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int64 -30,985
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5,970 | 98*100 + 2 = \left(99 + (-1)\right)*(99 + 1) + 2 = 99^2 + (-1) + 2 = 99^2 + 1 |
9,426 | 3^5 - ((-1) + 3)^5\cdot {3 \choose 1} + (3 + 2\cdot (-1))^5\cdot {3 \choose 2} = 150 |
16,547 | (m + 1/2)^2 = 1/4 + m^2 + m |
20,898 | \sigma * \sigma = (\sqrt{n + \sqrt{n + \sqrt{n + ...}}})^2 = n + \sigma |
51,976 | \frac{n}{n^2 + n} + \dotsm + \frac{n}{n^2 + 1} \lt x_n < \dfrac{n}{n^2 + 1} + \dotsm + \frac{n}{n^2 + 1}\Longrightarrow \frac{1}{n^2 + n}\cdot n^2 < x_n \lt \dfrac{1}{n^2 + 1}\cdot n^2 |
-4,553 | \frac{4}{4 \times \left(-1\right) + x} + \dfrac{3}{2 \times (-1) + x} = \frac{20 \times (-1) + x \times 7}{8 + x^2 - x \times 6} |
16,422 | (-1) + x \cdot x = \left(x + 1\right) \left((-1) + x\right) |
6,859 | (2 \cdot (-1) + 1)^2 + (0 + (-1))^2 + (2 \cdot (-1) + 0)^2 = 6 |
36,615 | 0 - y = -y \in X |
6,452 | 0 = 3\cdot (-1) + z^3 - z\cdot 3 \Rightarrow z = 2.1038 |
-7,571 | \frac{-18 \cdot i + 6}{4 - 2 \cdot i} = \frac{1}{4 - i \cdot 2} \cdot (6 - 18 \cdot i) \cdot \dfrac{2 \cdot i + 4}{4 + i \cdot 2} |
22,822 | \operatorname{E}\left[T^2\right] = \operatorname{E}\left[T\right]^2 |
10,287 | 1 = \frac{1}{a} \cdot a \Rightarrow \dfrac{1}{\frac{1}{a}} = a |
24,171 | (1 + 2)\cdot p = 3\cdot p |
32,511 | (k + 1)! - k! = k \cdot k! |
-3,140 | -2^{\frac{1}{2}} + 18^{1 / 2} + 50^{\frac{1}{2}} = -2^{1 / 2} + (9 \cdot 2)^{1 / 2} + \left(25 \cdot 2\right)^{\frac{1}{2}} |
44,389 | 4\times 7\times 13 = 364 |
-5,472 | \dfrac{1}{(10 + q) \cdot (q + 2) \cdot 9} \cdot (q \cdot 6 + 12) - \frac{15 \cdot \left(10 + q\right)}{9 \cdot (q + 2) \cdot (q + 10)} + \frac{q \cdot 36}{(10 + q) \cdot \left(2 + q\right) \cdot 9} = \frac{36 \cdot q + 6 \cdot (q + 2) - (10 + q) \cdot 15}{9 \cdot (q + 2) \cdot (10 + q)} |
28,390 | (j + 2)! = (2 + j)\cdot (1 + j)\cdot j\cdot ... |
-18,439 | \dfrac{(3\times (-1) + q)\times (10\times (-1) + q)}{q\times (q + 10\times (-1))} = \dfrac{1}{q^2 - 10\times q}\times (q^2 - 13\times q + 30) |
8,809 | \frac{1}{y + 1}\cdot \left(3\cdot y + 2\cdot (-1)\right) = \dfrac{1}{y + 1}\cdot \left(3\cdot (y + 1) + 5\cdot (-1)\right) = 3 - \frac{5}{y + 1} |
11,780 | H^{1 + n} = H^n\cdot H |
7,119 | d/dx (\left(x + (-1)\right) \left(x + 1\right)^3) = ((-1) + x) (x + 1) \cdot (x + 1)\cdot 3 + (x + 1)^3 |
24,668 | 0.352 = \frac{8^2}{20^2} + 2\frac{8^2}{20^2}*\frac{1}{20}12 |
252 | \dfrac{1}{h_1 \cdot h_2} + \tfrac{1}{(h_2 + (-1)) \cdot h_2 \cdot h_1} = \frac{1}{h_1 \cdot \left((-1) + h_2\right)} |
22,812 | c_1 - 1/2 + 10/4 = 0 \Rightarrow c_1 = -2 |
19,068 | -\frac{25}{7} = \sec{x} \Rightarrow -7/25 = \cos{x} |
