac{1}{1 - w}\cdot w - w = \dfrac{w^2}{1 - w} |
23,475 | (l + 1) \cdot (4 + l) \cdot (l + 3) \cdot (l + 2)/4 = \dfrac{1}{4} \cdot (l + 3) \cdot (1 + l) \cdot \left(2 + l\right) \cdot (l + 4) |
12,875 | X^0 = \frac{1}{X}*X |
7,919 | -x\cdot (-x)\cdot 6 + x^2\cdot 10 = 16 \implies x^2 = 1 |
26,550 | \frac{1}{1 + \sqrt{x}} = \frac{\left(-1\right) + \sqrt{x}}{x + (-1)} |
5,561 | a_n = \dfrac{1}{n\cdot 2}\cdot (n\cdot 2 + (-1)) \implies a_n = 1 - \frac{1}{2\cdot n} |
2,290 | s + (2 - s)/2 = \frac22\cdot s + \frac12\cdot (2 - s) = \frac{1}{2}\cdot (s + 2) |
21,473 | \frac{1}{z + (-1)}*z = \tfrac{z + (-1) + 1}{z + (-1)} |
23,352 | \frac{\partial}{\partial y} y^{\alpha} = y^{\alpha + (-1)}\cdot \alpha |
8,546 | (n + 1)^2 = n \cdot n + 2 \cdot n + 1 = (n + (-1))^2 + 2 \cdot n + (-1) + 2 \cdot n + 1 = \left(n + (-1)\right)^2 + 4 \cdot n |
21,666 | \left((x + f)^{1/2} = x \Rightarrow -f + x^2 - x = 0\right) \Rightarrow x = \left((f*4 + 1)^{1/2} + 1\right)/2 |
21,247 | x^{( n, l)} = x^{\alpha\cdot n + \beta\cdot l} = x^{\alpha\cdot n}\cdot x^{\beta\cdot l} |
25,921 | 3 \times (l + x) + l \times x = 0 \Rightarrow (x + 3) \times (3 + l) = 9,x,l \leq 0 |
28,977 | \pi \gt 2 \cdot 2^{1/2} = 2.828 \cdot \dots \gt 2.82 |
-26,573 | 16 - 49 \times y \times y = 4 \times 4 - (y \times 7)^2 |
19,209 | -(p^2 - p*r*2 + r^2*2) + p^2 + p*r*2 + 2*r^2 = 4*p*r |
15,165 | \frac{1}{A - B} = \frac{1}{\left(-B/A + 1\right) \cdot A} |
22,122 | \left(4 + y^2 - x^2 - 4*y = 0 \Rightarrow (2*(-1) + y)^2 - x * x = 0\right) \Rightarrow 0 = (-x + y + 2*\left(-1\right))*(x + y + 2*(-1)) |
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