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

Average Error: 0.1 → 0

Time: 16.9s

Precision: binary64

Cost: 6592

Math

\[x - \frac{3}{8} \cdot y \]

↓

\[\mathsf{fma}\left(-0.375, y, x\right) \]

FPCore

(FPCore (x y) :precision binary64 (- x (* (/ 3.0 8.0) y)))

↓

(FPCore (x y) :precision binary64 (fma -0.375 y x))

C

double code(double x, double y) {
	return x - ((3.0 / 8.0) * y);
}

↓

double code(double x, double y) {
	return fma(-0.375, y, x);
}

Julia

function code(x, y)
	return Float64(x - Float64(Float64(3.0 / 8.0) * y))
end

↓

function code(x, y)
	return fma(-0.375, y, x)
end

Wolfram

code[x_, y_] := N[(x - N[(N[(3.0 / 8.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(-0.375 * y + x), $MachinePrecision]

Derivation

1. Initial program 0.1

   \[x - \frac{3}{8} \cdot y \]

2. Simplified 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(-0.375, y, x\right)} \]
   Proof

Alternatives

Alternative 1
Error	16.3
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-5}:\\ \;\;\;\;y \cdot -0.375\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+107}:\\ \;\;\;\;y \cdot -0.375\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	0.1
Cost	320

\[x - 0.375 \cdot y \]

Alternative 3
Error	31.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (/ 3.0 8.0) y)))