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int64 -30,985
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-5,200 | \dfrac{1}{1000} \times 15.6 = 15.6/1000 |
16,328 | \left(\eta + 1\right)! = \eta! \cdot (\eta + 1) |
12,787 | (a + 6)*\left(a + 12\right) = a * a \Rightarrow -4 = a |
-8,782 | 54 \times π + π \times 9 + π \times 9 = π \times 72 |
-21,007 | \dfrac{-s \times 8 + 18 \times (-1)}{6 \times \left(-1\right) + 2 \times s} = 2/2 \times \frac{1}{3 \times (-1) + s} \times \left(9 \times \left(-1\right) - 4 \times s\right) |
25,321 | \frac12 \cdot (1 - z) \cdot \frac{1}{z^2 + 3} + \tfrac{1}{(z + 3) \cdot 2} = \frac{1}{2 \cdot (z + 3)} + \tfrac{1}{3 + z^2} \cdot \left(\dfrac{1}{2} + -1/2 \cdot z\right) |
1,297 | 9 + y^2 + y\cdot 6 = (y + 3)^2 |
6,079 | z^2 + z + 1 = (z + 1/2)^2 - 1/4 + 1 = (z + 1/2)^2 + \frac34 |
15,998 | \left(c^2 + x^2\right)*(b^2 + a * a) = (c*a - b*x)^2 + (c*b + x*a)^2 |
20,751 | T^{\frac{1}{2}}\cdot S^{\frac12}\cdot T^{1/2}\cdot S^{\frac12} = S\cdot T |
13,895 | \left(x_1 + x_2\right) \times \left(x_1 + x_2\right) = x_1 \times x_1 + x_1\times x_2\times 2 + x_2 \times x_2 |
16,329 | \frac{6}{3} \times 9 \times 9 \times 8 \times 7 = 9072 |
9,665 | \sin(x + \beta) = \sin(\beta) \cdot \cos(x) + \sin(x) \cdot \cos(\beta) |
28,841 | 1 + x^3 + x + x^2 = (1 + x) \cdot (x^2 + 1) |
-4,827 | \frac{9}{10^5} = \frac{9.0}{10^5} |
-18,476 | 3 k + 7 = 5 (k + 3 (-1)) = 5 k + 15 \left(-1\right) |
33,927 | (c - \delta)*2 = c - \delta - \delta - c |
1,393 | \mathbb{E}(x^2) + \mathbb{E}(V^2) + 2 \times \mathbb{E}(V \times x) = \mathbb{E}(\left(x + V\right) \times \left(x + V\right)) |
19,866 | 9 - \left(k + 2\cdot (-1)\right)^2 = (3 - k + 2\cdot \left(-1\right))\cdot (3 + k + 2\cdot (-1)) = (5 - k)\cdot \left(1 + k\right) |
5,946 | \sqrt{a^2 - 16 \cdot a + 48} = \sqrt{(a + 6 \cdot (-1))^2 + 12} > \sqrt{(a + 6 \cdot (-1))^2} = |a + 6 \cdot \left(-1\right)| = 6 - a |
27,710 | \frac{1}{\sqrt{z^2}} \cdot (z + 1) = \dfrac{1}{\left(-1\right) \cdot z} \cdot (z + 1) = -1 - 1/z |
-28,758 | -\frac{4}{3\cdot y + 6} + \dfrac{1}{3} = 1/3 - \dfrac{1/3\cdot 4}{y + 2} |
9,997 | 2*F_k = F_k + F_k |
22,498 | x \cdot 0 = (x + 0) \cdot (0 + 0) = x \cdot 0 + x \cdot 0 \Rightarrow x \cdot 0 = 0 |
-25,551 | \pi \cos{\pi t} = \frac{d}{dt} \sin{\pi t} |
648 | 1 + r_1*r_2 - r_1 - r_2 = 0 \implies 0 = (r_1 + (-1))*(r_2 + \left(-1\right)) |
25,173 | -c^2 + x^2 = \left(x + c\right) \cdot (-c + x) |
42,443 | 1/(\sqrt{2}) = \sqrt{2}/2 |
-27,711 | 6\times \sin(x) = \frac{\mathrm{d}}{\mathrm{d}x} (-6\times \cos(x)) |
35,581 | x + 1 + x + \left(-1\right) = 2x = -x |
