Calculates ex - 1. For values of x close to 0, the exact sum of expm1(x) + 1 is much closer to the true result of ex than exp(x).

Note

Math functions on ARM architecture may return different results in very high-precision calculationsc compared to Intel/AMD architectures.

ParameterTypeRequiredDefault ValueDescription
asstringoptional[a] _expm1 The name of the output field.
field[b]stringrequired   The name of the input field.

[a] Optional parameters use their default value unless explicitly set.

[b] The parameter name field can be omitted.

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Show omitted argument names for this function

math:expm1() Examples

Click + next to an example below to get the full details.

Calculate e Raised to Power Minus One

Calculate e^x - 1 using the math:expm1() or math:expm1() functions

Query
logscale
x := 0.00001
        | math:expm1(x, as=precise_result)
        | math:exp(x, as=standard_result)
Introduction

In this example, the math:expm1() function and math:exp() function are used to calculate e^x - 1 for a small value of x, demonstrating the superior precision of math:expm1() compared to using math:exp() and subtracting 1.

Step-by-Step

  1. Starting with the source repository events.

  2. logscale
    x := 0.00001

    Assigns a very small double-precision floating-point value 0.00001 to a field named x. This small value near zero demonstrates where math:expm1() provides better numerical precision.

  3. logscale
    | math:expm1(x, as=precise_result)

    Calculates e^x - 1 for the value in field x and returns the result in a new field named precise_result. If the as parameter is not specified, the result is returned in a field named _expm1 as default.

  4. logscale
    | math:exp(x, as=standard_result)

    Calculates e^x for the value in field x and returns the result in a new field named standard_result. If the as parameter is not specified, the result is returned in a field named _exp as default.

  5. Event Result set.

Summary and Results

The query is used to calculate exponential values minus one with high precision, which is particularly important in scientific and financial calculations involving very small values. The math:exp(x) function is also mentioned in this query to show that it is less precise due to floating-point rounding compared to the math:expm1() function.

The precise_result field contains the more accurate calculation using math:expm1(), while standard_result shows the result of using math:exp() and subtracting 1.

This query is useful, for example, to calculate small percentage changes in financial applications, compute precise scientific measurements near baseline values and analyze small deviations in statistical data.

Sample output from the incoming example data:

precise_resultstandard_result
0.00001000000500000170.0000100000050000166

The results show that math:expm1() provides more precise calculations for small values. For values close to zero, the difference between the two methods becomes significant in applications requiring high precision.

Note that while the difference between the two methods may appear small, it becomes crucial in applications requiring high precision, especially when dealing with very small values or when performing many successive calculations.

In short, best practise is to:

Use math:expm1(x) instead of math:exp(x) - 1 when:

  • x is close to 0

  • Precision is important

  • Working with small values

Use math:exp(x) - 1 when:

  • x is larger

  • Extreme precision is not required

  • Performance is more important than precision