id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-3,145 |
13^{1/2} + (16\cdot 13)^{1/2} = 208^{1/2} + 13^{1/2}
|
-2,341 |
\dfrac{1}{16}*8 - 1/16 = 7/16
|
52,373 |
(10^4 - 10 \cdot 9 \cdot 8 \cdot 7)/2 - \frac{\binom{4}{2}}{2}5 \cdot 5 + 5(-1) - 5\binom{3}{2} \cdot 8 = 2480 + 75 (-1) + 5(-1) + 120 (-1) = 2280
|
17,543 |
G_N*G_K*G_l = G_K*G_N*G_l
|
10,799 |
\tfrac{1}{-2 + t} - \frac{1}{-1 + t} = \frac{1}{-\frac{t}{2} + 1}*((-1)*1/2) + \frac{1}{-t + 1}
|
-7,895 |
(12 + i \times 15)/\left(-3\right) = 15 \times i/(-3) + 12/(-3)
|
7,830 |
-81 \cdot i = 81 \cdot (-i) = 81 \cdot \left(\cos{3 \cdot \pi/2} + i \cdot \sin{\frac{3}{2} \cdot \pi}\right)
|
8,240 |
123.4567 = \frac{1234567}{10^{7 + 3(-1)}}
|
19,867 |
57/64 = -\frac{7}{64} + 1
|
12,535 |
h^{-n + l} = \frac{1}{h^n}*h^l
|
30,090 |
\tilde{x}*a = 0.036*x/(0.0018*a) = 20*x/a
|
7,290 |
1 + 2 + 3 + \dots + l = l + 2
|
5,451 |
a^{x_1\cdot k}\cdot a^{x_2\cdot k} = a^{(x_2 + x_1)\cdot k}
|
-29,359 |
x \cdot (-1) \cdot (x + 4) = x \cdot x + 4 \cdot x - x + 4 \cdot (-1) = x^2 + 3 \cdot x + 4 \cdot (-1)
|
-29,045 |
y^{m + l} = y^l y^m
|
4,540 |
0 = z \cdot z + z + 1 \Rightarrow 1 = z^3
|
36,092 |
1260 = 2 * 2*3^2*5*7
|
-17,409 |
0.723 = 72.3/100
|
14,929 |
(2n + 1)! = (2n + 1)\cdot 2n\cdot (2n + \left(-1\right)) (2n + 2(-1)) \dotsm\cdot 2 = \left(2n + 1\right)\cdot 2n\cdot (2n + (-1))!
|
30,955 |
\sqrt{1 - \sin{2\cdot x}} = \sqrt{(\sin{x} - \cos{x}) \cdot (\sin{x} - \cos{x})} = \sqrt{\left(\cos{x} - \sin{x}\right) \cdot \left(\cos{x} - \sin{x}\right)}
|
6,036 |
x + y + y + c = x + c + 2 \cdot y
|
-30,859 |
\frac{z^2\cdot 12 + 12\cdot z \cdot z^2}{z^4 - z \cdot z} = \frac{1}{z + \left(-1\right)}\cdot 12
|
-7,701 |
\dfrac{-15 + 25*i}{-4 + i}*\dfrac{-i - 4}{-4 - i} = \dfrac{-15 + i*25}{i - 4}
|
-28,950 |
(l + 3) \cdot (l + 3 \cdot (-1)) = l^2 + 9 \cdot (-1)
|
21,607 |
345*x*123 = 345*x*123
|
27,963 |
z y x = z y x
|
7,117 |
\frac{1}{x^2 y^2} = \frac{1}{y^2 x^2}
|
-18,261 |
\tfrac{m \cdot m + m\cdot 3}{30\cdot (-1) + m^2 - m\cdot 7} = \frac{m}{(10\cdot (-1) + m)\cdot (m + 3)}\cdot (3 + m)
|
12,828 |
2u = (1 + u) (1 - u^2) = 1 - u^3 - u^2 + u
|
-27,493 |
8\cdot c \cdot c = 2\cdot c\cdot c\cdot 2\cdot 2
|
16,037 |
\cot(\tan^{-1}{j}) = 1/j
|
-459 |
\pi = -4\cdot \pi + \pi\cdot 5
|
-16,597 |
4\sqrt{4*2} = \sqrt{8}*4
|
23,782 |
\frac{-b - b}{2 \cdot a} = \dfrac{(-2) \cdot b}{2 \cdot a} = ((-1) \cdot b)/a
|
-11,626 |
-8i + 8 = -i \cdot 8 + 0 + 8
|
-19,047 |
