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

Average Error: 0.02% → 0.01%

Time: 6.8s

Precision: binary64

Cost: 6720

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

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.02

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

2. Applied egg-rr 0.02

   \[\leadsto \color{blue}{z \cdot y + z \cdot x} \]

3. Applied egg-rr 0.01

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

4. Final simplification 0.01

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

Alternatives

Alternative 1
Error	16.41%
Cost	324

\[\begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-47}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 2
Error	0.02%
Cost	320

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

Alternative 3
Error	47.29%
Cost	192

\[z \cdot y \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))