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int64 -30,985
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18,163 | \sin{z}*\cos{z} = 1/2*\sin{2*z} |
51,260 | 576 = 24 \cdot 24 |
-21,114 | \frac12*2*3/4 = 6/8 |
28,200 | 1 + \dfrac78 = 15/8 |
4,547 | 20 \cdot (3 + x^3) + 77 \cdot (-1) = 20 \cdot x^3 + 17 \cdot (-1) |
7,325 | 0 < 1 - t + x \implies x \gt (-1) + t |
15,985 | 2^m - 2^n = ((-1) + 2^{m - n})*2^n |
-3,455 | \sqrt{250} + \sqrt{160} - \sqrt{40} = -\sqrt{4 \cdot 10} + \sqrt{25 \cdot 10} + \sqrt{16 \cdot 10} |
34,599 | 3 (1 + k) = 2 + k*3 + 1 |
-26,546 | z^2 + 1 + 2 \times z = 1^2 + z \times 2 + z \times z |
19,967 | \frac1a*(u*(-1 + a) + 1) = (1 - u*\left(1 - a\right))/a |
-25,244 | \dfrac{1}{x^4}=x^{-4} |
5,038 | \tfrac{1}{C} \cdot C = \frac{C}{C} |
25,768 | 1 + 360 + 240 \left(-1\right) + 72 + 12 (-1) = 181 |
21,646 | \sin(x + \alpha) = \cos(x)\cdot \sin(\alpha) + \sin(x)\cdot \cos(\alpha) |
6,390 | (3 + \mathrm{i}*2) * (3 + \mathrm{i}*2) = 12 \mathrm{i} + 5 |
13,117 | 48 = (2 + 1)*(7 + 1)*\left(1 + 1\right) |
38,557 | 12^2 - 10\cdot 12 + 22 \left(-1\right) = 2 |
-20,323 | \tfrac14 \cdot 4 \cdot \dfrac{1}{-10} \cdot (2 \cdot y + 2) = (8 \cdot y + 8)/(-40) |
37,808 | 4! = (8 (-1) + 12)! |
9,861 | 7^5\cdot 5^3\cdot 3^3\cdot 2^2 = 226894500 |
-935 | \dfrac32 = \frac32 |
-22,324 | (z + 9)\cdot (z + 8\cdot \left(-1\right)) = z^2 + z + 72\cdot (-1) |
16,242 | (7! - 2\cdot 6!)/7! = \left(7 + 2\cdot (-1)\right)/7 = 5/7 |
5,227 | \lambda^2 - \lambda*x*2 + x^2 = (-x + \lambda)^2 |
40,014 | 479 = -{4 \choose 4} + {12 \choose 4} - {6 \choose 4} |
-23,104 | -3\cdot (-\tfrac{1}{3}\cdot 4) = 4 |
21,765 | (1 + p^{\tfrac{l}{2}})*(p^{l/2} + (-1)) = p^l + \left(-1\right) |
-27,102 | \sum_{n=1}^\infty \frac{1}{n \cdot 5^n} \cdot (-5)^n = \sum_{n=1}^\infty \frac{(-1)^n}{n \cdot 5^n} \cdot 5^n = \sum_{n=1}^\infty \frac1n \cdot (-1)^n |
-7,346 | 5/18 = \frac{1}{8}\cdot 4\cdot \dfrac59 |
-23,681 | \tfrac{1}{7}5*\dfrac{3}{8} = 15/56 |
36,406 | \left. d/dx x^{\left\{2\right\}} \right|_{\substack{ x=z }} = z + z = 2z |
54,343 | \frac{\frac{1}{\sin{\frac{1}{2 \cdot n}}}}{\sin^2{\dfrac12} \cdot \frac{1}{\sin{\frac{1}{2 \cdot n}}}} \cdot \sin{1/2} \cdot \sin{\frac{n + 1}{2 \cdot n}} = \sin{\frac{1}{2 \cdot n} \cdot (n + 1)}/\sin{1/2} = (\sin{\dfrac{1}{2}} \cdot \cos{\dfrac{1}{2 \cdot n}} + \cos{\frac{1}{2}} \cdot \sin{\frac{1}{2 \cdot n}})/\sin{\dfrac{1}{2}} |
