id,identifier,formula
1,slow,\frac{5x^3}{4}
2,medium,x^3
3,fast,\frac{4x^3}{5}
4,medium-slow,\frac{6x^3}{5} - 15x^2 + 100x - 140
5,slow-then-very-fast,"\begin{cases}
\frac{ x^3 \left( 100 - x \right) }{50},    & \text{if } x \leq 50  \\
\frac{ x^3 \left( 150 - x \right) }{100},   & \text{if } 50 < x \leq 68  \\
\frac{ x^3 \left( 1274 + (x \bmod 3)^2 - 9 (x \bmod 3) - 20 \left\lfloor \frac{x}{3} \right\rfloor \right) }{1000}, & \text{if } 68 < x \leq 98  \\
\frac{ x^3 \left( 160 - x \right) }{100},   & \text{if } x > 98  \\
\end{cases}"
6,fast-then-very-slow,"\begin{cases}
\frac{ x^3 \left( 24 + \left\lfloor \frac{x+1}{3} \right\rfloor \right) }{50},  & \text{if } x \leq 15  \\
\frac{ x^3 \left( 14 + x \right) }{50},     & \text{if } 15 < x \leq 35  \\
\frac{ x^3 \left( 32 + \left\lfloor \frac{x}{2} \right\rfloor \right ) }{50},   & \text{if } x > 35  \\
\end{cases}"