# Simplex Algorithm on the Casio 9860GII

With matrix capable calculator, simplex algorithm for common maximization problem can be solved easily like in the TI-84.

The Casio 9860GII is also equipped with equivalent matrix operations to solve the same problem.

# Overclock Tournament Round 3

In previous rounds, Casio fx-9860GII with overclocking software Ftune2 won both rounds in a Nelder-Mead logistic curve fitting speed test, although TI Nspire CAS CX with Nover closed the gap on the second round after a little optimization on the language by declaring most variables local in scope.

In this installment, the comparison focus on the basic calculation rather than the programming environment. This simple integration equation is to be computed by both overclocked calculators:

Again, Casio with Ftune2 outperform the TI Nspire.

# Nspire fight back in the overclock race

In a previous installment, fx-9860GII beats Nspire CX CAS in an overclocking match, computing the parameters for a logistic regression function by the Nelder-Mead algorithm programmed in their respective on-calculator environment. It is quite astonishing not only to see Nspire losing in the speed race, but also by how much it loses.

To give the CX a second chance, while still maintaining the overall fairness, the program on the Nspire is enhanced by localizing variables (33 of them) and nothing else. The declaration of scope for variables is believed to be a common technique for performance boost. The logic of the program remain unchanged, so is the tolerance parameter.

And the results – Nspire is catching up by doubled performance from 63 seconds to 33 seconds!

# Casio fx-9860GII Equation Solver performance improvement by overclocking

In last installment, the Casio overclocking utility Ftune2 improved the speed performance of a Nelder-Mead program by 4.5 times. For standard calculations, more impressive results are obtained from this nice utility. In this test, the standard normal distribution function is applied in the Casio fx9860GII Equation Solver and the task is to find the Z variable (as “T” in the below screen), given the cumulative probability distribution of 0.9 (as “A” in the below screen).

`A=1÷(√(2π))×∫(e^(-X²÷2),-999,T)`

In other words, the solver’s task is to find Z from the given area of 0.9 as shaded in the below chart, which is obtained for verifying the solver’s result of 1.28155156 using the command
`Graph Y=P(1.28155156)`.

And here is the result on speed performance:

00:38 No overclocking, back-lit OFF
00:40 No overclocking, back-lit ON
00:06 Overclocked 265.42 MHz, USB OFF, back-lit OFF
00:07 Overclocked 265.42 MHz, USB OFF, back-lit ON
00:05 Overclocked 265.42 MHz, USB ON, back-lit OFF
00:05 Overclocked 265.42 MHz, USB ON, back-lit ON

The performance gain by overclocking is 7.6 to 8 times, depending whether the back-lit is on for non-overclocked runs.

For the same equation solving by the TI Nspire using `nsolve()`, it took 01:30 to return a result of 1.28155156555.

However, using the built-in standard functions `NormCD()` for the Casio and `normCdf()` for the TI as below

```Casio fx-9860GII

A=NormCD(-999,T)

TI Nspire

nsolve(normCdf(-∞,x,0,1)=0.9,x)```

both units return results instantaneously (Nspire returns 1.28155193868 while Casio returns 1.281551566).