1/5 = \frac{X_x}{100 \cdot \pi} \cdot 100 \cdot \pi = X_x
|
17,702 |
(-I + Y_2)\cdot (Y_1 - I) = (Y_1 - I)\cdot \left(Y_2 - I\right)
|
-1,328 |
\dfrac{21}{35} = \frac{21\cdot 1/7}{35\cdot 1/7} = \frac{1}{5}\cdot 3
|
18,858 |
( r', x)\cdot ( r, i) := ( r\cdot r', i\cdot r' + r\cdot x)
|
8,583 |
\frac{1}{(-1)^{2 \cdot n}} \cdot (-1)^n = \frac{1}{(-1)^n}
|
-9,467 |
-m\cdot 2\cdot 2\cdot 2\cdot 3 = -24\cdot m
|
21,373 |
x^3 - x \cdot x = -x^2 + x^3
|
-20,901 |
35/(-5) = -5/(-5)\cdot (-\dfrac{7}{1})
|
-6,316 |
\dfrac{1}{x^2 - 9 \cdot x + 10 \cdot (-1)} \cdot \left(3 \cdot x + 30 \cdot (-1) + 2 \cdot x + 2 - x\right) = \dfrac{x \cdot 4 + 28 \cdot \left(-1\right)}{x^2 - x \cdot 9 + 10 \cdot (-1)}
|
-22,315 |
t^2 + 13\cdot t + 36 = (4 + t)\cdot (9 + t)
|
-20,356 |
\frac{1}{1 + 6*r}*(6*r + 1)*(-\frac{3}{5}) = \frac{1}{5 + r*30}*(3*(-1) - 18*r)
|
13,764 |
x^{2^k} = (x^4)^{2^{k + 2\cdot (-1)}} = \left(x + 1\right)^{2^{k + 2\cdot (-1)}} = x^{2^{k + 2\cdot (-1)}} + 1
|
26,636 |
3^2 + 4^2 + 12^2 + 84^2 + 3612 \cdot 3612 = 3613^2
|
28,335 |
(a^2\cdot \sinh^2{p} + a^2)^{\tfrac{1}{2}} = a\cdot (\sinh^2{p} + 1)^{1 / 2} = a\cdot \cosh{p}
|
31,723 |
abc = bc + 2ac + 3ab \geq 3(6a \cdot a b \cdot b c^2)^{\tfrac13}
|
20,999 |
e^{z*3} \sqrt{z} = \frac{1}{e^{-3z}}\sqrt{z}
|
-19,424 |
\frac18 \times 9 \times \dfrac67 = \frac{9 \times \frac{1}{8}}{7 \times \dfrac16}
|
-3,892 |
\frac{11}{4}\cdot i = i\cdot 11/4
|
26,554 |
N_1*N_2 = N_1*N_2
|
24,395 |
z^2\cdot D^2 + 6\cdot z\cdot D + 9\cdot (-1) = (z\cdot D)^2 + 5\cdot z\cdot D + 9\cdot (-1) = (z\cdot D + 2.5)^2 - 15.25
|
12,090 |
2/27 + 1/9 + \frac19 + \dfrac{2}{27} = 10/27
|
19,788 |
z*l - l*y = -0*l + (z - y)*l
|
10,389 |
0 = \gamma^2 + \gamma + 1 = (\gamma + 1/2)^2 + \frac{3}{4}
|
27,731 |
n^2 - n\cdot 2 + 1 = ((-1) + n)^2
|
-6,172 |
\frac{3}{4\cdot y + 24} = \frac{3}{(6 + y)\cdot 4}
|
21,405 |
\pi \frac{\cos(\pi z)}{\pi} = \cos(\pi z)
|
19,409 |
|x^n| = (1 + |x| + (-1))^n > 1 + (|x| + (-1)) \cdot n
|
39,187 |
\cos{\pi/4} = \sqrt{2}/2
|
2,700 |
28 = 2 \cdot 2 \cdot 3^0 \cdot 5^0 \cdot 7^1
|
17,930 |
k\cdot 0 = 0 = 0k
|
4,817 |
g = h rightarrow h^4 = g^4
|
-2,744 |
\sqrt{7}\cdot (2 + 5) = \sqrt{7}\cdot 7
|
28,271 |
\left(\cos(z \cdot 2) + 1\right)/2 = \cos^2(z)
|
13,347 |
m*n + n = (m + 1)*n
|
21,927 |
n^2 = b_{n + 1} - b_n = \dfrac{1}{n + 1 - n}\cdot (b_{n + 1} - b_n)
|
-22,151 |
30/27 = \dfrac{10}{9}
|
-18,053 |
3\cdot \left(-1\right) + 38 = 35
|
12,383 |
