Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

Average Error: 0.0 → 0.0

Time: 1.8s

Precision: binary64

Math

\[\frac{x \cdot y}{2} - \frac{z}{8} \]

↓

\[\mathsf{fma}\left(z, -0.125, y \cdot \left(x \cdot 0.5\right)\right) \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))

↓

(FPCore (x y z) :precision binary64 (fma z -0.125 (* y (* x 0.5))))

C

double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

↓

double code(double x, double y, double z) {
	return fma(z, -0.125, (y * (x * 0.5)));
}

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * y) / 2.0) - Float64(z / 8.0))
end

↓

function code(x, y, z)
	return fma(z, -0.125, Float64(y * Float64(x * 0.5)))
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(z * -0.125 + N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\frac{x \cdot y}{2} - \frac{z}{8} \]

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, -0.125, y \cdot \left(x \cdot 0.5\right)\right)} \]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(z, -0.125, y \cdot \left(x \cdot 0.5\right)\right) \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2.0) (/ z 8.0)))