Average Error: 0.1 → 0.1
Time: 9.9s
Precision: binary64
Cost: 6976
\[\left(x \cdot y + z\right) \cdot y + t \]
↓
\[\mathsf{fma}\left(x \cdot y, y, y \cdot z\right) + t \]
(FPCore (x y z t) :precision binary64 (+ (* (+ (* x y) z) y) t))
↓
(FPCore (x y z t) :precision binary64 (+ (fma (* x y) y (* y z)) t))
double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}
↓
double code(double x, double y, double z, double t) {
	return fma((x * y), y, (y * z)) + t;
}

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

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

\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(x \cdot y, y, y \cdot z\right) + t

Error

Derivation

  1. Initial program 0.1

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

  2. Applied egg-rr0.1

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

  3. Final simplification0.1

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

Alternatives

Alternative 1
Error5.3
Cost712
\[\begin{array}{l} t_1 := y \cdot z + t\\ \mathbf{if}\;z \leq -872437828875427.8:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.02489281656601 \cdot 10^{-56}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 2
Error0.1
Cost704
\[t + \left(y \cdot z + y \cdot \left(x \cdot y\right)\right) \]
Alternative 3
Error0.1
Cost576
\[t + y \cdot \left(x \cdot y + z\right) \]
Alternative 4
Error25.5
Cost456
\[\begin{array}{l} \mathbf{if}\;t \leq -8.377948394168908 \cdot 10^{-119}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 9.479400839423347 \cdot 10^{-153}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 5
Error13.1
Cost452
\[\begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + t\\ \end{array} \]
Alternative 6
Error13.8
Cost320
\[y \cdot z + t \]
Alternative 7
Error30.3
Cost64
\[t \]

Error

Reproduce

herbie shell --seed 2022294 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))