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

↓

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

(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	0.0

Derivation

Initial program 0.1
\[x \cdot \left(y + z\right) + z \cdot 5 \]
Applied egg-rr0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(z, 5, x \cdot \left(y + z\right)\right)} \]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right) \]

Alternatives

Alternative 1
Error	18.0
Cost	848

\[\begin{array}{l} t_0 := z \cdot \left(5 + x\right)\\ \mathbf{if}\;z \leq -6.820817376087832 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.0111534923617882 \cdot 10^{-122}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -2.794700044604555 \cdot 10^{-168}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;z \leq 4.259474682177983 \cdot 10^{-160}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.9
Cost	712

\[\begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -966.3580826460436:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.015152388874615239:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	23.1
Cost	588

\[\begin{array}{l} \mathbf{if}\;x \leq -0.010586985840304172:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.0884141016591867 \cdot 10^{-41}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+66}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 4
Error	11.7
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -0.010586985840304172:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.0884141016591867 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	0.1
Cost	576

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

Alternative 6
Error	35.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -6.271056366795618 \cdot 10^{-158}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.77120145618851 \cdot 10^{-115}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7
Error	40.0
Cost	192

\[x \cdot y \]

Reproduce

herbie shell --seed 2022316 
(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