\tan\left(-y\right) = \frac{\sin(-y)}{\cos(-y)} = \frac{1}{\cos(y)} \times (\left(-1\right) \times \sin(y)) = -\tan(y)
|
-5,853 |
\frac{1}{(9 + d) \cdot 2} \cdot 3 = \frac{3}{18 + 2 \cdot d}
|
41,642 |
1 = \sqrt{1} = \sqrt{(-1)*\left(-1\right)} = \sqrt{-1}*\sqrt{-1} = i * i = -1
|
29,376 |
0 = x rightarrow 0 = \|x\|
|
14,550 |
\lim_{l \to ∞} \sin\left(l\right) = a \Rightarrow \lim_{l \to ∞} \sin\left(l*2\right) = a \in (-1, 1)
|
-24,759 |
\frac{1}{4} \times (6^{1/2} + 2^{1/2}) = \cos(\tfrac{1}{12} \times \pi)
|
3,525 |
b^2 + \left(b + 23\cdot (-1)\right)^2 = 289 \Rightarrow 2\cdot b^2 - 46\cdot b + 240 = 0
|
15,167 |
x*S = x - x^2 + x^3 + x^4 + x^5 + x^6 = x - 1 - S - x + x^6 = 2*x - x^6 + (-1) + S
|
1,516 |
(x + 2)^{1/2} = (4 + x + 2*(-1))^{1/2} = 2*(1 + (x + 2*(-1))/4)^{1/2}
|
793 |
(z + 100 \cdot \left(-1\right))^2 + (y + 42 \cdot (-1))^2 = \left(z + 33 \cdot \left(-1\right)\right)^2 + (y + 74 \cdot (-1))^2 = (z + 26) \cdot (z + 26) + (y + 6 \cdot (-1))^2
|
-10,463 |
\left(20 + 4\cdot y\right)/\left(8\cdot y\right) = (y\cdot 2 + 10)/(4\cdot y)\cdot \frac22
|
-29,009 |
\tfrac{1}{2}*(0.01 - -0.01) = 0.01
|
-10,265 |
-\frac{1}{\nu + 2}\times 9\times 15/15 = -\frac{1}{30 + 15\times \nu}\times 135
|
49,539 |
-2*7 + 3*5 = 1
|
9,409 |
\left(x_2 \cdot x_1\right)^6 = (x_2^3)^2 \cdot (x_1^2)^3
|
10,705 |
\alpha\cdot (\gamma + x) = x\cdot \alpha + \alpha\cdot \gamma
|
30,695 |
0 < \left(l + \sqrt{l}\right)^{1/3} - l^{\frac{1}{3}} = \tfrac{l^{\frac13}}{\sqrt{l}} \dfrac{1}{1/(\sqrt{l})}\left((1 + \frac{1}{\sqrt{l}})^{\dfrac{1}{3}} + (-1)\right) \leq \frac{1}{l^{\frac16}*3}
|
-22,805 |
\frac{5 \cdot 12}{4 \cdot 12} = 60/48
|
34,938 |
det\left(p \cdot x - A \cdot Z\right) = det\left(x \cdot p - A \cdot Z\right)
|
14,248 |
n*0.09 = n/10*\frac{9}{10}
|
27,705 |
4 \cdot (n^2 + 6 \cdot n + 25) \leq 4 \cdot (n \cdot n + 6 \cdot n \cdot n + 25 \cdot n^2) = 128 \cdot n^2 \lt 1000 \cdot n^2
|
28,900 |
3^{k + 1} + (-1) = 3\cdot 3^k + (-1) = 2\cdot 3^k + 3^k + (-1)
|
-7,111 |
4/7\cdot \frac58 = \frac{1}{14}\cdot 5
|
7,151 |
(1 + x + ... + x^5)^8 = (\frac{1 - x^6}{1 - x})^8 = \dfrac{(1 - x^6)^8}{\left(1 - x\right)^8}
|
14,787 |
(2 \cdot z + 9) \cdot e^z - 2 \cdot e^z + C = (2 \cdot z + 9 + 2 \cdot \left(-1\right)) \cdot e^z + C = (2 \cdot z + 7) \cdot e^z + C
|
-4,267 |
\dfrac{72}{24}\cdot \dfrac{y^5}{y^4} = \frac{72\cdot y^5}{24\cdot y^4}
|
-6,705 |
10^{-1} + 6/100 = \frac{10}{100} + 6/100
|
-5,449 |
\frac{1}{1000}16.8 = 16.8/1000
|
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