?

\[x \cdot \left(y + z\right) + z \cdot 5 \]

↓

\[\mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right) \]

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

↓

(FPCore (x y z) :precision binary64 (fma z 5.0 (* x (+ z y))))

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

↓

double code(double x, double y, double z) {
	return fma(z, 5.0, (x * (z + y)));
}

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

↓

function code(x, y, z)
	return fma(z, 5.0, Float64(x * Float64(z + y)))
end

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(z * 5.0 + N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x \cdot \left(y + z\right) + z \cdot 5

↓

\mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right)

Original	0.1%
Target	0.1%
Herbie	0.03%

Derivation?

Initial program 0.1
\[x \cdot \left(y + z\right) + z \cdot 5 \]
Applied egg-rr0.03
\[\leadsto \color{blue}{\mathsf{fma}\left(z, 5, x \cdot \left(y + z\right)\right)} \]
Final simplification0.03
\[\leadsto \mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right) \]

Alternatives

Alternative 1
Error	38.07%
Cost	984

\[\begin{array}{l} \mathbf{if}\;x \leq -0.6:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-84}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-42}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+90}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2
Error	25.85%
Cost	850

\[\begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-168} \lor \neg \left(z \leq 3.8 \cdot 10^{-169}\right) \land \left(z \leq 5.6 \cdot 10^{-90} \lor \neg \left(z \leq 2.8 \cdot 10^{-41}\right)\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3
Error	19.53%
Cost	848

\[\begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ t_1 := z \cdot \left(5 + x\right)\\ \mathbf{if}\;x \leq -64000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-110}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	37.91%
Cost	721

\[\begin{array}{l} \mathbf{if}\;x \leq -0.6:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-85} \lor \neg \left(x \leq -6 \cdot 10^{-110}\right) \land x \leq 2.7 \cdot 10^{-42}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5
Error	0.1%
Cost	576

\[x \cdot \left(z + y\right) + z \cdot 5 \]

Alternative 6
Error	54.26%
Cost	192

\[z \cdot 5 \]

Reproduce?

herbie shell --seed 2023088 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

  (+ (* x (+ y z)) (* z 5.0)))

?

?

Error?

Target

Derivation?

Alternatives

Error

Reproduce?