Comparison of Formula Evaluators: TI-60X, TI-68, Sharp EL-5150, fx-4200P, fx-5000f

Comparison of Formula Evaluators

Happy New Year! Let’s start the new year by comparing formula evaluator calculators. The calculators featured are:

TI-60X (early 1990s)

TI-68 (late 1980s/1990s)

Sharp EL-5150 (late 1970s/early 1980s)

fx-4200P (late 1980s/early 1990s)

fx-5000f (late 1980s/early 1990s)

Formula evaluator: A calculator which strictly evaluates simple formulas. There are no loops, no solvers, no sums. The formula evaluates to one answer but can have more than one inputs.

Example:

Allowed: f(x) = x² + 3 – 1 / x

Allowed: f(a,b) = (a * b) / (a + b)

Not Allowed: f(x) = Σ(x² / 3, x = 0, 10)

Not Allowed: f(x) = [1 if x ≥ 0, else 0]

	TI-60X	TI-68	Sharp EL-5150	fx-4200P	fx-5000F
Battery	1 x CR2032	1 X CR2032	3 x SR44/LR44	1 x CR2032	2 x CR2032
Memory (bytes)	12 registers (84 bytes)	55 registers (440 bytes)	80 steps	279 steps	675 steps
Variables: Number and Type	12, Single letter: A through I, X, Y, Z	Up to three character variables (3 character variables take up 2 registers)	11: A – J, M	26 single letters for formulas only: A – Z; 6 separate numerical constants (K1-K6)	Letters and Greek characters for formulas only; separate numerical constants (K0-K9)
Does store values to variables take space?	Yes, each variable takes up a register	Yes, 1 register for 1 or 2 character variables, 2 for 3 character variables	No	No	No
How Formulas are accessed	[ 2nd ] [ EE ] (FMLA)	[ 2nd ] [ EE ] (FMLA)	AER Mode; up to 5 lines	[ IN ]/[ OUT ]	[ MODE ] 2: WRT Prog 0-9,A,B: 12 slots
Integration? ∫ f(x) dx	Yes	Yes	No	No	No
Base conversions?	Yes, with Boolean logic	Yes, with Boolean logic	No	Yes, 32 bit binary block	No
Complex numbers?	No	Yes, with trig and log complex calculations	No	No	No
Engineering symbols?	No	No	Display toggle switch	Display toggle switch	Display toggle switch
Conversions?	Yes. 4 pairs (in/cm, gal/L, lb/kg, °F/°C)	Yes. 4 pairs (in/cm, gal/L, lb/kg, °F/°C)	No	No	No
Scientific Constants?	No	No	No	No	Yes ([ALPHA] [ ln ] (CONST)), 13
Other		Special 13 digit precision mode	Landscape form		128 built in formulas

The four pairs of conversions included in the TI-60X and TI-68 are:

in/cm: inches/centimeters

gal/L: gallons/liters

lb/kg: pounds/kilograms

°F/°C: degrees Fahrenheit/degrees Celsius

The scientific constants included on the fx-5000F are:

c: Speed of Light

h: Planck’s Constant

G: Universal Gravitational Constant

e: Elementary Charge

me: Electron Mass

u: Atomic Mass Unit

k: Boltzmann Constant

Vm: Molar Volume of Ideal Gas at Standard, Temperature, and Pressure

g: Earth’s Gravity Constant

R: Molar Gas Constant

ε0: Permittivity of Vacuum

µ0: Permeability of Vacuum

All the constants are in SI units.

Out of the calculators listed, my favorites are the TI-68 and fx-5000F.

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.

AOS Calculators: Duplicating a Value Without Retyping It

AOS Calculators: Duplicating a Value Without Retyping It

Note: The following applies to scientific classic calculators who operate under the algebraic operating system (AOS) (that is what Texas Instrument’s calls it). I tested this procedure with the following calculators: TI-30X ECO, HP 10bII+ (Algebraic mode), and Casio fx-260 Solar.

