id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
9,759 |
2\cdot z\cdot x = x\cdot z + x\cdot z
|
10,839 |
(d + f)*\left(f - d\right) = f^2 - d^2
|
-10,602 |
\frac{1}{4n + 8(-1)}8 = 4/4\cdot \frac{1}{n + 2\left(-1\right)}2
|
7,140 |
5/1 = \frac{\frac{1}{6}}{1/6} \cdot 5
|
24,916 |
-y\cdot 8 + x^2 + y \cdot y - x\cdot 6 = 0 \Rightarrow (x + 3\cdot (-1)) \cdot (x + 3\cdot (-1)) + (4\cdot (-1) + y)^2 = 5^2
|
10,461 |
(p*y)^2 = (p*y)^2
|
-3,649 |
\frac{6}{p\cdot 7} = \frac{1/7}{p}\cdot 6
|
38,336 |
|y| = 0 \implies y = 0
|
7,545 |
r_i = 1 + 2^{m_i} \Rightarrow r_i + (-1) = 2^{m_i}
|
1,992 |
(b + (-1)) * (b + (-1)) + b*4 = (1 + b)^2
|
-27,693 |
-9 \cdot \cos{x} = \frac{\mathrm{d}}{\mathrm{d}x} (-9 \cdot \sin{x})
|
-10,419 |
\frac{20}{20} \times \frac{1}{n + 1} \times (10 \times (-1) + n) = \frac{20 \times n + 200 \times \left(-1\right)}{20 \times n + 20}
|
26,539 |
-x_0^2 b b + z_0^2 d^2 = (-x_0 b - d z_0) (-d z_0 + x_0 b)
|
-2,454 |
\sqrt{10} \cdot \left(5 + 1\right) = 6\sqrt{10}
|
-17,193 |
\cos^2{\theta} = 1 - \sin^2{\theta}
|
805 |
( \phi \times x, w) = \overline{\left( \phi \times w, x\right)} = ( x, \phi \times w)
|
3,171 |
f_2*c/\left(f_1\right) \coloneqq f_2*\dfrac{c}{f_1}
|
5,759 |
yw^T w = ww^T y
|
14,944 |
\frac100 = \frac10(0 + 0\left(-1\right)) = \frac{1}{0}0 - 0/0
|
16,339 |
r\cdot (-r + m) + r\cdot (n - r) + r^2 = r\cdot (m + n - r)
|
9,475 |
\frac{x}{a - g} = \frac{1}{-\frac{g}{x} + \frac1x\cdot a}
|
37,863 |
2\cdot \int \tfrac{\sqrt{(u + \left(-1\right))^2}}{\sqrt{(u + (-1))^2}\cdot \sqrt{u}}\,\mathrm{d}u = 2\cdot \int 1/(\sqrt{u})\,\mathrm{d}u = 2\cdot \int u^{-0.5}\,\mathrm{d}u
|
-3,661 |
\frac{1}{60} \cdot 108 \cdot \frac{m^3}{m^5} = \frac{108 \cdot m^3}{m^5 \cdot 60}
|
84 |
g\cdot 2 + (-1) = g - 1 - g
|
-4,357 |
10 \cdot p^2/7 = p^2 \cdot 10/7
|
22,863 |
y^{1/2} + x^{\frac{1}{2}} = z \Rightarrow x + y = z \cdot z
|
-10,386 |
(g \cdot 4 + 5 \cdot \left(-1\right))/g \cdot \frac44 = \frac{1}{g \cdot 4} \cdot (g \cdot 16 + 20 \cdot \left(-1\right))
|
-12,186 |
5/8 = s/(8 \pi)*8 \pi = s
|
10,285 |
X^3*A^2 = X^2 * X*A^2
|
-559 |
(e^{π \cdot i \cdot 7/12})^{17} = e^{17 \cdot \frac{7}{12} \cdot π \cdot i}
|
2,720 |
\frac{1}{2} + \dfrac{1}{4} = 3/4
|
7,018 |
d \approx b\Longrightarrow d \approx b
|
-19,047 |
\dfrac15 = \frac{D_s}{100 \pi}*100 \pi = D_s
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8,082 |
(x + z) * (x + z) - (x - z)^2 = 4*x*z
|
739 |
\frac{-2 + 3*(-1)}{5 - -10} = -\frac{5}{15} = -1/3
|
-11,122 |
