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

Average Accuracy: 87.6% → 87.6%

Time: 2.0s

Precision: binary64

Cost: 6720

Math

\[x - \left(y \cdot 4\right) \cdot z \]

↓

\[\mathsf{fma}\left(z, y \cdot -4, x\right) \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))

↓

(FPCore (x y z) :precision binary64 (fma z (* y -4.0) x))

C

double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}

↓

double code(double x, double y, double z) {
	return fma(z, (y * -4.0), x);
}

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(y * 4.0) * z))
end

↓

function code(x, y, z)
	return fma(z, Float64(y * -4.0), x)
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(y * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(z * N[(y * -4.0), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 86.3%

   \[x - \left(y \cdot 4\right) \cdot z \]

2. Simplified 86.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, y \cdot -4, x\right)} \]
   Step-by-step derivation

   [Start] 86.3	\[ x - \left(y \cdot 4\right) \cdot z \]
   sub-neg [=>] 86.3	\[ \color{blue}{x + \left(-\left(y \cdot 4\right) \cdot z\right)} \]
   +-commutative [=>] 86.3	\[ \color{blue}{\left(-\left(y \cdot 4\right) \cdot z\right) + x} \]
   *-commutative [=>] 86.3	\[ \left(-\color{blue}{z \cdot \left(y \cdot 4\right)}\right) + x \]
   distribute-rgt-neg-in [=>] 86.3	\[ \color{blue}{z \cdot \left(-y \cdot 4\right)} + x \]
   fma-def [=>] 86.3	\[ \color{blue}{\mathsf{fma}\left(z, -y \cdot 4, x\right)} \]
   distribute-rgt-neg-in [=>] 86.3	\[ \mathsf{fma}\left(z, \color{blue}{y \cdot \left(-4\right)}, x\right) \]
   metadata-eval [=>] 86.3	\[ \mathsf{fma}\left(z, y \cdot \color{blue}{-4}, x\right) \]

3. Final simplification 86.3%

   \[\leadsto \mathsf{fma}\left(z, y \cdot -4, x\right) \]

Alternatives

Alternative 1
Accuracy	65.6%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-96} \lor \neg \left(x \leq 2.2 \cdot 10^{-72}\right) \land x \leq 1.55 \cdot 10^{-36}:\\ \;\;\;\;-4 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	87.6%
Cost	448

\[x - z \cdot \left(y \cdot 4\right) \]

Alternative 3
Accuracy	50.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023157 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))