Symbolic differentiation (#4)
This commit is contained in:
Patrick Stevens
GitHub
115
Cargo.lock
generated
115
Cargo.lock
generated
@@ -2,6 +2,121 @@
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# It is not intended for manual editing.
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version = 3
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[[package]]
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name = "arrayvec"
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version = "0.7.2"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "8da52d66c7071e2e3fa2a1e5c6d088fec47b593032b254f5e980de8ea54454d6"
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[[package]]
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name = "bitvec"
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version = "1.0.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "1bc2832c24239b0141d5674bb9174f9d68a8b5b3f2753311927c172ca46f7e9c"
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dependencies = [
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"funty",
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"radium",
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"tap",
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"wyz",
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]
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[[package]]
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name = "funty"
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version = "2.0.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "e6d5a32815ae3f33302d95fdcb2ce17862f8c65363dcfd29360480ba1001fc9c"
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[[package]]
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name = "immutable-chunkmap"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "7617eb072b88069788fa9d5cadae34faebca64e5325ec5deaa2b4c96510f9e8c"
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dependencies = [
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"arrayvec",
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"packed_struct",
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"packed_struct_codegen",
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]
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[[package]]
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name = "little_learner"
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version = "0.1.0"
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dependencies = [
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"immutable-chunkmap",
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]
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[[package]]
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name = "packed_struct"
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version = "0.10.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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dependencies = [
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"bitvec",
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"packed_struct_codegen",
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]
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[[package]]
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name = "packed_struct_codegen"
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dependencies = [
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"proc-macro2",
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"quote",
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"syn",
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[[package]]
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name = "proc-macro2"
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dependencies = [
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"unicode-ident",
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[[package]]
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name = "quote"
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version = "1.0.26"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "4424af4bf778aae2051a77b60283332f386554255d722233d09fbfc7e30da2fc"
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dependencies = [
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"proc-macro2",
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]
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[[package]]
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name = "radium"
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version = "0.7.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "dc33ff2d4973d518d823d61aa239014831e521c75da58e3df4840d3f47749d09"
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[[package]]
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name = "syn"
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version = "1.0.109"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "72b64191b275b66ffe2469e8af2c1cfe3bafa67b529ead792a6d0160888b4237"
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dependencies = [
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"proc-macro2",
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"quote",
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"unicode-ident",
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]
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[[package]]
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name = "tap"
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version = "1.0.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "55937e1799185b12863d447f42597ed69d9928686b8d88a1df17376a097d8369"
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[[package]]
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name = "unicode-ident"
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version = "1.0.8"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "e5464a87b239f13a63a501f2701565754bae92d243d4bb7eb12f6d57d2269bf4"
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[[package]]
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name = "wyz"
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version = "0.5.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "05f360fc0b24296329c78fda852a1e9ae82de9cf7b27dae4b7f62f118f77b9ed"
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dependencies = [
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"tap",
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]
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@@ -6,3 +6,4 @@ edition = "2021"
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# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
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[dependencies]
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immutable-chunkmap = "1.0.5"
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157
src/expr_syntax_tree.rs
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157
src/expr_syntax_tree.rs
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@@ -0,0 +1,157 @@
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#![allow(dead_code)]
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use immutable_chunkmap::map;
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use std::ops::{Add, Mul};
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/*
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An untyped syntax tree for an expression whose constants are all of type `A`.
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*/
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#[derive(Clone, Debug)]
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pub enum Expr<A> {
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Const(A),
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Sum(Box<Expr<A>>, Box<Expr<A>>),
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Variable(u32),
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// The first `Expr` here is a function, which may reference the input variable `Variable(i)`.