Introduction: Going Back to 1976

Imagine it is 1976 and you have have an SR-56 from Texas Instruments. Here is what an SR-56 looks like: http://www.datamath.org/Sci/WEDGE/ZOOM_SR-56.htm

You are tasked to calculate 1.401103287^1.401103287 and do not want to write the number twice. According to page 53 of the SR-56 manual, one approach is to key in:

1.401103287 [ y^x ] [ CE ] [ = ]

Result: 1.604057054

For that particular calculator, SR-56, pressing [ CE ] once stores the number in the display as the second operand allowing the value to duplicated without having to retype the number.

If we tried that on a modern TI-30Xa/TI-30 ECO RS, the display would clear to zero instead of showed the previous number.

However, there are a few tricks we can employ to achieve the similar result.

Trick 1: Pressing the Reciprocal Key Twice

As long as the number in the display is nonzero, pressing [ 1/x ] [ 1/x ] registers the number in the display for as a second operand. In calculators operating in AOS, executing one-argument functions only operate and effect the number in the display only.

Pressing [ 1/x ] takes the reciprocal of the number and registers the number in the display. Pressing [ 1/x ] again returns the number.

**The keystrokes omits any [ 2^nd ] or [ SHIFT ] keys.

Example 1:

Expression: x * log x

Keystrokes: x [ × ] [ 1/x ] [ 1/x ] [ LOG ] [ = ]

5.8 * log 5.8

Keystrokes: 5.8 [ × ] [ 1/x ] [ 1/x ] [ LOG ] [ = ]

Result: 4.427882363

Example 2:

Expression: x^x

Keystrokes: x [ y^x ] [ 1/x ] [ 1/x ] [ = ]

3.088 ^ 3.088

Keystrokes: 3.088 [ y^x ] [ 1/x ] [ 1/x ] [ = ]

Result: 32.51797379

Example 3:

Expression: x * sin x

Keystrokes: x [ × ] [ 1/x ] [ 1/x ] [ SIN ] [ = ]

50° * sin 50°

Keystrokes: ([DRG] to DEG/[ MODE ] (DEG))

50 [ × ] [ 1/x ] [ 1/x ] [ SIN ] [ = ]

Result: 38.30222216

4^4 + 1 / (3^3)

Keystrokes:

4 [ y^x ] [ 1/x ] [ 1/x ] [ + ]

[ ( ] 3 [ y^x ] [ 1/x ] [ 1/x ] [ ) ] [ 1/x ] [ = ]

Result: 256.037037

If the calculator has a cube function (x^3), we can execute this keystroke:

4 [ y^x ] [ 1/x ] [ 1/x ] [ + ]

[ ( ] 3 [ x^3 ] [ ) ] [ 1/x ] [ = ]

Trick 2: Inverse Function Trick

This trick extends the reciprocal trick to include a function that acts on two (and theoretically more) “reversible” functions. This trick applies to the expressions with the following format:

f(x) OP g(x)

f(x)	f^-1(x)	f(x)	f^-1(x)	f(x)	f^-1(x)
SIN	SIN^-1	e^x	LN	X^3	∛
COS	COS^-1	LN	e^x	∛	X^3
TAN	TAN^-1	10^x	LOG	Hyperbolic	Inverse Hyperbolic
SIN^-1	SIN	LOG	10^x	Inverse Hyperbolic	Hyperbolic
COS^-1	COS	X^2	√
TAN^-1	TAN	√	X^2

OP covers the arithmetic operations: [ + ], [ - ], [ × ], [ ÷ ], [ y^x ], and [ y^(1/x) ]

The general keystroke sequence is: x [ f(x) ] [ OP ] [ f^-1(x) ] [ g(x) ] [ = ]

Let’s illustrate this with a few examples. Assume the calculator is in degrees mode.

Example 1:

sin 40° * cos 40°

f(x) = sin x, f^-1(x) = sin^-1 x, g(x) = cos x

Keystrokes: 40 [ SIN ] [ × ] [ SIN^-1 ] [ COS ] [ = ]

Result: 0.492403877

Example 2:

tan 32° * sin 32°

f(x) = tan x, f^-1(x) = tan^-1 x, g(x) = sin x

Keystrokes: 32 [ TAN ] [ × ] [ TAN^-1 ] [ SIN ] [ = ]

Result: 0.331130307

Example 3:

log 881 * ln 881

f(x) = log x, f^-1(x) = 10^x, g(x) = ln x

Keystrokes: 881 [ LOG ] [ × ] [ 10^x ] [ LN ] [ = ]

