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int64 -30,985
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-4,977 | 0.9*10^0 = 0.9*10^{\left(-3\right)*(-1) - 3} |
23,385 | A^3 = A \cdot A\cdot A = 2\cdot A \cdot A - I\cdot A = 2\cdot (2\cdot A - I) - A = 3\cdot A - 2\cdot I |
-2,174 | 5/14 - 3/14 = \frac{2}{14} |
22,931 | 1/2 + (y + 5/2)*(1 + 2*y) = 2*y^2 + 6*y + 3 |
4,774 | 6 \cdot l + 3 = (2 \cdot l + 1) \cdot 3 |
-3,212 | \sqrt{2}*\left(5 + 3 + 4\right) = 12*\sqrt{2} |
23,303 | z \cdot x^3 = f + \int x \cdot x^3\,\mathrm{d}x \Rightarrow f + \frac{x^5}{5} = x^2 \cdot x \cdot z |
-29,369 | (5 \cdot y + 1) \cdot (5 \cdot y + \left(-1\right)) = (5 \cdot y)^2 - 1 \cdot 1 = 25 \cdot y^2 + \left(-1\right) |
20,075 | z + (-1) = 1 + z + 2\cdot (-1) |
-9,881 | \left((-7) \cdot 10^{-1}\right)/4 = \frac{(-7)}{10 \cdot 4} = -\dfrac{1}{40}7 |
5,837 | x^j*j! = \frac{1}{\frac{1}{j!}*x^{-j}} |
4,470 | 29 = 6\times 7 + 6\times (-1) + 7\times (-1) |
4,841 | {k + p + (-1) \choose k} = {k + p + \left(-1\right) \choose (-1) + p} |
26,464 | {4 \cdot 2 \choose 3} = \frac{1}{(8 + 3 \cdot (-1))! \cdot 3!} \cdot 8! = \frac{6}{3 \cdot 2} \cdot 8 \cdot 7 = 56 |
9,067 | \left(-1\right) + 2 \cdot l = l^2 - (l + (-1))^2 |
48,092 | 14826240 = 15 \times 988416 |
-10,295 | \frac{5 x + 5}{x*20 + 40 (-1)} = \frac{1}{8 \left(-1\right) + x*4} (1 + x)*5/5 |
-30,288 | (0 + 80)/2 = \frac12 80 = 40 |
-4,942 | \frac{1}{10^6} \cdot 37.8 = \frac{1}{10^6} \cdot 37.8 |
29,058 | \sin^2(x) = \sin(x)\cdot \sin(x) |
31,136 | (x + 5*(-1))^2 - \sqrt{5} * \sqrt{5} = 5*(-1) + x * x - 10*x + 25 |
2,933 | (X + 3) \cdot (X + 3) \cdot (X + 3) = X^3 + 9\cdot X \cdot X + 27\cdot X + 27 = (X \cdot X + 5\cdot X + 7)\cdot (X + 4) + (-1) |
12,796 | \tfrac1n \cdot (n + (-1)) \cdot \pi = (n + (-1)) \cdot \pi/n |
-2,217 | \frac{9}{19} - \frac{3}{19} = \frac{1}{19}\cdot 6 |
-23,302 | 8/21 = 6/7\cdot \frac{4}{9} |
10,987 | -(\frac12)^2 + \frac{1}{10}\cdot 3 = \frac{1}{20} |
21,127 | (2 + z) (z + 3) = z z + z*6 + 6 - z |
4,767 | n + 4 \cdot (-1) = 1 \Rightarrow n = 5 |
3,006 | -y^3 + z^3 = (z^2 + zy + y * y) (-y + z) |
49,101 | {13 \choose 2} = {2 + 11 \choose 2} |
17,046 | \cos(2 y) = 1 - 2 \sin^2(y) |
26,698 | \frac22 \cdot I \cdot 2^{1 / 2} = I \cdot 2^{1 / 2} \gt I |
50,890 | \infty + \infty = 0 |
20,373 | \frac{1}{(-y + 1)^5} = (1 + y + y y + y^3 + ...)^5 |
-24,039 | 1 + \frac{6}{6} = 1 + 1 = 2 |
-7,652 | \tfrac{1}{-2i - 1}(5i + 5) = \frac{1}{-1 - i \cdot 2}\left(5 + i \cdot 5\right) \frac{1}{i \cdot 2 - 1}(-1 + 2i) |
15,964 | 1/50 = \frac{1}{500} \cdot 10 |
32,637 | 0 = a^7 + 1 = (a + 1) (a^6 - a^5 + a^4 - a * a * a + a * a - a + 1) |
