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ddrg
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math_formulas

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int64
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23,214
3\cdot 1300/(27405) = \tfrac{3900}{27405}
16,990
k = \left\{\cdots, 2, k, 1\right\}
-29,006
1.5 = \dfrac{1}{2} \cdot ((-1) \cdot 4.4 + 7.4)
45,124
13 \times 0.75 = 9.75
-4,928
5.3/10 = 5.3/10 \cdot 10^2 = 5.3 \cdot 10^1
-4,840
\frac{1}{10} \cdot 7.2 = \frac{7.2}{10}
-3,925
\tfrac{1}{4 \times t^4} \times 8 \times t^3 = 8/4 \times \dfrac{t^3}{t^4}
3,036
0 + z^3 + z \cdot z + z\cdot 0 = (z + 0) \cdot (z + 0)\cdot (z + 1)
5,290
\pi + \frac{1}{6}\pi = 7\pi/6
18,003
\dfrac12 \cdot \left(\left(b + a\right)^2 - a^2 - b^2\right) = a \cdot b
28,909
\frac{1}{w^2} + w \cdot w = (w - 1/w)^2 + 2
29,461
X^6 = (X^2 + 2 \times X) \times (X^2 + 2 \times X) = X^4 + 4 \times X^3 + 4 \times X^2 = X^3 + 2 \times X^2 + 4 \times X^2 + 8 \times X + 4 \times X^2 = 11 \times X^2 + 10 \times X
15,641
\cos(-\theta_x + \theta_i) + \cos(\theta_x - \theta_i) = \cos(-\theta_x + \theta_i)\cdot 2
-24,370
\frac{1}{6 + 8}70 = 70/14 = \frac{70}{14} = 5
-5,390
39.6\times 10^1 = 10^{-4 + 5}\times 39.6
18,981
-a^2 + (1 + a) * (1 + a) = a*2 + 1
34,472
\frac{|z|}{z^2} = \frac{1}{|z|^2} \times |z| = 1/|z|
14,894
x + (x + 1) \cdot x = 2 \cdot x + x \cdot x
46,094
5\cdot 10 + 10^{1 + \left(-1\right)} + 3 = 5\cdot 10 + 10^0 + 3 = 50 + 1 + 3 = 54
3,069
7 = \dfrac{s^3 + \left(-1\right)}{s + (-1)} = s^2 + s + 1
24,906
s_1^{s_2^x} = s_1^{s_2^x}
6,190
\frac16\cdot \left(x + 1 + 1\right)\cdot (1 + 2\cdot \left(1 + x\right))\cdot (x + 1) = 1 \cdot 1 + 2^2 + 3^2 + \dots + x^2 + (x + 1)^2
53,162
\cos(n\cdot z) = \sum_{k=0}^{n/2} \binom{n}{2\cdot k}\cdot (-1)^k\cdot \sin^{2\cdot k}(z)\cdot \cos^{n - 2\cdot k}\left(z\right) = \sum_{k=0}^\frac{n}{2} \binom{n}{2\cdot k}\cdot (-1)^k\cdot (1 - \cos^2(z))^k\cdot z\cdot \cos^{n - 2\cdot k}(z)
-9,432
-4 \cdot y - y^2 \cdot 16 = -y \cdot y \cdot 2 \cdot 2 \cdot 2 \cdot 2 - y \cdot 2 \cdot 2
-1,228
-\dfrac{1}{4}3 \left(-\frac173\right) = \frac{(-3) (-3)}{4*7} = 9/28
12,482
\tan(x_0) = 1\Longrightarrow x_0 = \pi/4
3,526
0 = -(9 + z)^2*3 + 12 \Rightarrow 4 = \left(9 + z\right)^2
29,716
\frac{1}{\left(n + 1\right)\cdot (n + (-1))} = \frac12\cdot \left(\frac{1}{n + (-1)} - \frac{1}{n + 1}\right)
6,175
0 = b^4 - 2b^3 - 2b + 1 = (b^2 - (1 + 3^{1/2}) b + 1) \left(b^2 - (1 - 3^{1/2}) b + 1\right)
25,027
-3^{\frac{1}{2}}*9 = -27^{\frac{1}{2}}*3
19,668
\frac{1}{5^{\dfrac{1}{3}}}\cdot \int 1\,dx = \int \dfrac{1}{5^{1/3}}\,dx
24,632
\cos(2*B) = 2*\cos^2(B) + (-1)
15,032
