# Symbolics.jl simplify exp(0) to 1

**URL:** <https://discourse.julialang.org/t/symbolics-jl-simplify-exp-0-to-1/135970>\
**Category:** New to Julia\
**Tags:** symbolics\
**Created:** [March 2, 2026, 6:32pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplify-exp-0-to-1/135970 "2026-03-02T18:32:41Z")\
**Posts on this page:** 1\
**Showing post:** 2

<div class="post-metadata">

**Author:** ![langestefan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/langestefan/32/207923_2.png) [@langestefan](https://discourse.julialang.org/u/langestefan)\
**Post date:** [March 2, 2026, 6:47pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplify-exp-0-to-1/135970/2 "2026-03-02T18:47:55Z")

</div>

It would be nice to have such simple rules available by default. You could define the rules yourself.

For example:

```julia
rules = RuleSet([
    @rule(exp(0) => 1),
    @rule(sin(-(~x)) => -(sin(~x))),
    @rule(cos(-(~x)) => cos(~x))
])

H2 = map(H) do h
    re = simplify(real(h), rewriter=rules)
    im_part = simplify(imag(h), rewriter=rules)
    re + im * im_part
end

```

Will yield

```julia
2×2 Matrix{Complex{Num}}:
 0 cos(-α)*sin(t*sin(-α))*exp(t*cos(-α)) - cos(α)*sin(t*sin(-α))*exp(t*cos(-α)) + (sin(-α) + sin(α))*cos(t*sin(-α))*exp(t*cos(-α)) + im*(-cos(-α)*cos(t*sin(-α))*exp(t*cos(-α)) + cos(α)*cos(t*sin(-α))*exp(t*cos(-α)) + (sin(-α) + sin(α))*sin(t*sin(-α))*exp(t*cos(-α)))
 0 cos(-α)*cos(t*sin(-α))*exp(t*cos(-α)) - cos(α)*cos(t*sin(-α))*exp(t*cos(-α)) - (sin(-α) + sin(α))*sin(t*sin(-α))*exp(t*cos(-α)) + im*(cos(-α)*sin(t*sin(-α))*exp(t*cos(-α)) - cos(α)*sin(t*sin(-α))*exp(t*cos(-α)) + (sin(-α) + sin(α))*cos(t*sin(-α))*exp(t*cos(-α)))

```

I’m not sure why the `cos(-α)` is not taking…

edit:

This works:

```julia
rules = RuleSet([
    @rule(exp(0) => 1),
    @rule(sin((-1) * (~x)) => -(sin(~x))),
    @rule(cos((-1) * (~x)) => cos(~x)),
])

```

that yields

```julia
2×2 Matrix{Complex{Num}}:
 0 0
 0 0

```

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