exupero's blog

# New stack math compendium

In the previous post I described a couple new approaches to my original compendium of stack math algorithms. Below is the updated compendium. The error is calculated using this script, which for algorithms that aren't simple multiplication or division checks the error at a few powers of ten and reports the worst accuracy.

If you have any improvements to suggest, or would like to see some additional conversions, feel free to email me.

ConversionLess accurateMore accurate
Celsius → Fahrenheit
`9 * 5 / 32 +`
`double -tenth +32`
(exact)
Fahrenheit → Celsius
`32 - 5 * 9 /`
`-32 halve +tenth`
(1% error)
15% tip
`0.15 *`
`tenth +half`
(exact)
Multiply by π
`3.14159 *`
`triple +tenth`
(5% error)
`triple +twentieth`
(0.3% error)
Divide by π
`3.14159 /`
`third -tenth`
(6% error)
`third -twentieth`
(0.5% error)
kilometers → miles
`0.6214 *`
`two-thirds`
(7% error)
`two-thirds -tenth +twentieth`
(1% error)
miles → kilometers
`1.609 *`
`+half`
(7% error)
`[+half] left [tenth] right +`
(0.6% error)
meters → feet
`3.281 *`
`triple`
(9% error)
`triple +tenth`
(0.6% error)
feet → meters
`3.281 /`
`third`
(9% error)
`third -tenth`
(2% error)
inches → centimeters
`2.54 *`
`tenfold quarter`
(2% error)
centimeters → inches
`2.54 /`
`tenth quadruple`
(2% error)
miles → feet
`5280 *`
`five-thousandfold`
(5% error)
`five-thousandfold +twentieth`
(0.6% error)
feet → miles
`5280 /`
`five-thousandth`
(6% error)
`five-thousandth -twentieth`
(0.3% error)
kilograms → pounds
`2.205 *`
`double`
(9% error)
`double +tenth`
(0.2% error)
pounds → kilograms
`2.205 /`
`halve`
(10% error)
`halve -tenth`
(0.8% error)
hours → seconds
`3600 *`
`four-thousandfold`
(10% error)
`four-thousandfold -tenth`
(exact)
seconds → hours
`3600 /`
`four-thousandth`
(10% error)
`four-thousandth +tenth`
(1% error)
mi/h → ft/s
`1.467 *`
`+half`
(2% error)
ft/s → mi/h
`1.467 /`
`two-thirds`
(2% error)
sq. miles → acres
`640 *`
`seven-hundredfold`
(9% error)
`seven-hundredfold -tenth`
(2% error)
acres → sq. miles
`640 /`
`seven-hundredth`
(9% error)
`seven-hundredth +tenth`
(0.6% error)
acres → sq. feet
`43560 *`
`ten-thousandfold quadruple`
(8% error)
`ten-thousandfold quadruple +tenth`
(1% error)
sq. feet → acres
`43560 /`
`ten-thousandth quarter`
(9% error)
`ten-thousandth quarter -tenth`
(2% error)
sq. kilometers → acres
`247.1 *`
`thousandfold quarter`
(1% error)
acres → sq. kilometers
`247.1 /`
`thousandth quadruple`
(1% error)
pounds → troy ounces
`14.58 *`
`tenfold +half`
(3% error)
`[tenfold +half] left [halve] right -`
(0.5% error)
troy ounces → pounds
`14.58 /`
`tenth two-thirds`
(3% error)
US cups → fluid ounces
`8 *`
`quadruple double`
(exact)
fluid ounces → US cups
`8 /`
`quarter halve`
(exact)
liquid gallons → US cups
`16 *`
`quadruple quadruple`
(exact)
US cups → liquid gallons
`16 /`
`quarter quarter`
(exact)
liquid gallons → liters
`3.785 *`
`quadruple`
(6% error)
`quadruple -twentieth`
(0.4% error)
liters → liquid gallons
`3.785 /`
`quarter`
(5% error)
`quarter +twentieth`
(0.6% error)
sphere radius → surface area
`square 4 * 3.14159 *`
`square tenfold +quarter`
(0.5% error)
sphere radius → volume
`cube 4 * 3 / 3.14159 *`
`cube quadruple`
(5% error)
`cube quadruple +twentieth`
(0.3% error)
sphere surface area → radius
`4 / 3.14159 / sqrt`
`tenth -quarter sqrt`
(3% error)
`hundredth quadruple double sqrt`
(0.3% error)
sphere volume → radius
`4 / 3 * 3.14159 / cube-root`
`quarter cube-root`
(2% error)