3 + \frac12\cdot (x\cdot z\cdot x + y\cdot x\cdot y + z\cdot y\cdot z) = 3 + (x\cdot y^2 + y\cdot z^2 + z\cdot x^2)/2
232
2 + 5\cdot j = m\Longrightarrow m = 5\cdot (j + 2\cdot (-1)) + 4\cdot 3
26,380
\dfrac{1}{5^2} \times (-5 \times 5 + 12^2) = \tfrac{13^2}{5 \times 5} + 2 \times (-1)
3,526
12 - (y + 9)^2\cdot 3 = 0 \Rightarrow 4 = (9 + y)^2
-15,818
74/10 = 9*9/10 - \frac{1}{10}*7
-11,999
4/15 = \frac{1}{6\times \pi}\times s\times 6\times \pi = s
24,964
45 + 15\cdot (-1) = 30
8,876
e^{((-1)\cdot z)/2}/2 = \frac{\mathrm{d}}{\mathrm{d}z} (-e^{\left(\left(-1\right)\cdot z\right)/2} + 1)
-29,424
3\cdot 12/5 = \frac{36}{5}
-16,032
5\cdot 4\cdot 3 = \frac{1}{(5 + 3\cdot (-1))!}\cdot 5! = 60
-16,825
-7 = -4 \cdot p^2 + 6 \cdot p - 7 \cdot 2 \cdot p - -21 = -4 \cdot p \cdot p + 6 \cdot p - 14 \cdot p + 21
3,213
(f^2 h^2)^2 = \left(\left(h f\right) \left(h f\right)\right)^2 = f^4 h^4
24,724
\int (h_1 \cdot z^2 + h_2 \cdot z + f)\,\mathrm{d}z = z \cdot f + z^3 \cdot \frac13 \cdot h_1 + z^2 \cdot h_2/2
-20,422
\tfrac{1}{35 x + 14}\left(14 \left(-1\right) + 70 x\right) = \frac177 \frac{x\cdot 10 + 2(-1)}{2 + x\cdot 5}
34,603
1 = \tan{x} \implies x = π/4
-602
\left(e^{\frac{1}{12}i \cdot 17 \pi}\right)^{20} = e^{\frac{17}{12}\pi i \cdot 20}
23,627
(x - j + 1)*(x - j + 2)/2 = (-(j + \left(-1\right)) + x + 1)*\left(-(j + (-1)) + x\right)/2
11,307
2(1 + z^2) \cdot (1 + z^2) \left(8z^2 + z \cdot 15 + 2\right) \left(z \cdot 2 + 5\right) = 2(5 + z \cdot 2) (z \cdot z \cdot 6 + z \cdot 15 + z^2 \cdot 2 + 2) (1 + z^2)^2
3,177
\tfrac{2}{l \cdot 2 + 1} = \frac{k + 1}{1 + 2 \cdot x} \Rightarrow 1 + k = \frac{1}{l \cdot 2 + 1} \cdot (4 \cdot x + 2)
16,657
\left(y - 35.7 = 4.1 \cdot \left(-1.34\right)\Longrightarrow 35.7 + 4.1 \cdot (-1.34) = y\right)\Longrightarrow y = 30.206
24,125
1 = \frac{0.5^z}{0.7*0.3^{\left(-1\right) + z}} \Rightarrow z \approx 1.7
-2,309
1/17 = \dfrac{1}{17}*7 - 6/17
4,023
b^l = b^{l + 0} = b^l b^0
1,002
1 + u^4 = -u^2 \cdot 2 + u^4 + 2 \cdot u \cdot u + 1
-22,296
24 + z^2 - 11 z = (8(-1) + z) (3(-1) + z)
28,127
a = e\cdot a = a\cdot e = \dfrac{a}{e} + e/a
9,980
\frac{y}{y^2 + 1 - 3\cdot y} = \dfrac{y}{(1 - y)\cdot (-2\cdot y + 1) - y^2}
21,220
a - -c + f = a - f + c
26,168
x*2 \gt 3 - x \implies x > 1
6,069
1 = C + E \Rightarrow -E + 1 = C
-29,973
n \times x^{\left(-1\right) + n} = d/dx x^n
170
-\frac{1}{(m + 1)^2} + \frac{(1 + m) \cdot (1 + m)}{(1 + m) \cdot (1 + m)} = -\frac{1}{(m + 1) \cdot (m + 1)} + 1
-4,478
5*(-1) + y * y - y*4 = (y + 5*\left(-1\right))*\left(1 + y\right)
-2,228
-\dfrac{1}{12} + \frac{8}{12} = \tfrac{7}{12}
26,539
\left(-a\cdot y_0 - x_0\cdot b\right)\cdot (x_0\cdot b - a\cdot y_0) = -x_0^2\cdot b^2 + a^2\cdot y_0 \cdot y_0