(x + 2 \left(-1\right))^2 + b = (x + 2 (-1)) (x + 2 (-1)) + b = x^2 - 4 x + 4 + b
|
-11,591 |
-i*4 + 0 + 20*(-1) = -20 - i*4
|
-15,892 |
-7/10\cdot 10 + 5\cdot \tfrac{1}{10}\cdot 3 = -\frac{55}{10}
|
10,410 |
\left(x,r_2\right) = x\cdot r_2 - r_2\cdot x = 2\cdot x\cdot r_2
|
12,171 |
4^m + m^4 = (2^m)^2 + (m^2)^2 = (2^m + m^2)^2 - 2*2^m m^2
|
21,030 |
7 = 3(-1) + 13 + 2\left(-1\right) + (-1)
|
-18,944 |
\dfrac79 = \frac{1}{4 \cdot \pi} \cdot A_s \cdot 4 \cdot \pi = A_s
|
10,577 |
\frac{\mathrm{d}}{\mathrm{d}z} \left(2 + z + z^2 + z^3\right) = 3 \cdot z^2 + 1 + 2 \cdot z
|
33,028 |
-\cos(-\pi + z) = \cos(z)
|
19,687 |
\dfrac26 \cdot \pi = \pi/3
|
6,398 |
8 = {4 \choose 1}*{2 \choose 1}*{2 \choose 0}
|
18,876 |
y = 2 \cdot \left(-1\right) + z \Rightarrow z - y + 2 \cdot (-1) = 0
|
24,478 |
\frac{\mathrm{d}}{\mathrm{d}u} \arctan(u) = \dfrac{1}{\sec^2(\arctan\left(u\right))} = \dfrac{1}{1 + u^2}
|
4,721 |
E[X\cdot A] = E[X]\cdot E[A]
|
6,490 |
(p^2 + q^2)*\left(r^2 + s^2\right) = (p*r + q*s)^2 + (q*r - p*s) * (q*r - p*s) = (p*r - q*s)^2 + (p*s + q*r)^2
|
-13,641 |
4 + \frac{1}{4} \cdot 8 = 4 + 2 = 4 + 2 = 6
|
-2,436 |
6^{1 / 2} + (4\cdot 6)^{1 / 2} + \left(16\cdot 6\right)^{\frac{1}{2}} = 6^{\frac{1}{2}} + 24^{\frac{1}{2}} + 96^{\frac{1}{2}}
|
32,323 |
det\left(x_1 x_2 x_3\right) = -det\left(x_3 x_2 x_1\right) = det\left(x_2 x_3 x_1\right)
|
11,111 |
15 = (0^2 + 2^2 + 1^2)\cdot (1^2 + 1^2 + 1^2)
|
25,467 |
\dfrac{1}{2}*(-\cos{2*\theta} + 1) = \sin^2{\theta}
|
1,059 |
\dfrac1t = \dfrac{1 - 1/t}{(-1) + t}
|
-26,147 |
-2*\cos\left(4*\pi\right) - -2*\cos(3*\pi) = -2 + 2*(-1) = -4
|
-9,606 |
\frac{16}{25} = 0.64
|
13,723 |
(Z^{1/2} - B^{1/2})^2 = Z + B - 2 \cdot (Z \cdot B)^{1/2} = 36 - (Z \cdot B)^{1/2}
|
3,493 |
\sin(A)\cdot \cos\left(D\right) = (\sin\left(A + D\right) + \sin\left(A - D\right))/2
|
11,958 |
13/11 = 1 + 2/11 = 1 + \frac{1}{11 \cdot 1/2} = 1 + \frac{1}{5 + 1/2}
|
28,440 |
\dfrac{(-1) + 2 \cdot m}{4 \cdot m^2} = \dfrac{1}{4 \cdot m^2} \cdot (m + \left(-1\right)) + \dfrac{1}{4 \cdot m \cdot m} + \frac{m + (-1)}{m^2 \cdot 4}
|
-18,591 |
5\times a + 9\times \left(-1\right) = 10\times (5\times a + 5\times (-1)) = 50\times a + 50\times \left(-1\right)
|
13,154 |
\sqrt{y \pm 2\cdot \sqrt{y + (-1)}} = \sqrt{\sqrt{y + \left(-1\right)} \pm 1 \cdot \sqrt{y + \left(-1\right)} \pm 1} = |\sqrt{y + \left(-1\right)} \pm 1|
|
18,627 |
M^2 = M^{1/2}*M*M^{1/2}
|
12,497 |
\psi\cdot a\cdot d = a\cdot d\cdot \psi
|
2,059 |
(l + 2)\cdot (l + 1)! = (l + 2)!