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// For example, `(fun x y -> x + y) 3 4` is expressed as:
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// Apply(0, Apply(1, Sum(Variable(0), Variable(1)), Const(4)), Const(3))
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Apply(u32, Box<Expr<A>>, Box<Expr<A>>),
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Mul(Box<Expr<A>>, Box<Expr<A>>),
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}
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impl<A> Expr<A> {
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fn eval_inner<const SIZE: usize>(e: &Expr<A>, ctx: &map::Map<u32, A, SIZE>) -> A
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where
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A: Clone + Add<Output = A> + Mul<Output = A>,
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{
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match &e {
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Expr::Const(x) => x.clone(),
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Expr::Sum(x, y) => Expr::eval_inner(x, ctx) + Expr::eval_inner(y, ctx),
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Expr::Variable(id) => ctx
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.get(id)
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.unwrap_or_else(|| panic!("No binding found for free variable {}", id))
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.clone(),
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Expr::Apply(variable, func, arg) => {
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let arg = Expr::eval_inner(arg, ctx);
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let (updated_context, _) = ctx.insert(*variable, arg);
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Expr::eval_inner(func, &updated_context)
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}
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Expr::Mul(x, y) => Expr::eval_inner(x, ctx) * Expr::eval_inner(y, ctx),
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}
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}
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pub fn eval<const MAX_VAR_NUM: usize>(e: &Expr<A>) -> A
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where
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A: Clone + Add<Output = A> + Mul<Output = A>,
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{
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Expr::eval_inner(e, &map::Map::<u32, A, MAX_VAR_NUM>::new())
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}
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pub fn apply(var: u32, f: Expr<A>, arg: Expr<A>) -> Expr<A> {
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Expr::Apply(var, Box::new(f), Box::new(arg))
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}
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pub fn sum(x: Expr<A>, y: Expr<A>) -> Expr<A> {
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Expr::Sum(Box::new(x), Box::new(y))
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}
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pub fn mul(x: Expr<A>, y: Expr<A>) -> Expr<A> {
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Expr::Mul(Box::new(x), Box::new(y))
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}
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pub fn differentiate(one: &A, zero: &A, var: u32, f: &Expr<A>) -> Expr<A>
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where
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A: Clone,
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{
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match f {
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Expr::Const(_) => Expr::Const(zero.clone()),
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Expr::Sum(x, y) => Expr::sum(
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Expr::differentiate(one, zero, var, x),
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Expr::differentiate(one, zero, var, y),
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),
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Expr::Variable(i) => {
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if *i == var {
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Expr::Const(one.clone())
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} else {
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Expr::Const(zero.clone())
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}
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}
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Expr::Mul(x, y) => Expr::sum(
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Expr::Mul(
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Box::new(Expr::differentiate(one, zero, var, x.as_ref())),
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(*y).clone(),
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),
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Expr::Mul(
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Box::new(Expr::differentiate(one, zero, var, y.as_ref())),
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(*x).clone(),
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),
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),
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Expr::Apply(new_var, func, expr) => {
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if *new_var == var {
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panic!(
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"cannot differentiate with respect to variable {} that's been assigned",
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var
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)
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}
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let expr_deriv = Expr::differentiate(one, zero, var, expr);
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Expr::mul(
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expr_deriv,
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Expr::Apply(
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*new_var,
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Box::new(Expr::differentiate(one, zero, *new_var, func)),
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(*expr).clone(),
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),
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)
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}
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}
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn test_expr() {
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let expr = Expr::apply(
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0,
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Expr::apply(
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1,
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Expr::sum(Expr::Variable(0), Expr::Variable(1)),
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Expr::Const(4),
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),
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Expr::Const(3),
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);
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assert_eq!(Expr::eval::<2>(&expr), 7);
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}
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#[test]
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fn test_derivative() {
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let add_four = Expr::sum(Expr::Variable(0), Expr::Const(4));
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let mul_five = Expr::mul(Expr::Variable(1), Expr::Const(5));
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{
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let mul_five_then_add_four = Expr::apply(0, add_four.clone(), mul_five.clone());
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let mul_then_add_diff = Expr::differentiate(&1, &0, 1, &mul_five_then_add_four);
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for i in 3..10 {
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// (5x + 4) differentiates to 5
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assert_eq!(
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Expr::eval::<2>(&Expr::apply(1, mul_then_add_diff.clone(), Expr::Const(i))),
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5
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);
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}
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}
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{
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let add_four_then_mul_five = Expr::apply(1, mul_five.clone(), add_four.clone());
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let add_then_mul_diff = Expr::differentiate(&1, &0, 0, &add_four_then_mul_five);
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for i in 3..10 {
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// ((x + 4) * 5) differentiates to 5
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assert_eq!(
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Expr::eval::<2>(&Expr::apply(0, add_then_mul_diff.clone(), Expr::Const(i))),
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5
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);
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}
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}
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}
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}
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@@ -1,3 +1,5 @@
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mod expr_syntax_tree;
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use std::iter::Sum;
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use std::ops::{Mul, Sub};
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