30,563 | 3 \cdot 3 + 1^2 - 3 = 7 |
-4,704 | \dfrac{y*3 + 14}{y^2 + 4(-1)} = -\frac{2}{y + 2} + \frac{5}{y + 2\left(-1\right)} |
22,001 | x - \tfrac{1}{3!}\cdot x^3 + \dfrac{x^5}{5!} - ... = \sin{x} |
428 | (2 \cdot 10^{1/2})^2 + \left(5 \cdot 10^{1/2}\right)^2 = 40 + 250 = 290 = (290^{1/2})^2 |
20,002 | y^3 - \left(5 + i\right) y \cdot y + y \cdot (i \cdot 5 + 2) + 10 (-1) = (5(-1) + y) (y \cdot y - iy + 2) |
5,956 | (z - y) \cdot (z^1 + z^0 \cdot y + \ldots + z \cdot y^0 + y^1) = z^2 - y^2 |
19,013 | \tan^{-1}(∞) = \frac{1}{2} \cdot \pi |
-5,412 | 2.56 \cdot 10 = \frac{2.56}{10^6} \cdot 10 = \dfrac{2.56}{10^5} |
37,037 | \sin(f + g) = \sin\left(f\right) \cdot \cos(g) + \sin(g) \cdot \cos\left(f\right) |
10,398 | g^{h + b} = g^b \cdot g^h |
11,879 | \sqrt{l + 3} = (l + 2)^2 + (-1) = (l + 3)^2 - 2 \cdot (l + 3) |
-25,026 | -1 - y - y \cdot y - y^3 - y^4 - \ldots = -\frac{1}{-y + 1} |
-19,304 | 3/4*3/7 = \frac{3*\frac14}{7*\frac{1}{3}} |
7,070 | -3\cdot d_2\cdot g\cdot d_1 + d_2^3 + g^3 + d_1 \cdot d_1 \cdot d_1 = \tfrac{1}{2}\cdot (d_1 + d_2 + g)\cdot \left((-g + d_1)^2 + (d_2 - g)^2 + (-d_1 + d_2)^2\right) |
37,973 | F + Q := F \cup Q |
26,344 | l + n + 1 + 1 = 1 + n + 1 + l |
9,452 | (a + l) \cdot (a + l) = a^2 + 2\cdot a\cdot l + l^2 = i + 2\cdot a\cdot l - i = 2\cdot a\cdot l |
52,557 | 349 = 205 + 144 |
26,501 | p \times {k \choose p} = {k + (-1) \choose (-1) + p} \times k |
15,901 | 2*\left(2 + 3*n\right) = 4 + 6*n |
26,652 | s^6 s^{12} = s^{18} |
11,595 | \sqrt{2} + 5^{1/3} = y rightarrow \left(-\sqrt{2} + y\right)^3 = 5 |
9,131 | \left(o^y + 3\right) (o^y + (-1)) + 4 = o^{2y} + 2o^y + 1 = (o^y + 1)^2 |
27,625 | x = \pi/4 \implies \cos^5(x) - \sin^5(x) = 0 \neq \cos(5 \cdot \pi/4) |
-6,693 | \frac{8}{10} + \frac{1}{100}\cdot 3 = \tfrac{3}{100} + \frac{1}{100}\cdot 80 |
-19,691 | \frac{15}{7} = \frac{5\cdot 3}{7} |
37,373 | a = h \Rightarrow a = h |
6,192 | \frac{1}{1 + m}m = 1 - \tfrac{1}{1 + m} |
4,064 | \mathbb{E}(R - Y)^2 + Var(-Y + R) = \mathbb{E}((R - Y)^2) |
8,818 | \frac{657720}{30^4}*1 = \frac{203}{250} |
24,758 | \sin\left(y + z\right) = \sin(y) \cos(z) + \cos(y) \sin(z) |
40,906 | \frac{4!}{\left(4 + 2 \cdot (-1)\right)! \cdot 2!} = \dfrac{1}{2 \cdot 2} \cdot 24 = 6 |
-20,393 | \frac{-14 \cdot t + 56 \cdot (-1)}{t \cdot 70 + 35} = 7/7 \cdot \tfrac{8 \cdot (-1) - 2 \cdot t}{5 + t \cdot 10} |
7,221 | (z + x) \cdot \left(x^2 - x \cdot z + z^2\right) = z \cdot z \cdot z + x^3 |
16,123 | 2\cdot 1/31/25 = \frac{1}{775}\cdot 2 |
15,851 | -\frac{1}{6}\cdot 2\cdot \frac15\cdot 2 + 1 = \frac{13}{15} |
20,658 | (1 - \cos\left(4\cdot x\right))^{\frac{1}{2}} = \left(2\cdot \sin^{22}(x)\right)^{1 / 2} = 2^{1 / 2}\cdot |\sin(2\cdot x)| |
