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ddrg
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math_formulas

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int64
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30,623
1 + k\times x + x = 1 + (k + 1)\times x \leq (1 + x)^k
27,765
8*y = 90 \Rightarrow y = \frac{45}{4} = 11.25
-23,016
110/44 = 22\cdot 5/(2\cdot 22)
16,067
(1^2 + 2^2) \cdot 5^2 = 5 5^2
25,722
10 \cdot (-1) + 2^6 = 54
-6,149
\dfrac{t\times 2}{t^2 + t\times 10 + 9} = \dfrac{t\times 2}{\left(t + 1\right)\times \left(t + 9\right)}
21,587
\frac{1}{2} \cdot π = \sin^{-1}(1)
23,505
\frac{\sin{y\cdot 2}}{\cos{y\cdot 2}} = \tan{2\cdot y}
-18,549
\frac{10}{4} = \tfrac{1}{2}\cdot 5
26,786
\frac{1}{3 + \left(-1\right)}\cdot (12^3 + (-1) + 9\cdot (-1)) = 859
-24,811
490 + \left(-1\right) = 489
-9,885
\frac{18}{25} = 0.72
-26,496
12\times y = 2\times 6\times y
10,869
-H + y = \left(\sqrt{-H + y}\right)^2
-16,888
-6 = -6\cdot (-5\cdot i) - -12 = 30\cdot i + 12 = 30\cdot i + 12
28,166
u_1 + u_2 = ( {u_1}_1, {u_1}_2) + ( {u_2}_1, {u_2}_2) = \left( {u_1}_1 + {u_2}_1, {u_1}_2 + {u_2}_2\right)
35,043
48\times 2 = 96
-10,758
-\frac{1}{40 t^3}40 = 4/4 \left(-\frac{10}{t^3\cdot 10}\right)
-29,721
\frac{\mathrm{d}}{\mathrm{d}x} x^l = l\cdot x^{l + \left(-1\right)}
25,907
\left\lfloor{((-1) + a + b)/b}\right\rfloor = \left\lfloor{\tfrac{1}{b}*(b + (-1)) + \tfrac{a}{b}}\right\rfloor
11,470
2/(2\cdot z) + \frac{z}{z\cdot 2} = \frac{1}{2\cdot z}\cdot (2 + z)
12,003
x = \sin^{-1}(q) = q + \frac{q^3}{2} \cdot 1/3 + \frac{1}{2 \cdot 4} \cdot 3 \cdot \frac{x^5}{5}
15,632
a*((-1) + b) - b = a*b - a - b
27,767
a*\dfrac{1}{x}/c = \frac{x*\frac{a}{x}}{x*c} = \frac{a}{x*c}
11,811
p + 1 = \frac{p * p + (-1)}{(-1) + p}
48,017
\frac{1}{(w-z)^2}=\frac{d}{dw}(\frac{1}{w-z}) = \frac{1}{z^2}+\frac{2w}{z^3}+\frac{3w^2}{z^4}+..