148 | n^{19} - n^7 = (n^5 - n)\cdot (n^{14} + n^{10} + n^6) |
-10,705 | 3/3\cdot \frac{3}{16 + c\cdot 16} = \frac{1}{48 + 48\cdot c}\cdot 9 |
13,739 | (1 + y)^s*(1 + y)^t = (y + 1)^{s + t} |
15,739 | -3*((-1) + 2^{20}) + 3^{20} = 3*(1 + 3^{19} - 2^{20}) |
9,393 | 121 = (1 + 10)\times 121/11 |
-602 | e^{20\cdot i\cdot \pi\cdot 17/12} = (e^{\frac{1}{12}\cdot \pi\cdot i\cdot 17})^{20} |
37,439 | 10 + 5\cdot (-1) + 2 = 7 |
2,570 | r\cdot y = y\cdot r |
-2,146 | π\cdot 4/3 - 7/4\cdot π = -π\cdot 5/12 |
-20,480 | -\frac{1}{-10} \cdot 10 \cdot (-\frac{1}{4}) = \frac{10}{-40} |
9,190 | \frac14\cdot \frac{1}{5\cdot 5}\cdot 5 = 1/20 |
1,232 | 1 - 3 \times x = -\left(x + 2\right) \times 3 + 7 |
13,439 | \cos(\theta) = \sqrt{4 - y * y}/2 \Rightarrow \cos(\theta)*2 = \sqrt{-y^2 + 4} |
-24,984 | π \cdot 6 = 3 \cdot π \cdot 2 |
40,859 | 2^{3 + \left(-1\right)} = 2 \cdot 2 = 4 |
-1,569 | \frac{1}{5} \cdot 8 = 8/5 |
17,842 | \cos\left(2 \cdot y + y\right) = \cos{3 \cdot y} |
7,897 | x + x\cdot \frac{1}{2}\cdot (x + \left(-1\right)) = x\cdot \left(x + 1\right)/2 |
-18,341 | \frac{1}{\left(t + 9\right)*(7*(-1) + t)}*(9 + t)*t = \frac{t^2 + 9*t}{63*(-1) + t^2 + t*2} |
7,743 | 3x^2 + 4x + 3 = \frac{\text{d}}{\text{d}x} (x \cdot x \cdot x + x^2\cdot 2 + 3x + 4) |
-4,096 | \frac{1}{72}144 \frac{s}{s^3} = \frac{144 s}{72 s^3}1 |
8,724 | \sin(2 \cdot t) = \sin(t) \cdot \cos\left(t\right) \cdot 2 |
34,360 | -x + x^3 + x^2 = x^2 + x x - x + x^2 - x + x x - x*2 + 1 + x x^2 - x x*3 + 3 x + (-1) |
3,789 | (a - b) * (a - b) = a^2 + b * b - 2*a*b = (a + b)^2 - 4*a*b |
-20,482 | \frac{1}{28 + n\cdot 70}\cdot (4\cdot \left(-1\right) - n\cdot 10) = -1/7\cdot \dfrac{4 + n\cdot 10}{n\cdot 10 + 4} |
46,005 | 29 = 25 + 5 + (-1) |
12,546 | \cos^2{H} = 1/2 \cdot (\cos{H \cdot 2} + 1) |
1,344 | 4 + 2 \cdot (s^2 + s \cdot 2 + 1) + s + 1 = s \cdot s \cdot 2 + 5 \cdot s + 7 |
3,393 | x^2 + x + 1/4 + 3/4 = 3/4 + \left(1/2 + x\right)^2 |
22,412 | d + z^2\cdot f + z\cdot g = 0 \Rightarrow (-g +- \sqrt{g^2 - 4\cdot d\cdot f})/\left(2\cdot f\right) = z |
-30,875 | 24 = 28 + 4\left(-1\right) |
-2,836 | \sqrt{2} \sqrt{16} - \sqrt{2} \sqrt{9} = 4\sqrt{2} - 3\sqrt{2} |
23,384 | 1/M = \tfrac{1}{M + 2\cdot (-1)}\cdot \left(-\frac{1}{(-1) + M} + 1\right)\cdot (-1/M + 1) |
13,335 | 10 = 5\cdot 2 = 5\cdot (3 + (-1)) = 5\cdot (\left(3^4\right)^{\frac14} + (-1)) |
481 | -2 \cdot 34 + (431 - 12 \cdot 34) \cdot 3 = 431 \cdot 3 - 38 \cdot 34 |
-3,057 | 9*\sqrt{7} = \sqrt{7}*\left(5 + 4\right) |
30,946 | U_0/(U_1) = \dfrac{1}{U_1}U_0 |
22,967 | n \cdot 2 - (-1) + n = n + 1 |