3,870
g\cdot a/\left(h\cdot x\right) = \dfrac{g\cdot a}{x\cdot h}
34,431
y = z^{\tfrac1l}\Longrightarrow 0 = y^l - z
24,616
48 = k\cdot 16^2 \Rightarrow \frac{1}{16}\cdot 3 = k
37,694
\cos{\frac25\cdot \pi} = -\frac{1}{4}\cdot (-\sqrt{5} + 1)
5,466
(1 - z) \cdot (1 + z + z^2 + \dotsm + z^k) = -z^{1 + k} + 1
2,999
2*(0*(-1) + z) = y + \left(-1\right) rightarrow y = 2*z + 1
11,577
\left(1 + x\right)*(1 + \delta) + (-1) = \delta + x + \delta*x
18,219
G^n \cdot G = G^{n + 1} = G \cdot G^n
25,663
-b/r = \frac{1}{r}\cdot ((-1)\cdot b)
25,714
0 - 2 \times x^3 + 9 \times x^2 - 12 \times x + 5 = 5 - 2 \times x^3 + 9 \times x^2 - 12 \times x
-4,754
\frac{4}{5\cdot (-1) + x} - \frac{2}{x + 3} = \frac{1}{15\cdot (-1) + x^2 - 2\cdot x}\cdot (2\cdot x + 22)
15,866
\theta \cdot \tau_e = \theta \cdot \tau_e
4,303
\dfrac{1}{2} - 1/3 = 1/(3*2)
3,491
(y + 3)^{1 / 2}\cdot (y + 5\cdot (-1))^{1 / 2} = \left(\left(y + 3\right)\cdot (y + 5\cdot (-1))\right)^{1 / 2} = \left(y^2 - 2\cdot y + 15\cdot (-1)\right)^{\frac{1}{2}} = ((y + (-1))^2 - 4^2)^{\frac{1}{2}}
25,240
b\cdot h\cdot g\cdot e = e\cdot g\cdot h\cdot b
45,242
10 = 2 \cdot 2^2 + 2
25,199
2^{20} + (-1) = (2^{10} + (-1)) \cdot (2^{10} + 1) = (2^5 + (-1)) \cdot (2^5 + 1) \cdot \left(2^{10} + 1\right)
27,159
\left(1 = \frac1y + y \Leftrightarrow 0 = y^2 - y + 1\right) \Rightarrow y^3 + 1 = (y + 1) \cdot (y \cdot y - y + 1) = 0
-17,520
59 (-1) + 92 = 33
-5,313
\tfrac{4.2}{10} = 4.2\times 10^{-1}/1000 = 4.2/10000
5,346
\cos(\tan^{-1}\left(x\right)) = \frac{1}{(x^2 + 1)^{\frac{1}{2}}}
-12,252
\dfrac{17}{18} = \frac{s}{18*\pi}*18*\pi = s
18,650
(-h + b) (b^{\left(-1\right) + k} + hb^{2(-1) + k} + \cdots + h^{k + 2\left(-1\right)} b + h^{k + (-1)}) = -h^k + b^k
13,299
(f - b)\cdot \left(b^2 + f \cdot f + b\cdot f\right) = f^3 - b^3
1,494
(k + 3)! = k! (k + 1) (k + 2) (k + 3) \approx k! k^3
13,058
104 = 2 \cdot x + 8 \Rightarrow x = \frac12 \cdot (104 + 8 \cdot (-1)) = 48
10,189
4^{m + (-1)} = (2*2)^{m + (-1)} = (2 * 2)^{m + (-1)} = 2^{2*(m + \left(-1\right))} = 2^{2*m + 2*(-1)}
-9,185
16 + x\cdot 72 = 2\cdot 2\cdot 2\cdot 2 + 2\cdot 2\cdot 2\cdot 3\cdot 3\cdot x
24,678
-(-\cosh(x) + \sinh\left(x\right)) \cdot (\sinh(x) + \cosh(x)) = 1 \implies (\sinh(x) + \cosh(x)) \cdot 5 = 1
17,540
b + f = b \cdot f \Rightarrow (\left(-1\right) + b) \cdot \left(\left(-1\right) + f\right) = 1
33,161
e^{i \cdot s} - e^{-i \cdot s} = \cos{s} + i \cdot \sin{s} - \cos{s} - i \cdot \sin{s} = 2 \cdot i \cdot \sin{s}
-20,921
\frac{1}{(-60) \cdot p} \cdot \left((-1) \cdot 42 \cdot p\right) = \frac{1}{10} \cdot 7 \cdot \dfrac{(-6) \cdot p}{p \cdot \left(-6\right)}
7,920
\frac{x}{ds} = 1 rightarrow x = ds