Herbie's input format is designed for expressing mathematical functions, which Herbie can then search for accurate implementations of. It also allows specifying the distribution that Herbie draws inputs from when evaluating the accuracy of an expression.
Herbie uses the FPCore format for its input expression, which looks like this:
(FPCore (inputs ...) properties ... expression)
Each input is a variable, like
x, which can be used
in the expression, whose accuracy Herbie will try to improve.
Properties are described below.
The expression is written in prefix form, with every function call parenthesized, as in Lisp. For example, the formula for the hypotenuse of a triangle with legs a and b is
(FPCore (a b) (sqrt (+ (* a a) (* b b))))
We recommend the
.fpcore file extension for Herbie input files.
Herbie supports all functions from math.h with floating-point-only inputs and outputs. The best supported functions, far from the full list, include:
-is both negation and subtraction
Herbie also supports the constants
Herbie links against
libm to ensure that every
function has the same behavior in Herbie as in your code. However,
on Windows platforms some functions are not available in the
libm. In these cases Herbie will use a fallback
implementation and print a warning; turning off the
the precision:fallback option
disables those functions instead.
if for conditional expressions:
(if cond if-true if-false)
if epxression evaluates the
cond and returns either
it is true or
if-false if it is not. Conditionals may use:
Note that unlike the arithmetic operators, the comparison functions can take any number of arguments.
Intermediate variables can be defined using
(let ([variable value] ...) body)
let expression, all the values are evaluated
first, and then are bound to their variables in the body. This
means that the value of one variable can't refer to another
variable in the same
let block; nest
constructs if you want to do that.
Note that Herbie treats intermediate values only as a notational convenience, and inlines their values before improving the formula's accuracy. Using intermediate variables will not help Herbie improve a formula's accuracy or speed up its run-time.
Herbie includes experimental support for complex numbers; however, this support is currently limited to the basic arithmetic operations. Some of Herbie's internal mechanisms for improving expression accuracy also do not yet support complex-number expressions.
All input parameters are real numbers; complex numbers must be
conj are available on complex numbers. Note that
complex and real operations use the same syntax; however, complex
and real arithmetic cannot be mixed:
(+ (complex 1 2)
1) is not valid. A type checker will report such errors.
Complex operations use the Racket implementation, so results may differ (slightly) for the complex library used in your language, especially for non-finite complex numbers. Unfortunately, complex number arithmetic is not as standardized as float-point arithmetic.
In the future, we hope to support complex-number arguments and fully support all complex-number operations.
Herbie also allows several FPCore properties specified on inputs for additional meta-data:
Several additional properties can be found in the benchmark suite and are used for testing, but are not supported and can change without warning.
Herbie's output uses custom FPCore properties in its output to provide meta-data about the Herbie improvement process:
:herbie-error-input ([pts err] ...)
:herbie-error-output ([pts2 err1] [pts2 err2])
Herbie's output also passes through any
:pre properties on its inputs.
Herbie 0.9 used a different input
format, which is not supported Herbie 1.0 and later. To
simplify the transition, the
converts from the old to the new format.
To use the conversion tool, run:
racket infra/convert.rkt file.rkt > file.fpcore