Compound (Fused) Operations

Compound operations perform multiple arithmetic steps in a single call for performance. Use these instead of chaining separate operations.

Formula reference:

Method	Formula	Instead of
AddAndMul(X, Y, Z)	self = (X + Y) * Z	Add(X,Y) then Mul(Z)
SubAndMul(X, Y, Z)	self = (X - Y) * Z	Sub(X,Y) then Mul(Z)
MulAndAdd(X, Y, Z)	self = X * Y + Z	Mul(X,Y) then Add(Z)
MulAndSub(X, Y, Z)	self = X * Y - Z	Mul(X,Y) then Sub(Z)
DivAndAdd(X, Y, Z)	self = X / Y + Z	Div(X,Y) then Add(Z)
DivAndSub(X, Y, Z)	self = X / Y - Z	Div(X,Y) then Sub(Z)
AddScaled(Y, yScale)	self = self + Y * yScale	Mul then Add
SubScaled(Y, yScale)	self = self - Y * yScale	Mul then Sub
SqrAddScaled(X, Y, yScale)	self = sqr(X) + sqr(Y) * yScale	Sqr twice, Mul, Add

Scale variants: Most compound methods have scale factor overloads:

• AddAndMul(X, Y, Z, zScale) → self = (X + Y) Z zScale
• MulAndAdd(X, Y, Z, zScale) → self = X Y + Z zScale

Performance: Compound operations are 2-3x faster than separate calls because:

1. Single pass through memory (cache-friendly)
2. No temporary arrays allocated
3. Vectorized (SIMD) implementation

When to use: Whenever your formula matches one of the patterns above. The AI should recognize expressions like (A + B) * C and suggest AddAndMul.