21,669 | -1.281551 = \frac{1}{10}(500 - \mu) rightarrow \mu = 512.816 |
-14,535 | \dfrac{1}{4 + 2 \cdot (-1)} \cdot 10 = 10/2 = 10/2 = 5 |
19,574 | \left(2^2\right)^{1 / 2} = \left((-2)^2\right)^{\frac{1}{2}} |
11,589 | z_1^4 + 4 \cdot z_2^4 = z_1^4 + 4 \cdot z_1^2 \cdot z_2 \cdot z_2 + 4 \cdot z_2^4 - 4 \cdot z_1^2 \cdot z_2^2 = (z_1^2 + 2 \cdot z_2^2)^2 - (2 \cdot z_1 \cdot z_2)^2 |
7,958 | z = \sqrt{i + \sqrt{i + ...}} = \sqrt{i + z} rightarrow -i + z^2 - z = 0 |
37,765 | \sin(5 x) = e^{i \sin(5 x)} = \cos(\sin(5 x)) + i \sin(\sin(5 x)) |
402 | \dfrac{dy}{z} = dz/y = \frac{1}{z - y}\cdot \left(dy - dz\right) |
20,841 | I - 1/2 + \dfrac52 = 0 \Rightarrow -2 = I |
6,578 | m_1\cdot m_2\cdot d_2\cdot d_1 = d_1\cdot m_1\cdot d_2\cdot m_2 |
670 | \left(h - x\right) \cdot \left(h - x\right) = (h - x) \cdot \left(h - x\right) = h^2 - 2 \cdot h \cdot x + x^2 |
1,351 | (A - I)*A*G = G*A*(-I + A) |
6,732 | p^4 + 256\cdot (-1) = (p^2 - 4^2)\cdot (p \cdot p + 4^2) = (p + 4\cdot (-1))\cdot \left(p + 4\right)\cdot (p^2 + 16) |
-11,763 | \left(10/7\right) \cdot \left(10/7\right) = \dfrac{100}{49} |
-6,921 | 140 = 4\cdot 7\cdot 5 |
2,218 | (z + \left(-1\right))^3 + z^2*3 - 3 z + 1 = z z z |
-2,542 | \sqrt{2}\cdot (1 + 4\cdot (-1) + 5) = 2\cdot \sqrt{2} |
-10,616 | -\frac{20}{10 x^3} = -\dfrac{1}{2x^3}4\cdot \frac{1}{5}5 |
53,986 | 1 + 1 + 3 + 3 = 8 |
26,948 | \frac{\partial}{\partial y} y^n = y^{(-1) + n} \times n |
3,636 | \frac{1 + n}{(\left(-1\right) + n)!\cdot 2} = \frac{1}{(n + (-1))!} + \frac{1}{2\cdot (2\cdot (-1) + n)!} |
2,114 | 3 \cdot p^3 + 10 \cdot p \cdot p + 14 \cdot p + 8 = 3 \cdot p^3 + 6 \cdot p \cdot p + 6 \cdot p + 4 \cdot p^2 + 8 \cdot p + 8 = (3 \cdot p + 4) \cdot \left(p^2 + 2 \cdot p + 2\right) |
-20,404 | \tfrac18*1 = \frac{-9*y + 9*(-1)}{72*\left(-1\right) - y*72} |
26,818 | 1/\tan(t) = \cot(t) |
24,533 | 44 \cdot 52 \cdot 48/2 = 54912 |
16,376 | z^2 = \left(z + 2\right) \left(z + 2\right) - (z + 7 (-1)) (z + 7 (-1)) = (z + 2 + z + 7 (-1)) (z + 2 - z + 7) = 9\cdot (2 z + 5 (-1)) = 18 z + 45 (-1) |
10,581 | 90 be h = \frac{90 heb}{\left(-1\right) + 2} + \tfrac{be h}{1 + 0(-1)}0 |
-30,859 | \tfrac{12}{z + (-1)} = \frac{1}{z^4 - z \cdot z}\cdot (12\cdot z^2 + z^3\cdot 12) |
-22,795 | 26\cdot 3/(5\cdot 26) = \frac{1}{130}\cdot 78 |
19,353 | Q*\Sigma^{\tfrac12} = \Sigma^{\dfrac12}*Q |
12,770 | 2 * 2 + 14^2 = -5^2 + 15^2 |
-9,292 | 12*(-1) - y*10 = -y*2*5 - 2*2*3 |
47,154 | \frac{129}{31} = 4+\frac{5}{31} = 4+\frac{1}{\frac{31}{5}} = 4+\frac{1}{6+\frac{1}{5}} |
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