-4,366 | 7/6 \cdot b = 7 \cdot b/6 |
17,559 | 2^{m + 4} = 2^{m + 3} + 2^{2 + m} + 2^{m + 1} + 2^m + 2^m |
4,402 | ( \rho(x), y) = \left( \rho(x), \rho(\rho^{-1}(y))\right) = \left( x, \rho^{-1}(y)\right) |
46,957 | {11 \choose 4} {4 \choose 2} = \frac{1}{7! \cdot 4!}11! \frac{1}{2! \cdot 2!}4! = \frac{11!}{7! \cdot 2! \cdot 2!} |
-2,544 | \sqrt{10} + \sqrt{10}*4 = \sqrt{10} + \sqrt{10}*\sqrt{16} |
-7,594 | \frac{i*20 - 25}{5 - i*4}*\frac{5 + 4*i}{5 + 4*i} = \frac{20*i - 25}{5 - 4*i} |
15,893 | 2 + 2*(n + 2*(-1)) = 2*\left((-1) + n\right) |
29,915 | \sin{x\cdot 3} = \sin(8\cdot x - 5\cdot x) |
2,649 | \left(Y \cdot Y^q\right) \cdot \left(Y \cdot Y^q\right) \cdot \left(Y \cdot Y^q\right) = Y \cdot Y^q \cdot Y \cdot Y^q \cdot Y \cdot Y^q = Y^q \cdot Y \cdot Y^q \cdot Y \cdot Y^q \cdot Y = \left(Y^q \cdot Y\right)^3 |
28,793 | p - r - p = 2\cdot p - r |
8,347 | \dfrac{1}{z - b_m} \cdot (z - d_m) + \left(-1\right) = \frac{1}{z - b_m} \cdot \left(z - d_m - z + b_m\right) = \frac{1}{z - b_m} \cdot (b_m - d_m) |
38,318 | (1-\frac{1}{\epsilon})^{2} - 4 = (1 - \frac{1}{\epsilon} - 2)(1 - \frac{1}{\epsilon} + 2) = -(1 + \frac{1}{\epsilon})(1-\frac{1}{\epsilon}) = \frac{1}{\epsilon^{2}} - 1 |
-23,821 | \tfrac{1}{2 + 8}20 = 20/10 = \frac{1}{10}20 = 2 |
43,365 | 10 10 + 5^2 = 100 + 25 = 125 = 121 + 4 = 11 11 + 2 2 |
19,751 | \frac{\pi}{2^{1/2}} = \frac{\pi}{2} \cdot 2^{1/2} |
10,295 | 4 + 27*2 + x*81 = x*81 + 58 |
13,276 | e^{\ln(c^{\epsilon})} = c^{\epsilon} |
7,151 | (1 + y + \dots + y^5)^8 = \left(\frac{1}{1 - y}*(1 - y^6)\right)^8 = \dfrac{(1 - y^6)^8}{(1 - y)^8} |
43,209 | 12/50 \cdot 13/51 \cdot \tfrac{39}{52} + \dfrac{39}{50} \cdot 12/51 \cdot \frac{13}{52} + 39/51 \cdot \frac{1}{52} \cdot 13 \cdot 12/50 = \frac{1}{{52 \choose 3}} \cdot {39 \choose 1} \cdot {13 \choose 2} |
20,034 | a \cdot 2 - 2 \cdot b = (a - b) \cdot 2 |
-20,572 | -7/4 \cdot \frac{1}{3 \cdot (-1) + k} \cdot (3 \cdot (-1) + k) = \frac{1}{12 \cdot (-1) + 4 \cdot k} \cdot (21 - 7 \cdot k) |
25,381 | \frac{1}{A \cdot D} = \frac{1}{D \cdot A} |
9,180 | \sin^4(z) + \cos^4\left(z\right) = (\sin^2(z) + \cos^2(z))^2 - 2\sin^2(z) \cos^2(z) = 1 - \frac12\sin^{22}(z) |
2,349 | x^2 + \left(-1\right) = (x + (-1))\cdot (x + 1) = \sqrt{x^2 + (-1)}\cdot \sqrt{x^2 + (-1)} |
-4,770 | \frac{3}{x + (-1)} + \frac{1}{x + 4\cdot (-1)}\cdot 3 = \frac{x\cdot 6 + 15\cdot \left(-1\right)}{x^2 - x\cdot 5 + 4} |
-19,468 | 5*1/2/(1/7*5) = \frac52*\dfrac{1}{5}*7 |
38,576 | 21 = 26 + 5*(-1) |
-619 | (e^{\pi \cdot i \cdot 5/3})^5 = e^{5 \cdot \frac{1}{3} \cdot i \cdot \pi \cdot 5} |
30,726 | z^2 \cdot 2 + z \cdot 3 + 1 = \left(1 + z \cdot 2\right) \cdot (z + 1) |
7,973 | (m + 1)^2 - m^2 = m\cdot 2 + 1 |