Result: 19.97005314

Example 4:

e^3.5 / √3.5

f(x) = e^x, f^-1(x) = ln x, g(x) = √x

Keystrokes: 3.5 [ e^x ] [ ÷ ] [ LN ] [ √ ] [ = ]

Result: 17.70095363

Example 5:

√4.555 + e^4.555

f(x) = √x, f^-1(x) = x^2, g(x) = e^x

Keystrokes: 4.555 [ √ ] [ + ] [ x^2 ] [ e^x ] [ = ]

Result: 97.24099983

The inverse function “recovers and registers” the original x. It’s kind of simulating the LAST x feature on RPN calculators.

Sources

Datamath. “Texas Instruments SR-56“ December 5, 2001. http://www.datamath.org/Sci/WEDGE/SR-56.htm

Texas Instruments. Programmable Slid-Rule Calculator SR-56: Owner’s Manual. Dallas, TX. 1976

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

All posts are 100% generated by human effort.  The author does not use AI engines and never will.

TI-30Xa Algorithms: Linear Regression

 TI-30Xa Algorithms: Linear Regression

Welcome to the March 2024 installment of TI-30Xa Algorithms.

Linear Regression with a TI-30Xa?

Today’s task is to fit bi-variate data to the line:

y = m * x + b

with the TI-30Xa. What? This calculator does not have a linear regression mode. Yes, with it is possible. We are going to use the technique shown in by the TI-36 Solar Guidebook from 1985 (see Source below). The TI-36 Solar was part of Texas Instruments’ line in the late 1980s and the early 1990s.

You can read my review on the TI-36 Solar from September 26, 2020 here:

https://edspi31415.blogspot.com/2020/09/retro-review-ti-36-solar.html

Where the TI-36 Solar only had one memory register, the TI-30Xa has three memory registers, and they are going to come in handy here.

Procedure

Caution: Be sure the calculator is on the entire time. Turning off the calculator will clear out statistics mode.

1. Enter the y data. Store the mean (y-bar) into memory register 2. Store the population deviation (σy) into memory register 3.

Keystrokes:

Mean of y-data: [ 2^nd ] [ x^2 ] {x-bar} [ STO ] [ 2 ]

Population of y-data: [ 2^nd ] [ ÷ ] { σxn } [ STO ] [ 3 ]

2. Clear the stat registers and enter the x data. As we are entering the x data, use memory register 1 to calculate Σxy.

Keystrokes:

Clear Stat Registers: [ 2^nd ] [ 7 ] {CSR}

1^st Point:

x1 [ × ] y1 [ = ] [ STO ] [ 1 ]

x1 [ Σ+ ]

Every point there after:

x_i [ × ] y_i [ = ] [ 2^nd ] [ RCL ] {SUM} [ 1 ]

x_i [ Σ+ ]

3. Calculate the slope, and replace Σxy with the slope.

m = ( y-bar * Σx – Σxy) / ( x-bar * Σx - Σx^2)

Keystrokes:

[ ( ] [ RCL ] [ 2 ] [ × ] [ 2^nd ] [ ( ] [ - ] [ RCL ] [ 1 ] [ ) ]

[ ÷ ] [ ( ] [ 2^nd ] [ x^2 ] [ × ] [ 2^nd ] [ ( ] [ - ] [ 2^nd ] [ ) ] [ = ] [ STO ] [ 1 ]

4. Calculate the y-intercept, replace y-bar with the y-intercept.

b = -m * x-bar + y-bar

Keystrokes:

[ RCL ] [ 1 ] [ +/- ] [ × ] [ 2^nd ] [ x^2 ] [ + ] [ RCL ] [ 2 ] [ = ] [ STO ] [ 2 ]

5. Calculate the correlation. If the correlation is close to -1 or +1, the linear fit will be excellent.

r = m * σx / σy

Keystrokes:

[ RCL ] [ 1 ] [ × ] [ 2^nd ] [ ÷ ] [ ÷ ] [ RCL ] [ 3 ] [ = ]