5,151 | (a\cdot q^{n + 2\cdot \left(-1\right)}\cdot a\cdot q^n)^{1/2} = \left(a^2\cdot q^{2\cdot (n + (-1))}\right)^{1/2} = a\cdot q^{n + (-1)} |
16,993 | \frac{\sin(x*y^2)}{y^2 + x^2} = \frac{y^2*x}{y^2 + x * x}*\frac{1}{y^2*x}*\sin(y^2*x) |
24,703 | z^{12} + \left(-1\right) = \left(1 + z^6\right) (\left(-1\right) + z^6) |
8,374 | 2 - 2\cdot h \Rightarrow 2\cdot (-h + 1) = 0 |
8,511 | \sin(x) + \sin(y) + \sin(q) = 0 = \cos(x) + \cos(y) + \cos(q) |
27,100 | d = d/3 + \frac{1}{3}*d + \frac{d}{3} |
-6,749 | \dfrac{4}{100} + \tfrac{1}{100}*10 = 10^{-1} + \frac{4}{100} |
-8,803 | π\cdot 9 + π\cdot 9 + 30\cdot π = π\cdot 48 |
3,954 | c \cdot (h + a) = a \cdot c + c \cdot h |
-10,605 | \frac{16}{16 r + 12} = \frac{1}{4}4*\frac{1}{3 + 4r}4 |
-186 | \frac{1}{5!*(8 + 5*(-1))!}*8! = \binom{8}{5} |
30,573 | -G \geq -C \Rightarrow C \geq G |
-4,063 | \dfrac{a^4}{a^2} = \frac{a^4}{a\cdot a}\cdot 1 = a^2 |
11,614 | (b + c)*e = e*c + e*b |
27,495 | 1 + 2^2 + 3^2 + \cdots \cdot n^2 = n/6 \cdot (n + 1) \cdot (2 \cdot n + 1) |
6,700 | \theta + 2\cdot (-1) + \theta + (-1) = 2\cdot \theta + 3\cdot (-1) |
-1,244 | (1/5 (-2))/(1/6 (-1)) = -6/1 (-2/5) |
28,677 | (1 + 1/100)\cdot 10000 = 10000 + 1/100\cdot 10000 |
3,046 | k \cdot 4 = -(k + 2 \cdot (-1)) - 2 + 2 \cdot k + 3 \cdot k |
-27,066 | \sum_{n=1}^\infty 1/n = \sum_{n=1}^\infty \frac1n \cdot (3 - 2)^n |
13,359 | \left(1/2 + l\right)^2 = \frac14 + l l + l |
21,879 | (-1 + \sqrt{-3})/2 = \frac{\sqrt{3} i}{2} - 1/2 |
1,327 | \sigma_\phi x = x\sigma_\phi |
21,396 | 6 n + 3 = 3*(n*2 + 1) |
-18,612 | 5 r + 6 (-1) = 6 (r + 2) = 6 r + 12 |
-657 | e^{3\frac{7πi}{4}} = \left(e^{πi*7/4}\right)^3 |
-6,104 | \frac{6 + 11*p}{p^2*10 + p*40 + 320*(-1)} = \tfrac{1}{p^2*10 + p*40 + 320*(-1)}*(10*(-1) + 6*p + 24*(-1) + 5*p + 40) |
-20,151 | -4/1 \cdot \frac{(-9) \cdot t}{(-9) \cdot t} = \tfrac{36 \cdot t}{t \cdot (-9)} \cdot 1 |
28,901 | (5 * 5 + 5^2)*2 = 6^2 + 8^2 |
35,530 | \left(3 + \left(-1\right)\right)/6 = \frac{1}{3} |
18,852 | 2 \cdot 1 \cdot (100+100+100-2(10+10+10)+4\cdot 1^2) = 488 |
-22,291 | \lambda^2 - 11 \cdot \lambda + 18 = (2 \cdot (-1) + \lambda) \cdot (\lambda + 9 \cdot (-1)) |
23,375 | x^2 + x*3 - 5*x + 15*(-1) = \left(3 + x\right)*\left(x + 5*\left(-1\right)\right) |
33,425 | 0 = A + B \implies -B^2 + A^2 = 0 |
42,313 | (6 - 2\cdot 5^{1/2})^{1/2} = (-20^{1/2} + 6)^{1/2} |
