Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
37,488
|x - g| = -(x - g) = g - x
12,304
(t - s) (t - s) = (-s + t) * (-s + t)
5,419
50 (11 + 60)/2 = 1775
30,623
1 + n\cdot z + z = 1 + (n + 1)\cdot z \leq (1 + z)^n
-155
9*8*7 = \frac{9!}{(9 + 3(-1))!}
10,902
((3/4)^f + 1)*4^f = 3^f + 4^f
15,257
1/15 = \frac{1}{3 \times 5} = 19 \times 16 = 16 \times 3 \times 6 + 16 = 6 + 16 = 22
33,911
\frac{145}{3} = -7/3 + \frac13\cdot 152
10,644
\dfrac{1}{c}(c + a + b) + (-1) = (b + a)/c
32,587
675 = 3^3 \cdot 5 \cdot 5
23,778
16/9 = \tfrac{1920}{1080}
-19,305
5/3\cdot 5/4 = \dfrac{5\cdot \dfrac14}{\dfrac15\cdot 3}
8,448
(1/2 + z)^2 = \left(1 + z \cdot 2\right) \cdot \left(1 + z \cdot 2\right)/4
12,219
1/4 = \frac{1}{H_1}*(x_1 - H_1) \Rightarrow H_1*5/4 = x_1
-9,758
-1/5\cdot 9/20 = \left((-1)\cdot 9\right)/(5\cdot 20) = -\tfrac{1}{100}9
22,437
(-1) + n = 2 + n + 3*(-1)
19,510
\frac{\mathrm{d}x}{\mathrm{d}s} = 1 + \left(s - x\right) \cdot \left(s - x\right) = 1 + (x - s)^2
24,346
\overline{y_1} \cdot \overline{y_2} = \overline{y_1 \cdot y_2}
-2,406
\sqrt{6} \sqrt{4} + \sqrt{9} \sqrt{6} = 3\sqrt{6} + \sqrt{6} \cdot 2
19,988
24 - 7\cdot x = -2 \Rightarrow 26/7 = x
-10,486
-\dfrac{1}{q^2\cdot 60}\cdot (48\cdot q + 72) = 12/12\cdot (-\frac{1}{q \cdot q\cdot 5}\cdot (6 + 4\cdot q))
9,152
Cov[W, Y] = \mathbb{E}[WY] - \mathbb{E}[W] \mathbb{E}[Y] = \mathbb{E}[WY]
9,108
xz - z\xi = z*(x - \xi)
22,293
X*x^{1/2} = X*x^{\frac{1}{2}}
31,199
120 = 1 + 2 + 3\cdot \dots + 15
1,723
(2\left(-1\right) + n) (1 + n) = n^2 - n + 2\left(-1\right)
25,893
n - 2*k = 2 \Rightarrow k = (n + 2*(-1))/2
-20,527
\frac{56}{-48} = -7/6 \cdot (-8/(-8))
-16,700
-3 = -3 \cdot \left(-2 \cdot y\right) - 21 = 6 \cdot y - 21 = 6 \cdot y + 21 \cdot (-1)
19,803
g - x = -(-g + x)
-1,797
-\pi \cdot \frac{7}{4} + \frac{1}{4} \cdot \pi = -\pi \cdot 3/2
-4,335
\tfrac{y}{y^3}\cdot 60/50 = \frac{60\cdot y}{50\cdot y \cdot y \cdot y}\cdot 1
24,743
(\xi + 1)\cdot n = \xi\cdot n + n
3,743
\frac{3}{4} \cdot 1 = \frac14 \cdot 3
32,809
\min{\frac{1}{20}\cdot 120,\frac{1}{8}\cdot 80} = \min{6,10} = 6
-22,971
9\times 10/(10\times 5) = 90/50
10,650
x = t^3 \Rightarrow t = x^{\frac{1}{3}}
16,060
(a + b)^3 = a * a * a + 3*a^2*b + 3*a*b^2 + b^3 = a * a^2 + 0*a^2*b + 0*a*b^2 + b^3 = a * a^2 + b^3
-27,485
22 \times x^3 = 11 \times 2 \times x \times x \times x
-4,330
q\cdot 5 = q\cdot 5
11,296
u^2 + v \cdot v\cdot 3 = (u + v)^2 + \left(u + v\right)\cdot (-u + v) + (v - u)^2
28,368
y^2 - 2 y + 1 \geq 0 \implies y^2 + 1 \geq y*2
17,497
1/2 = \frac{1}{100} + \frac{1}{99}*49*99/100
8,224
\frac{1}{6^3}*(1 + 5/6 + 5/6) = \frac{1}{81}
9,158
0 = a^4 \cdot t^2 \cdot 4 - 4 \cdot t^3 \cdot a^2 + 1 \Rightarrow \frac{1}{t \cdot 2} \cdot (t^2 \pm \sqrt{t^4 + (-1)}) = a^2
23,456
\cos(\frac12\cdot \pi - z) = \sin{z}
29,943
\tan{x} = \frac{1}{\cos{x}} \times \sin{x}
22,877
\sin(y + x) = \sin{y} \cdot \cos{x} + \cos{y} \cdot \sin{x}
2,111
\dfrac{144}{2^{15}} = \frac{1}{2048} \cdot 9 \approx 0.0043945
42,268
\frac{1}{2}\cdot \left(214\cdot \left(-1\right) + 360\right) = 73
18,161
(d + g)/x = (g + x + d)/x + (-1)
6,837
\tanh{J} = \frac{1}{e^{2J} + 1}(e^{2J} + (-1)) = 1 - \frac{1}{e^{2J} + 1}2
42,354
32 \times 35 \times 36 = 40320 = 8!