6. Use slope (m) and intercept (b) to predict x and y values:

y’ = m * x0 + b

Keystrokes: [ RCL ] [ 1 ] [ × ] x0 [ + ] [ RCL ] [ 2 ] [ = ]

x’ = (y0 – b) / m

Keystrokes: [ ( ] y0 [ - ] [ RCL ] [ 2 ] [ ) ] [ ÷ ] [ RCL ] [ 1 ] [ = ]

Key Map

[ RCL ] [ 1 ]: first Σxy, then m

[ RCL ] [ 2 ]: first y-bar, then b

[ RCL ] [ 3 ]: σy

[ 2^nd ] [ x^2 ]: x-bar

[ 2^nd ] [ ÷ ]: σxn

Example

Fit a line to the data:

X	Y
12	100
13	98.7
14	97.1
16	94.9
18	92.6
20	90

1. Enter the y data. Store the mean (y-bar) into memory register 2. Store the population deviation (σy) into memory register 3.

100 [ Σ+ ]

98.7 [ Σ+ ]

97.1 [ Σ+ ]

94.9 [ Σ+ ]

92.6 [ Σ+ ]

90 [ Σ+ ] (display n = 6)

Mean of y-data: [ 2^nd ] [ x^2 ] [ STO ] [ 2 ] (y-bar = 95.55)

Population of y-data: [ 2^nd ] [ ÷ ] [ STO ] [ 3 ] (σy = 3.465424457)

2. Clear the stat registers and enter the x data. As we are entering the x data, use memory register 1 to calculate Σxy.

Keystrokes:

Clear Stat Registers: [ 2^nd ] [ 7 ] {CSR}

12 [ × ] 100 [ = ] [ STO ] [ 1 ]

12 [ Σ+ ]

13 [ × ] 98.7 [ = ] [ 2^nd ] [ RCL ] [ 1 ] (SUM 1)

13 [ Σ+ ]

14 [ × ] 97.1 [ = ] [ 2^nd ] [ RCL ] [ 1 ] (SUM 1)

14 [ Σ+ ]

16 [ × ] 94.9 [ = ] [ 2^nd ] [ RCL ] [ 1 ] (SUM 1)

16 [ Σ+ ]

18 [ × ] 92.6 [ = ] [ 2^nd ] [ RCL ] [ 1 ] (SUM 1)

18 [ Σ+ ]

20 [ × ] 90 [ = ] [ 2^nd ] [ RCL ] [ 1 ] (SUM 1)

20 [ Σ+ ]

RCL 1: Σxy = 8827.7

[ 2^nd ] [ x^2 ]: x-bar = 15.5

3. Calculate the slope, and replace Σxy with the slope.

[ ( ] [ RCL ] [ 2 ] [ × ] [ 2^nd ] [ ( ] [ - ] [ RCL ] [ 1 ] [ ) ]

[ ÷ ] [ ( ] [ 2^nd ] [ x^2 ] [ × ] [ 2^nd ] [ ( ] [ - ] [ 2^nd ] [ ) ] [ = ] [ STO ] [ 1 ]

Slope: m = -1.230526316

4. Calculate the y-intercept, replace y-bar with the y-intercept.

[ RCL ] [ 1 ] [ +/- ] [ × ] [ 2^nd ] [ x^2 ] [ + ] [ RCL ] [ 2 ] [ = ] [ STO ] [ 2 ]

Intercept: b = 114.6231579

5. Calculate the correlation.

[ RCL ] [ 1 ] [ × ] [ 2^nd ] [ ÷ ] [ ÷ ] [ RCL ] [ 3 ] [ = ]

Correlation: r = -0.999092386

The line is:

y = -1.230526316 * x + 114.6231579

6. Predict values.

If x = 15, predict the y value (y’):

[ RCL ] [ 1 ] [ × ] x0 [ + ] [ RCL ] [ 2 ] [ = ]

y’ = 96.16526316

If y = 95, predict the x value (x’):

[ ( ] y0 [ - ] [ RCL ] [ 2 ] [ ) ] [ ÷ ] [ RCL ] [ 1 ] [ = ]

x’ = 15.94696322

Source

Alley, Chris M., Brenda M. Cornitius, et al. TI-36 Solar Guidebook Texas Instruments Incorporated. Dallas, TX. 1985, 1986, 1987. pp. 4.6 – 4.13

Eddie

All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.