- Started with
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
43.7
- Using strategy
rm 43.7
- Applied flip-+ to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\color{red}{\left(a + \frac{5.0}{6.0}\right)} - \frac{2.0}{t \cdot 3.0}\right)\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\color{blue}{\frac{{a}^2 - {\left(\frac{5.0}{6.0}\right)}^2}{a - \frac{5.0}{6.0}}} - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
43.7
- Applied frac-sub to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{red}{\left(\frac{{a}^2 - {\left(\frac{5.0}{6.0}\right)}^2}{a - \frac{5.0}{6.0}} - \frac{2.0}{t \cdot 3.0}\right)}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{blue}{\frac{\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]
51.0
- Applied associate-*r/ to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{red}{\left(b - c\right) \cdot \frac{\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\frac{\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]
51.1
- Applied frac-sub to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \color{red}{\left(\frac{z \cdot \sqrt{t + a}}{t} - \frac{\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}}\]
58.8
- Applied simplify to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{red}{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{blue}{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}\]
58.8
- Applied simplify to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}{\color{red}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}{\color{blue}{\left(a - \frac{5.0}{6.0}\right) \cdot \left({t}^2 \cdot 3.0\right)}}}}\]
58.8
- Applied taylor to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}{\left(a - \frac{5.0}{6.0}\right) \cdot \left({t}^2 \cdot 3.0\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\left(0.8333333333333333 \cdot c + 1.0 \cdot \left(c \cdot a\right)\right) - 1.0 \cdot \left(b \cdot a\right)\right)}}\]
1.2
- Taylor expanded around inf to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \color{red}{\left(\left(0.8333333333333333 \cdot c + 1.0 \cdot \left(c \cdot a\right)\right) - 1.0 \cdot \left(b \cdot a\right)\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\left(\left(0.8333333333333333 \cdot c + 1.0 \cdot \left(c \cdot a\right)\right) - 1.0 \cdot \left(b \cdot a\right)\right)}}}\]
1.2
- Applied simplify to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\left(0.8333333333333333 \cdot c + 1.0 \cdot \left(c \cdot a\right)\right) - 1.0 \cdot \left(b \cdot a\right)\right)}} \leadsto \frac{x}{x + e^{\left(2.0 \cdot c\right) \cdot 0.8333333333333333 + \left(2.0 \cdot 1.0\right) \cdot \left(a \cdot \left(c - b\right)\right)} \cdot y}\]
0.0
- Applied final simplification
- Started with
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
4.1
- Using strategy
rm 4.1
- Applied flip-+ to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\color{red}{\left(a + \frac{5.0}{6.0}\right)} - \frac{2.0}{t \cdot 3.0}\right)\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\color{blue}{\frac{{a}^2 - {\left(\frac{5.0}{6.0}\right)}^2}{a - \frac{5.0}{6.0}}} - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
6.1
- Applied frac-sub to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{red}{\left(\frac{{a}^2 - {\left(\frac{5.0}{6.0}\right)}^2}{a - \frac{5.0}{6.0}} - \frac{2.0}{t \cdot 3.0}\right)}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{blue}{\frac{\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]
6.9
- Applied associate-*r/ to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{red}{\left(b - c\right) \cdot \frac{\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\frac{\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]
6.9
- Applied frac-sub to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \color{red}{\left(\frac{z \cdot \sqrt{t + a}}{t} - \frac{\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}}\]
7.3
- Applied simplify to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{red}{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{blue}{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}\]
4.2
- Applied simplify to get
\[\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}{\color{red}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}{\color{blue}{\left(a - \frac{5.0}{6.0}\right) \cdot \left({t}^2 \cdot 3.0\right)}}}}\]
4.2