28,472
|\varphi_1| = |\varphi_2| = p \implies |\varphi_2 \varphi_1| = p
22,944
(-1) + x^l = ((-1) + x) \cdot (-e^{\pi \cdot 2/l} + x) \cdot ... \cdot e^{2 \cdot ((-1) + l) \cdot \pi/l}
36,477
47\cdot 257 - 66\cdot 183 = 12079 + 12078 (-1) = 1
26,716
16 z = z + 15 z
-23,703
5/24 = \frac{1}{6}*5/4
27,717
\left(6x + y \cdot 5 = 1 + x \cdot 7 + y \cdot 3\Longrightarrow 0 = x - 2y + 1\right)\Longrightarrow (-1) + y \cdot 2 = x
19,150
\left(k + z\right)\cdot (-k + z) = z^2 - k^2
-21,910
-\frac{1}{12} \cdot 8 + 4/8 = -\tfrac{16}{12 \cdot 2} \cdot 1 + \frac{1}{8 \cdot 3} \cdot 12 = -16/24 + 12/24 = -\dfrac{1}{24} \cdot (16 + 12) = -\frac{4}{24}
17,849
z^{\frac{2}{6}} = z^{\frac13}
31,442
\dfrac14 (9 + 9 + 10 + 11) = 9.75
17,837
(-\tfrac{1}{x^2 + x + 1}(x + 2) + \frac{1}{(-1) + x})/3 = \frac{1}{x^3 + \left(-1\right)}
-30,253
\tfrac{1}{x + 7}(x^2 + 49 (-1)) = \dfrac{1}{x + 7}(x + 7) (x + 7(-1)) = x + 7(-1)
41,004
2*50 + 16*\left(-1\right) = 84
6,572
(x - \beta)^2 = -x \cdot \beta \cdot 2 + x^2 + \beta^2
11,682
y z - z_0 y + z_0 y - z_0 y_0 = -y_0 z_0 + y z
17,079
\overline{cd} = \bar{c} \bar{d} = -c \cdot (-d) = cd
11,401
2/31 = \frac{1}{31} + \frac{30}{30} \cdot 1/31
-5,864
\dfrac{s*2}{s^2 - 11*s + 18}*1 = \frac{s*2}{(s + 2*\left(-1\right))*(s + 9*(-1))}
-7,873
\frac{1}{-3 - i}\cdot (2 - i\cdot 16) = \frac{1}{-3 - i}\cdot (-16\cdot i + 2)\cdot \frac{i - 3}{i - 3}
34,663
\frac15*1 = 1/5 = \tfrac{1}{5}
22,868
\cos{x} = \left(-1\right) + \cos^2{\dfrac{x}{2}}*2
-12,015
4/5 = t/(8*\pi)*8*\pi = t
35,459
A_n/(Y_n) = A_n/(Y_n)
39,283
18 = (6 \cdot (-1) + 12) \cdot 3
24,573
2z^2 = z \cdot z + z^2
20,185
2 U = U + U
39,307
B_0 = 0 \cup B_0
15,718
\dfrac{1}{2!*2!}*5! = \frac{120}{4} = 30
20,363
\|-(-e + f) + g - b\| = \|-(b - e) + g - f\|
18,135
(180 + y^2 + 20 \cdot y) \cdot \left(y^2 - 2 \cdot y + 18 \cdot \left(-1\right)\right) = y^4 + 18 \cdot y^3 + 122 \cdot y^2 - y \cdot 720 + 3240 \cdot (-1)
32,863
\binom{m}{i} = \frac{1}{i!\cdot (m - i)!}\cdot m!
26,858
y \cdot x = \frac12 \cdot (x \cdot y + x \cdot y)
-26,426
\frac{1}{3125\cdot 5^8} = 5^{-5 + 8\cdot (-1)} = \frac{1}{1220703125}
17,305
f^\gamma = d^y = (fd)^{\gamma y}
-20,045
\tfrac77 \cdot \dfrac{3 \cdot (-1) - x \cdot 9}{4 \cdot (-1) - x \cdot 5} = \frac{21 \cdot (-1) - x \cdot 63}{28 \cdot (-1) - 35 \cdot x}
29,831
c + z = y \cdot e^{-z^2} \Rightarrow e^{-z^2} \cdot c + e^{-z^2} \cdot z = y
9,201
z^{r_1 + r_2} = z^{r_2} z^{r_1}
53,537
\tfrac{x}{10 \cdot k + 3} = g \Rightarrow x = 10 \cdot k \cdot g + 3 \cdot g
4,280
\cos(f)*\cos\left(h\right) = \tfrac12*(\cos(h - f) + \cos(f + h))
27,499
\dfrac{1601}{1138} = 1 + \frac{463}{1138}
-23,155
((-3) \times \frac12)/2 = -3/4
-26,419
\dfrac{1}{390625 \cdot 9765625} = 5^{-8 - 10} = 5^{-8 + 10 \cdot \left(-1\right)} = 1/3814697265625
27,688
d/dz y^3 + \frac{\partial}{\partial z} (z^2*y) = -\frac{dy}{dz} + \frac{dz}{dz}
9,942
((-1) + z) (z^2 + z + 1) = (-1) + z^3
-23,000
26/39 = \dfrac{1}{3*13}26
10,166
10^3*4 + 10^2*5 + 10^1*7 + 6*10^0 = 4576
11,181
\frac{d}{dz} (z\cdot |z|) = |z| + \tfrac{z}{|z|}\cdot z = \frac{2\cdot z^2}{|z|}