-19,167 | 11/30 = \frac{A_s}{9 \cdot π} \cdot 9 \cdot π = A_s |
4,571 | (A' \cap R) \cup (R \cap (A' \cap x)) = A' \cap ((A' \cap R) \cup (R \cap x)) |
-16,572 | 117^{1 / 2} \cdot 2 = 2 \cdot (9 \cdot 13)^{\frac{1}{2}} |
24,763 | -\sin{d}*\sin{b} + \cos{b}*\cos{d} = \cos(d + b) |
11,461 | \frac{1}{20} \cdot (1 + 2 + 3 + \dots + 20) = 21/2 = 10.5 |
1,652 | 0 \cdot (-1) + 3 = 1 + 2 + \left(-1\right) \Rightarrow 2 = 3 |
21,127 | (z + 2)*\left(z + 3\right) = z^2 + 6*z + 6 - z |
19,453 | -i\cdot \sin{\theta} + \cos{\theta} = \cos{-\theta} + i\cdot \sin{-\theta} |
19,964 | z^2 + z^2 + 1 = z \cdot z + z + z + z \cdot z = z^2 + z + z + z \cdot z + 1 |
6,901 | \sin^2(y) = \frac{1}{-4} \times (e^{i \times y} - e^{-i \times y}) \times (e^{i \times y} - e^{-i \times y}) = -(e^{2 \times i \times y} + 2 \times (-1) + e^{-2 \times i \times y})/4 |
-4,324 | \dfrac{x^4}{10\cdot x^2} = \frac{x^4\cdot \frac{1}{x^2}}{10}\cdot 1 |
-9,319 | -2 \cdot 2 \cdot 2 \cdot 5 a + 2 \cdot 2 \cdot 2 \cdot 5 = 40 - 40 a |
-24,658 | 1\cdot 2/(9\cdot 2) = 2/18 |
8,827 | 1 - 27/216 - 111/216 = \dfrac{1}{216} 78 \approx 0.3611 |
4,312 | \sin(x + d) = \cos\left(x\right)\cdot \sin(d) + \sin(x)\cdot \cos\left(d\right) |
1,845 | -D\times 4 = 1 \Rightarrow D = -1/4 |
-18,111 | 79 + 9\cdot (-1) = 70 |
22,623 | 0 = y^2 + 2 \cdot i \cdot y + 2 \cdot (-1) = \left(y + i\right)^2 + (-1) = (y + (-1) + i) \cdot (y + 1 + i) |
4,870 | -\frac{1}{4} \cdot r + \dfrac{n}{2} = \frac12 \cdot (n - \frac{r}{2}) |
13,717 | -z^d + z^f = -(-z^f + 1) + 1 - z^d |
-2,575 | 5^{1 / 2} = 5^{\frac{1}{2}}*(3 + 2 (-1)) |
-6,634 | \frac{1}{36 (-1) + q^2 - q \cdot 5}4 = \dfrac{4}{(q + 9\left(-1\right)) \left(q + 4\right)} |
-20,871 | \dfrac{1}{7 \cdot (-1) + 7 \cdot z} \cdot (2 \cdot z + 2 \cdot (-1)) = \frac{2}{7} \cdot \frac{z + \left(-1\right)}{(-1) + z} |
-18,416 | \frac{r\cdot (r + (-1))}{(r + (-1))\cdot (2 + r)} = \frac{-r + r^2}{2\cdot (-1) + r^2 + r} |
28,869 | \sum_{m=1}^\infty \sin{m} = \sin{1} + \sin{2} + \sin{3} + \ldots + \sin{m} |
-18,610 | 46 = \frac12 \times 92 |
1,797 | (1 + h)^k \geq k \cdot h + 1 \Rightarrow (1 + h) \cdot (1 + k \cdot h) \leq (1 + h)^k \cdot (1 + h) = (1 + h)^{k + 1} |
6,143 | -d^3 + a^3 = \left(-d + a\right)\cdot (d \cdot d + a^2 + a\cdot d) |
32,625 | \frac{1}{2}\cdot (1 + (2\cdot 178 + 1)^2)\cdot π = 63725\cdot π \approx 200197.991850009574121 |
21,736 | \gamma_2 \cdot n + \gamma_1 \cdot q \cdot n = \gamma \implies \frac1n \cdot \gamma = \gamma_2 + q \cdot \gamma_1 |
-19,661 | 4 \cdot 7/\left(8\right) = \frac{28}{8} |
7,034 | \sin\left(2 \pi\right) = \sin(10 \pi) |
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