GAUSS

PUBLISHED EXAMPLE TABLE IS BROKEN, so the figure is taken from the page's prose and then derived. The GAUSS page's example table has a Formula column reading '=GAUSS(2) (with a leading apostrophe, i.e. the formula as literal text) and a Result column whose cell contains the string '=GAUSS(2)' rather than any number -- the table's own result cell was never evaluated. The only figure Microsoft actually publishes for this example is inside the Description column: "Probability that a member of a standard normal population will fall between the mean and 2 standard deviations from the mean (result is 0.47725)". Derived independently with mpmath at 50 digits from the definition the page gives -- GAUSS(z) = NORM.S.DIST(z,TRUE) - 0.5 = erf(z/sqrt(2))/2 -- giving 0.4772498680518207928, which rounds to exactly the published 0.47725.

Derived from the identity the page itself states: "Because NORM.S.DIST(0,True) always returns 0.5, GAUSS(z) will always be 0.5 less than NORM.S.DIST(z,True)." At z = 0 that is 0.5 - 0.5 = 0 exactly. An exact value, so asserted with no ROUND wrapper.

Microsoft states: "Because NORM.S.DIST(0,True) always returns 0.5, GAUSS (z) will always be 0.5 less than NORM.S.DIST(z,True)." Written as a difference computed inside the engine under test, so it holds an engine to its OWN normal distribution rather than to a figure from outside -- an engine whose erf is slightly off passes only if both functions are off together, which is what the identity actually claims.

Not published; derived from the definition. The standard normal density is symmetric about 0, so the signed area from the mean out to -z is the negative of the area out to +z. mpmath at 50 digits: GAUSS(-2) = -0.4772498680518207928 exactly negates GAUSS(2). This is worth asserting because an implementation built on a one-sided series or table can easily return the ABSOLUTE probability 0.47725 for a negative z.

Excel documents: "If z is not a valid data type, GAUSS returns the #VALUE! error value." (The page's companion clause, "If z is not a valid number, GAUSS returns the #NUM! error value", is not asserted anywhere in this corpus because the page never says which numbers are not valid ones -- the whole real line has a finite answer -- and this corpus does not invent an input to fit an undocumented guard.)

PUBLISHED EXAMPLE TABLE IS BROKEN, so the figure is taken from the page's prose and then derived. The GAUSS page's example table has a Formula column reading '=GAUSS(2) (with a leading apostrophe, i.e. the formula as literal text) and a Result column whose cell contains the string '=GAUSS(2)' rather than any number -- the table's own result cell was never evaluated. The only figure Microsoft actually publishes for this example is inside the Description column: "Probability that a member of a standard normal population will fall between the mean and 2 standard deviations from the mean (result is 0.47725)". Derived independently with mpmath at 50 digits from the definition the page gives -- GAUSS(z) = NORM.S.DIST(z,TRUE) - 0.5 = erf(z/sqrt(2))/2 -- giving 0.4772498680518207928, which rounds to exactly the published 0.47725.

Derived from the identity the page itself states: "Because NORM.S.DIST(0,True) always returns 0.5, GAUSS(z) will always be 0.5 less than NORM.S.DIST(z,True)." At z = 0 that is 0.5 - 0.5 = 0 exactly. An exact value, so asserted with no ROUND wrapper.

Microsoft states: "Because NORM.S.DIST(0,True) always returns 0.5, GAUSS (z) will always be 0.5 less than NORM.S.DIST(z,True)." Written as a difference computed inside the engine under test, so it holds an engine to its OWN normal distribution rather than to a figure from outside -- an engine whose erf is slightly off passes only if both functions are off together, which is what the identity actually claims.

Not published; derived from the definition. The standard normal density is symmetric about 0, so the signed area from the mean out to -z is the negative of the area out to +z. mpmath at 50 digits: GAUSS(-2) = -0.4772498680518207928 exactly negates GAUSS(2). This is worth asserting because an implementation built on a one-sided series or table can easily return the ABSOLUTE probability 0.47725 for a negative z.

Excel documents: "If z is not a valid data type, GAUSS returns the #VALUE! error value." (The page's companion clause, "If z is not a valid number, GAUSS returns the #NUM! error value", is not asserted anywhere in this corpus because the page never says which numbers are not valid ones -- the whole real line has a finite answer -- and this corpus does not invent an input to fit an undocumented guard.)

PUBLISHED EXAMPLE TABLE IS BROKEN, so the figure is taken from the page's prose and then derived. The GAUSS page's example table has a Formula column reading '=GAUSS(2) (with a leading apostrophe, i.e. the formula as literal text) and a Result column whose cell contains the string '=GAUSS(2)' rather than any number -- the table's own result cell was never evaluated. The only figure Microsoft actually publishes for this example is inside the Description column: "Probability that a member of a standard normal population will fall between the mean and 2 standard deviations from the mean (result is 0.47725)". Derived independently with mpmath at 50 digits from the definition the page gives -- GAUSS(z) = NORM.S.DIST(z,TRUE) - 0.5 = erf(z/sqrt(2))/2 -- giving 0.4772498680518207928, which rounds to exactly the published 0.47725.

Derived from the identity the page itself states: "Because NORM.S.DIST(0,True) always returns 0.5, GAUSS(z) will always be 0.5 less than NORM.S.DIST(z,True)." At z = 0 that is 0.5 - 0.5 = 0 exactly. An exact value, so asserted with no ROUND wrapper.

Microsoft states: "Because NORM.S.DIST(0,True) always returns 0.5, GAUSS (z) will always be 0.5 less than NORM.S.DIST(z,True)." Written as a difference computed inside the engine under test, so it holds an engine to its OWN normal distribution rather than to a figure from outside -- an engine whose erf is slightly off passes only if both functions are off together, which is what the identity actually claims.

Not published; derived from the definition. The standard normal density is symmetric about 0, so the signed area from the mean out to -z is the negative of the area out to +z. mpmath at 50 digits: GAUSS(-2) = -0.4772498680518207928 exactly negates GAUSS(2). This is worth asserting because an implementation built on a one-sided series or table can easily return the ABSOLUTE probability 0.47725 for a negative z.

Excel documents: "If z is not a valid data type, GAUSS returns the #VALUE! error value." (The page's companion clause, "If z is not a valid number, GAUSS returns the #NUM! error value", is not asserted anywhere in this corpus because the page never says which numbers are not valid ones -- the whole real line has a finite answer -- and this corpus does not invent an input to fit an undocumented guard.)