Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B

Average Accuracy: 100.0% → 100.0%

Time: 2.3s

Precision: binary64

Cost: 6720

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

\[\left(x + y\right) \cdot z \]

↓

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

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) z))

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot z \]

2. Applied egg-rr 44.9%

   \[\leadsto \color{blue}{\sqrt[3]{{\left(\left(x + y\right) \cdot z\right)}^{3}}} \]
   Proof

   [Start] 100.0	\[ \left(x + y\right) \cdot z \]
   add-cbrt-cube [=>] 44.9	\[ \color{blue}{\sqrt[3]{\left(\left(\left(x + y\right) \cdot z\right) \cdot \left(\left(x + y\right) \cdot z\right)\right) \cdot \left(\left(x + y\right) \cdot z\right)}} \]
   pow3 [=>] 44.9	\[ \sqrt[3]{\color{blue}{{\left(\left(x + y\right) \cdot z\right)}^{3}}} \]

3. Applied egg-rr 100.0%

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

   [Start] 44.9	\[ \sqrt[3]{{\left(\left(x + y\right) \cdot z\right)}^{3}} \]
   rem-cbrt-cube [=>] 100.0	\[ \color{blue}{\left(x + y\right) \cdot z} \]
   *-commutative [=>] 100.0	\[ \color{blue}{z \cdot \left(x + y\right)} \]
   +-commutative [=>] 100.0	\[ z \cdot \color{blue}{\left(y + x\right)} \]
   distribute-lft-in [=>] 100.0	\[ \color{blue}{z \cdot y + z \cdot x} \]
   fma-def [=>] 100.0	\[ \color{blue}{\mathsf{fma}\left(z, y, z \cdot x\right)} \]

4. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	448

\[z \cdot x + z \cdot y \]

Alternative 2
Accuracy	82.8%
Cost	324

\[\begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{-102}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 3
Accuracy	100.0%
Cost	320

\[z \cdot \left(y + x\right) \]

Alternative 4
Accuracy	53.9%
Cost	192

\[z \cdot y \]

Reproduce

herbie shell --seed 2023151 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))