13,838
1 = 2 + E + B \Rightarrow B = -1 - E = -1 - -2 = 1
19,426
\left(x + 3\right)^2 - x\cdot 6 = (3 + x)^2 - 6\cdot x
1,310
\frac{x^2 + (-1)}{x + (-1)} = \frac{1}{x + (-1)} \cdot (x + 1) \cdot (x + (-1)) = x + 1
17,528
{5 \choose 0} + {5 \choose 1} + \ldots + {5 \choose 5} = 2^5
16,064
\frac{k}{x} = \dfrac{k*1^{-1}}{x}
-18,273
\dfrac{1}{\left(y + 5\right)\cdot (y + 9)}\cdot (y + 9)\cdot y = \frac{y^2 + y\cdot 9}{y^2 + y\cdot 14 + 45}
28,534
\frac{t^k}{e^{-\beta t}} = t^k e^{\beta t}
17,001
1/\left(ag\right) = \dfrac{1}{ag}
1,130
\frac{84!}{(3\cdot (-1) + 84)!\cdot 3!} = 95284
-26,139
10\cdot (e^{14} + (-1)) = 10\cdot e^{14} - 10\cdot e^0
-9,093
70.7\% = \dfrac{1}{100}*70.7
14,088
t = \frac{\xi \cdot \frac1t}{z \cdot 1/t} \cdot \xi/t = \tfrac{\xi^2}{z \cdot t}
-16,944
-6 = -6*2*z - 30 = -12*z - 30 = -12*z + 30*(-1)
46,202
1 + 2 \times 2 = 5
20,774
8 + 2 \cdot \left(-1\right) + 4 \cdot (-1) - (-1) = 3 \neq 0
-267
\frac{10!}{\left(4(-1) + 10\right)!} = 10*9*8*7
24,044
T^6 = 0 \Rightarrow T \cdot T^2 = 0
12,617
\dfrac{1}{1 + z} = \dfrac{1}{z*\left(1/z + 1\right)}
2,693
-(g^2 + g\times 2 + 14\times (-1)) - g = -g \times g - g\times 3 + 14
16,595
\sin{B} = \sin(π*2 + B)
30,053
j {n \choose j} = (n - j + 1) {n \choose j + (-1)} = n {n + (-1) \choose j + (-1)}
34,276
\left(-1\right)^2 \cdot \left(-1\right) + 1 + (-1) = -1
2,242
13/8 = 1 + 5/8 = 1 + \dfrac{1}{8*\frac15} = 1 + \frac{1}{1 + 3/5}
-16,772
2 = 2\cdot 5\cdot f + 2\cdot 8 = 10\cdot f + 16 = 10\cdot f + 16
-20,997
\dfrac{1}{q \cdot 8}(-4q + 12 (-1)) = 4/4 \dfrac{1}{2q}(-q + 3\left(-1\right))
-19,548
\frac{1}{5}*4*9/7 = 4*9/(5*7) = 36/35
4,970
(x \cdot 2 + y) \cdot (2 \cdot y + x) = 2 \cdot x^2 + x \cdot y \cdot 5 + 2 \cdot y^2
-2,603
6 \cdot \sqrt{7} = \sqrt{7} \cdot (5 + 4 + 3 \cdot \left(-1\right))
25,655
4^{100} - 3^{100} = 100\cdot g^{99} = \frac1g\cdot 100\cdot g^{100}
-3,654
\frac{64}{72 q^2}q^4 = \dfrac{1}{72}64 \frac{q^4}{q^2}
11,867
\frac{1}{y^2}*((-1)*(y'^2 + 1)^{\frac{1}{2}}) = \frac{\partial}{\partial x} (\frac{1}{(1 + y'^2)^{\frac{1}{2}}*y}*y')
10,168
1/42 + 1/42 + 1/42 + 1/42 + \frac{1}{42} + \frac{1}{42} + 1/42 = 7/42 = \dfrac16 \approx 0.167
48,400
\dfrac{1}{2^6} \cdot 12! = \binom{12}{2} \cdot \binom{8}{2} \cdot \binom{6}{2} \cdot \binom{2}{2} \cdot \binom{4}{2} \cdot \binom{10}{2}
29,821
6!\cdot 4!\cdot 4315\cdot 5! = 8947584000
6,586
1 + 255 + 250\cdot (-1) = 6
10,504
det\left(-W \times T + x\right) = det\left(x - T \times W\right)