14,626 | 16 + 9^k - 1^k = 15 + 3^{k*2} |
-21,028 | -7/5 \cdot \frac{4 + z}{z + 4} = \tfrac{28 \cdot (-1) - 7 \cdot z}{z \cdot 5 + 20} |
28,572 | \sin(z + 2 \cdot \pi) = \Im{\left(e^{i \cdot z + i \cdot 2 \cdot \pi}\right)} = \Im{(e^{i \cdot z})} = \sin\left(z\right) |
8,374 | 2 - 2\cdot a\Longrightarrow 2\cdot (1 - a) = 0 |
-22,030 | \frac{1}{7}*10 = \dfrac{40}{28} |
1,642 | \dfrac12\cdot (3\cdot (-1) + \sqrt{3 + \sqrt{2}\cdot 2} \cdot \sqrt{3 + \sqrt{2}\cdot 2}) = \sqrt{2} |
16,410 | 4^n + 15 \cdot n + \left(-1\right) = (3 + 1)^n + 15 \cdot n + \left(-1\right) |
17,896 | 0 = x^3 - x + 24 (-1)\Longrightarrow 3 = x |
21,185 | -\frac{3*x + 4*y}{5*z - 8*w} = -\dfrac{(3*x - 4*y)*(-1)}{\left(5*z - 8*w\right)*(-1)} = \frac{3*x + 4*y}{8*w - 5*z} |
-12,038 | \frac13\cdot 2 = s/(16\cdot \pi)\cdot 16\cdot \pi = s |
-22,123 | \frac18 \cdot 40 = 5 |
-3,858 | \dfrac{63}{54}\cdot \frac{1}{x^5}\cdot x^5 = \frac{63\cdot x^5}{x^5\cdot 54} |
32,371 | g \cdot f + d \cdot g + f \cdot d = \left(-(g^2 + f \cdot f + d^2) + (g + f + d)^2\right)/2 |
3,260 | (a^2 + a*f + f^2)*(a - f) = a * a * a - f^3 |
-2,885 | \sqrt{3}*2 = \sqrt{3}*(5 + 1 + 4 (-1)) |
13,457 | \sqrt{2\cdot y + 1} = y - (y^2 - 2\cdot y + 1)/7 = \dfrac17\cdot (-y^2 + 9\cdot y + 1) |
24,080 | \|x_t - x_{1 + t}\|^2 \leq 0 \Rightarrow x_t = x_{t + 1} |
2,108 | \frac{1}{a \cdot \frac{1}{b}} = \dfrac{b}{a} |
-16,844 | 8 = 8*5*p + 8*(-1) = 40*p - 8 = 40*p + 8*(-1) |
-12,252 | \frac{1}{18}*17 = \frac{s}{18*\pi}*18*\pi = s |
25,299 | q^2 + 2*w*q + w^2 = \left(q + w\right) * \left(q + w\right) |
22,300 | \frac{5!}{(5 + 2\cdot \left(-1\right))!}\cdot \frac{10!}{(10 + 3\cdot (-1))!}\cdot 7!\cdot \frac{1}{(7 + 2\cdot (-1))!}\cdot 3! = 720\cdot 42\cdot 20\cdot 6 = 3628800 |
-20,087 | \frac{5 (-1) + y}{3 y + 4}*\tfrac{7}{7} = \frac{1}{28 + 21 y} (7 y + 35 (-1)) |
31,023 | 49 \cdot \left(-1\right) + 3 \cdot 11 \cdot 11 = 314 |
15,221 | B\cdot \mathbb{E}\left(x\right) = B\cdot \mathbb{E}\left(x\right) |
9,466 | \sin{b} \sin{x} + \cos{b} \cos{x} = \cos(-b + x) |
6,209 | \ln\left(2\right)/\left(\ln(4)\right) = \frac{1}{2} |
22,182 | A\cdot x - x\cdot A = A \Rightarrow A^2 = A^2\cdot x - A\cdot A\cdot x |
-21,015 | -7/5*\frac{10*k}{10*k} = \frac{(-70)*k}{50*k} |
-23,635 | 3/28 = \frac{3\cdot 1/4}{7} |
45,482 | -\frac82 = -\frac82 |
4,710 | \frac{1}{16^{\frac14 \cdot 3} \cdot 27^{2/3}} = \frac{1}{\left(27^2\right)^{1/3} \cdot (16^3)^{\frac{1}{4}}} |
6,829 | g*(b*a + b*a) = (b*a + b*a)*g |
7,242 | -\frac14\pi = \frac14((-1) \pi) |
19,825 | \left(k + 2\right)\cdot (k + 3) - 5\cdot (2 + k) + 4 = k^2 |
8,303 | x^2 + x \cdot 2 + 1 = \left(x + 1\right)^2 |
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