Failed attempt at fixing docker build

Dockerfile

@@ -1,34 +1,28 @@
-FROM rust:alpine AS builder
+FROM alpine:latest AS builder
+
+ENV PATH "$PATH:/root/.cargo/bin"
 
 # Switch to the nightly build
-RUN rustup default nightly
-
 WORKDIR /usr/src/app
 
-# Install build dependencies & create a new dummy project
-# that we use as a build cache
-RUN apk update && \
-    apk add --no-cache openssl openssl-dev musl-dev && \
-    cargo init --bin
+# Install build dependencies, install rustup & create dummy project
+RUN apk update && apk add --no-cache openssl-dev build-base curl && \
+    { curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh -s -- -y --default-toolchain nightly; } && \
+    rustup target add x86_64-unknown-linux-musl
 
 # Build the dependencies
 # This is done separately to reduce average compile time
 # Afterwards, we remove the dummy src directory
-COPY Cargo.toml Cargo.lock ./
-RUN cargo build --release && \
-    rm src/*.rs
-
 # Now, we build our own source code
-COPY src/ ./src
-RUN cargo install --path .
+COPY Cargo.toml Cargo.lock ./
+COPY src/ ./src/
+RUN cargo build --release --target x86_64-unknown-linux-musl
 
 
 # Now, we create the actual image
-FROM alpine:latest
+FROM scratch
 
 # Install dependencies
-RUN apk update && apk add --no-cache openssl
+COPY --from=builder /usr/src/app/target/x86_64-unknown-linux-musl/release/rust-api /rust-api
 
-COPY --from=builder /usr/local/cargo/bin/rust-api /usr/local/bin/rust-api
-
-CMD ["rust-api"]
+CMD ["/rust-api"]