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Release v1.0.0
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‎.github/workflows/build.yml‎

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---
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# Github Actions build for swift
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# -*- compile-command: "yamllint -f parsable build.yml" -*-
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name: build
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# Trigger the workflow on push or pull request
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on:
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push:
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branches:
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- '*'
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tags:
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- '*'
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pull_request:
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workflow_dispatch:
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inputs:
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manual:
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required: true
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default: true
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jobs:
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build:
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if: ${{ github.repository == 'ncw/find_arctan_formulae' || github.event.inputs.manual }}
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timeout-minutes: 60
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strategy:
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fail-fast: false
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matrix:
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job_name: ['go1.23', 'go1.22']
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include:
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- job_name: go1.23
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os: ubuntu-latest
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go: '1.23.x'
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gotests: true
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integrationtest: true
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check: true
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- job_name: go1.22
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os: ubuntu-latest
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go: '1.22.x'
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gotests: true
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integrationtest: true
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check: false
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name: ${{ matrix.job_name }}
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runs-on: ${{ matrix.os }}
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steps:
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- name: Checkout
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uses: actions/checkout@v4
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with:
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fetch-depth: 0
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- name: Install Go
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uses: actions/setup-go@v5
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with:
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go-version: ${{ matrix.go }}
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- name: Print Go version and environment
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shell: bash
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run: |
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printf "Using go at: $(which go)\n"
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printf "Go version: $(go version)\n"
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printf "\n\nGo environment:\n\n"
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go env
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printf "\n\nSystem environment:\n\n"
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env
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- name: Go module cache
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uses: actions/cache@v4
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with:
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path: |
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~/go/pkg/mod
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~/.cache/go-build
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~/.cache/golangci-lint
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key: ${{ runner.os }}-go-${{ hashFiles('**/go.sum') }}
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restore-keys: |
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${{ runner.os }}-go-
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- name: Build
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shell: bash
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run: |
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go build ./...
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- name: Unit tests
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shell: bash
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run: |
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go test -v
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if: matrix.gotests
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- name: Regression tests
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shell: bash
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run: |
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go build -v
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./regression.sh
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if: matrix.gotests
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- name: Code quality test
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uses: golangci/golangci-lint-action@v6
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with:
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version: latest
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if: matrix.check

‎.github/workflows/goreleaser.yaml‎

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name: goreleaser
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on:
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workflow_dispatch:
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pull_request:
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push:
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permissions:
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contents: write
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jobs:
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goreleaser:
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runs-on: ubuntu-latest
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steps:
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- name: Set Vars
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if: ${{ !startsWith(github.ref, 'refs/tags/v') }}
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run: echo "GORELEASER_FLAGS=--snapshot" >> $GITHUB_ENV
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- name: Checkout
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uses: actions/checkout@v4
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with:
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fetch-depth: 0
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- name: Set up Go
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uses: actions/setup-go@v5
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- name: Run GoReleaser
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uses: goreleaser/goreleaser-action@v6
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with:
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distribution: goreleaser
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version: '~> v2'
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args: release --clean ${{ env.GORELEASER_FLAGS }}
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env:
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GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
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- name: Upload all builds
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uses: actions/upload-artifact@v4
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with:
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name: builds
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path: |
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dist/*.zip
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dist/*.txt
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dist/*.json

‎.gitignore‎

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*.test
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*.prof
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/find_arctan_formulae
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/dist/
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_junk/
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‎.goreleaser.yaml‎

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# Release the Go binary
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version: 2
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before:
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hooks:
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# You may remove this if you don't use go modules.
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- go mod download
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# you may remove this if you don't need go generate
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- go generate ./...
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builds:
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- env:
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- CGO_ENABLED=0
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goos:
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- linux
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- windows
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- darwin
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- freebsd
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- netbsd
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- openbsd
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goarch:
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- amd64
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- 386
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- arm
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- arm64
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archives:
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-
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format: zip
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files:
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- README.md
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- LICENSE
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- score_arctan.py
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name_template: >-
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{{- .ProjectName }}_
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{{- title .Os }}_
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{{- if eq .Arch "amd64" }}x86_64
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{{- else if eq .Arch "386" }}i386
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{{- else }}{{ .Arch }}{{ end }}
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{{- if .Arm }}v{{ .Arm }}{{ end -}}
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checksum:
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name_template: 'checksums.txt'
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snapshot:
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version_template: "{{ .Tag }}-beta"
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changelog:
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sort: asc
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filters:
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exclude:
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- '^docs:'
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- '^test:'

‎README.md‎

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This reposistory also contains `score_arctan.py` which is used to process the log files generated by `find_arctan_relations`.
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There is an accompanying paper which explains how this program works which can be found on arXiv at https://arxiv.org/abs/2508.08307
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The full set of results found with this program are available at https://doi.org/10.5281/zenodo.16758216
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The top results are available in the [results-by4-top.txt](results-by4-top.txt) and [results-by4-top.csv](results-by4-top.csv) files in this repository.
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Here is an example of formulae found this this program which are the lowest known Lehmer measure relations with 5 and 6 terms.
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```math
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\begin{alignat*}{2}
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\tfrac{\pi}{4} &= 29\,\arctan\left(\tfrac{1}{68}\right) &+& 42\,\arctan\left(\tfrac{1}{117}\right) \\
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& -15\,\arctan\left(\tfrac{1}{2675143}\right) &-& 5 \,\arctan\left(\tfrac{1}{2976163}\right) \\
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& -5\,\arctan\left(\tfrac{1}{302342643}\right) \\
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\lambda &= 1.4572 \\
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\tfrac{\pi}{4} &= 83\,\arctan\left(\tfrac{1}{107}\right) &+& 17\,\arctan\left(\tfrac{1}{1710}\right) \\
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& -44\,\arctan\left(\tfrac{1}{225443}\right) &-& 68\,\arctan\left(\tfrac{1}{2513489}\right) \\
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& +22\,\arctan\left(\tfrac{1}{42483057}\right) &+& 34\,\arctan\left(\tfrac{1}{7939642926390344818}\right) \\
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\lambda &= 1.3291
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\end{alignat*}
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```
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## Features
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- Groups primes (excluding 2) into combinations of configurable size.
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## Installation
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Download [the latest release](https://github.com/ncw/find_arctan_formulae/releases/latest) or build from source:
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```bash
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git clone https://github.com/ncw/find_arctan_formulae.git
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cd find_arctan_formulae

‎RELEASE.md‎

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# Making a release
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Compile and test
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Then run
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goreleaser --clean --snapshot
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To test the build
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When happy, tag the release
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git tag -s -m "Release v1.0.XX" v1.0.XX
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Push to GitHub
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git push --follow-tags origin
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The github action should build the release

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