|
1,841 |
\left|{U - i\cdot Y}\right| = \left|{\overline{U + i\cdot Y}}\right| = \overline{\left|{U + i\cdot Y}\right|}
|
16,900 |
-3p^2/4 = \frac{1}{1}((- 3 / 4) p^2)
|
26,653 |
(a + x) \times \left(a - x\right) = -x^2 + a^2
|
32,955 |
495 = \frac{1}{4!*8!}12!
|
-10,755 |
\tfrac{1}{r\cdot 2 + 4}\cdot (r\cdot 3 + 2\cdot (-1))\cdot \frac22 = \frac{1}{8 + r\cdot 4}\cdot (6\cdot r + 4\cdot (-1))
|
43,443 |
1997^{2^m} = 1997^{2^m} \neq (1997 \cdot 1997)^m
|
7,869 |
\cos(h)\cdot \sin\left(z\right) + \cos(z)\cdot \sin(h) = \sin(z + h)
|
-1,330 |
56/12 = 56*1/4/\left(12*\dfrac{1}{4}\right) = \frac{14}{3}
|
16,798 |
A' \times C' \times x + A = (A' \times x + A) \times (A + C')
|
-16,591 |
112^{\tfrac{1}{2}} \cdot 2 = 2 \cdot (16 \cdot 7)^{1 / 2}
|
-5,467 |
\frac{1}{14\cdot (-1) + n\cdot 2} = \frac{1}{(7\cdot \left(-1\right) + n)\cdot 2}
|
-11,936 |
8.712/100 = 8.712\cdot 0.01
|
-4,394 |
\frac{\frac{1}{4}}{y}\cdot 11 = \frac{11}{4\cdot y}
|
30,723 |
\left(2 - z = 1.75 - 0.5 \cdot z \Rightarrow 0.25 = z \cdot 0.5\right) \Rightarrow 0.5 = z
|
2,856 |
\dfrac{A^X}{D} = A^X/D
|
983 |
Z_2 - Z_1 = C \implies Z_1 + C = Z_2
|
-5,708 |
\frac{1}{(p + 2\cdot \left(-1\right))\cdot 4} = \dfrac{1}{4\cdot p + 8\cdot (-1)}
|
-25,023 |
-4 \cdot x + x^3 \cdot 64/3 - \dfrac{1}{5} \cdot 1024 \cdot x^5 + x^7 \cdot 16384/7 - \ldots = \operatorname{atan}(-x \cdot 4)
|
-2,018 |
-\frac{\pi}{4} = -\frac14 \pi + 0
|
36,360 |
f^{1 + x} = f^x f
|
3,637 |
\left((n + 1)^2 - n^2\right)/n = \frac1n\cdot \left(n^2 + 2\cdot n + 1 - n^2\right) = (2\cdot n + 1)/n
|
-1,701 |
-2\pi + \pi\cdot 17/6 = 5/6 \pi
|
-20,680 |
\frac{21 \cdot (-1) - 9 \cdot l}{-24 \cdot l + 6 \cdot (-1)} = 3/3 \cdot \dfrac{1}{-8 \cdot l + 2 \cdot (-1)} \cdot \left(-3 \cdot l + 7 \cdot (-1)\right)
|
16,478 |
1 = \cos(0) = \cos(Q - Q) = \cos(Q) \cdot \cos(-Q) - \sin(Q) \cdot \sin\left(-Q\right)
|
2,248 |
M\cdot x_\eta = x_d \implies x_d/M = x_\eta
|
4,498 |
1/\cos(z) + \sin(z) = \frac{1}{\cos\left(z\right)} (1 + \sin(z) \cos(z))
|
-10,731 |
3/3\cdot \dfrac{1}{4\cdot \left(-1\right) + n\cdot 12}\cdot 5 = \frac{15}{n\cdot 36 + 12\cdot (-1)}
|
28,683 |
8400 = \frac{7!}{3!*1!*3!} \frac{6!}{1!*3!*2!}
|
-7,410 |
\dfrac{2}{15} = 6/10 \cdot 2/9
|
-12,013 |
\frac{1}{3} = \frac{1}{6 \cdot \pi} \cdot r \cdot 6 \cdot \pi = r
|
30,491 |
84*90 = (87 + 3(-1)) (87 + 3) = 87^2 - 3^2 = 7569 + 9(-1) = 7560
|
8,189 |
z_1 \cdot z_1^2 + z_1 - z_2^2 = 1 \implies \left(-1\right) + z_1^3 + z_1 = z_2 \cdot z_2
|
26,650 |
\frac1hd = d/h
|
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