10,866
E + Z + F = E + Z + F = E + Z + F
-29,058
x^5\times x^6 = x^{5 + 6} = x^{11}
-13,395
1 + 2*\frac19*18 = 1 + 2*2 = 1 + 2*2 = 1 + 4 = 5
9,295
3^{3^k} \cdot 3^{3^k} = 3^{2 \cdot 3^k} = 9^{3^k} = (9^{3^{k + (-1)}})^2 \cdot 9^{3^{k + (-1)}}
-6,018
\frac{2}{50 + 5\times x} = \dfrac{1}{(x + 10)\times 5}\times 2
12,399
x^4 + 5 \cdot x + 1 = (x \cdot x + 1) \cdot (x^2 + (-1)) + 5 \cdot x + 5 \cdot (-1) = (x + \left(-1\right)) \cdot (x^3 + x^2 + x + 6)
25,472
\frac{\pi^{\frac{1}{2}}}{\left(\frac{1}{2}\right)!} = 2
-430
\left(e^{7 \cdot \pi \cdot i/6}\right)^{11} = e^{\frac{7}{6} \cdot \pi \cdot i \cdot 11}
-21,521
\frac{1}{8} \cdot 4 = \frac{2}{4}
10,171
\cos\left(-\arccos{t}\right) = \cos(\arccos{t}) = t
35,177
\frac{\frac{1}{3}}{2}\cdot 1 + 1/3\cdot 0 + 1/3/2 = \frac13
-452
\frac{64}{3}\times \pi - 20\times \pi = \frac{4}{3}\times \pi
-9,495
-2 \cdot 3 \cdot 5 + q \cdot 3 \cdot 3 \cdot 5 = q \cdot 45 + 30 (-1)
23,127
(-1) + c^2 + c = 0 \implies \frac{1}{2}*(-1 \pm 5^{\frac{1}{2}}) = c
23,377
\frac{1}{15625}\times 25146 = 1.609344
17,504
b^2 + bd = b^2 + bd
46,721
e^x:=\exp(x)
-8,713
\sqrt[3]{1715} = \sqrt[3]{7\times 7\times 7} \times \sqrt[3]{5} = 7 \sqrt[3]{5}
27,172
(\sin(h + f) + \sin(f - h))/2 = \cos{h}*\sin{f}
-20,885
\frac{1}{5} \cdot 4 \cdot \frac{-r \cdot 9 + 7}{-9 \cdot r + 7} = \frac{28 - r \cdot 36}{35 - r \cdot 45}
3,858
1728 = (3^{1/2}\cdot 2)^6
5,697
(1/2)! = \sqrt{\pi/4}
-16,361
10*\sqrt{4}*\sqrt{7} = 10*2*\sqrt{7} = 20*\sqrt{7}
-15,811
-30/10 = 4/10\cdot 6 - 9\cdot 6/10
29
0 = BA + AB \implies -AB = BA
9,331
\frac{\partial}{\partial x} \left(x\cdot w\right) = w\cdot \frac{\text{d}x}{\text{d}x} + x\cdot \frac{\text{d}w}{\text{d}x}
15,344
x - \sqrt{26} \leq 0 \Rightarrow x \leq \sqrt{26}
19,756
0 = 0 \cdot ( 1, 4, 0) + 0 \cdot \left( 2, 2, 2\right)
-29,135
4 \cdot \left(-1\right) + 0 + 3 \cdot (-2) = -10
-26,647
(2\cdot \left(-1\right) + 11\cdot c^2)^2 = 4 + c^4\cdot 121 - 44\cdot c \cdot c
33,534
-\cos{v} = \cos(\pi - v)
45,082
5^2\cdot 37 = 925
3,979
3\left(z*2 + 2yy'\right) (y^2 + z^2)^2 = (2z - y' y*2) (z^2 - y * y)*2
15,253
\frac{1}{x^2 + 1}*(2*x^2 + x*|x| + 2) = \frac{3*x^2 + 2}{x^2 + 1} = 3 - \frac{1}{x^2 + 1}
14,830
\left(2^6 + 8 \times 2^2 + 2 \times 2 \times 2^2 \times 3\right)/12 = 12
24,123
d/dy e^{-2 \times y} = -2 \times e^{-2 \times y}
3,138
e \geq 2*\left(2 - n + e\right) \Rightarrow 2*n + 4*(-1) \geq e
26,129
(-z + d)/B = 1\Longrightarrow d = B + z