7,957 | \cos{z} = \frac{\sin{2\cdot z}}{\sin{z}\cdot 2} |
13,812 | \sin{x} = \frac{2\cdot \tan{x/2}}{1 + \tan^2{\dfrac{1}{2}\cdot x}} |
-4,765 | -\dfrac{3}{y + 2} - \dfrac{1}{y + 4} \cdot 5 = \frac{1}{8 + y^2 + 6 \cdot y} \cdot (-8 \cdot y + 22 \cdot (-1)) |
-20,122 | \dfrac{y + 6}{-8y} \times \dfrac{10}{10} = \dfrac{10y + 60}{-80y} |
5,712 | \left(4 - x*3 = z \implies -3 x = z + 4 (-1)\right) \implies x = \left(4 \left(-1\right) + z\right)/(-3) |
46,235 | [2]^2 = [4] |
25,362 | \left( d, h, e\right) = ( h, e, d) = ( e, d, h) |
-20,207 | -\frac{4}{5}\cdot \frac{1}{-8\cdot n + 4\cdot (-1)}\cdot (4\cdot (-1) - 8\cdot n) = \dfrac{32\cdot n + 16}{20\cdot (-1) - n\cdot 40} |
3,261 | \frac{1}{1 + \cos\left(x\right)}\cdot \sin\left(x\right) = \frac{1}{\sin(x)}\cdot \left(-\cos(x) + 1\right) |
25,468 | 13\cdot \binom{4}{3}\cdot \binom{48}{4} = 10118160 |
18,953 | 29^{32} + \left(-1\right) = (1 + 29^{16}) ((-1) + 29^{16}) |
-10,623 | \frac{10}{x\cdot 2 + 3}\cdot 12/12 = \frac{120}{x\cdot 24 + 36} |
16,949 | 1 + 3 + 3^2 + \dots + 3^{k + \left(-1\right)} = \dfrac{1}{2}*(3^k + \left(-1\right)) |
26,584 | (-1) + w \cdot w^2 = (w + (-1)) \cdot (1 + w^2 + w) |
2,974 | (1 + 4) \cdot \left(1 + 2\right) \cdot (6 + 1) = 105 |
13,177 | 3 + (m + (-1))*3 = m*3 |
-20,557 | \left(2(-1) - x \cdot 18\right)/(\left(-10\right) x) = 2/2 \frac{1}{x \cdot (-5)}((-1) - x \cdot 9) |
-30,913 | 3 + 4 \cdot m = 4 \cdot m + 3 |
25,200 | -c^2 + h^2 = (h - c)\cdot (h + c) |
30,032 | 1 = (z + 1)/(13*z) = \dfrac{1}{13} + 1/(13*z) |
22,308 | 4^2\cdot (4^2 + \left(-1\right))/3 = 4^2 + 4 \cdot 4^2 |
-6,304 | \frac{q*5}{(9 (-1) + q) (9 + q)} = \frac{q*5}{q^2 + 81 (-1)} |
10,635 | (\sin(\dfrac{z}{2}) + \cos(z/2))^2 = 1 + 2*\sin(z/2)*\cos\left(z/2\right) = 1 + \sin(z) |
-13,941 | \frac{35}{1 + 6} = \tfrac{35}{7} = \frac{35}{7} = 5 |
-16,502 | 2 \cdot 44^{\frac{1}{2}} = 2 \cdot (4 \cdot 11)^{1 / 2} |
36,952 | {(-1) + 2\cdot m - k \choose m} = {m + m - k + (-1) \choose m} |
15,599 | z^5 + x^5 = (z + x)*(x^4 - x^3*z + z^2*x^2 - z^3*x + z^4) |
-11,528 | -i \times 5 - 37 = -12 + 25 \times \left(-1\right) - 5 \times i |
7,971 | y^3 + 1 + y + y^2 = (1 + y)\cdot (1 + y^2) |
38,634 | U = \frac{\pi}{\pi} U |
-1,885 | \pi*23/12 = \frac14*7*\pi + \frac{\pi}{6} |
36,175 | \left(x + z\right)*\alpha = \alpha*x + \alpha*z |
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