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

↓

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

(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	0.1
Cost	6848

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

Alternative 2
Error	24.6
Cost	1248

\[\begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+202}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+76}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-63}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-109}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-15}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+169}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3
Error	12.7
Cost	848

\[\begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-109}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	24.2
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-63}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-109}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-15}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5
Error	1.0
Cost	712

\[\begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -250000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	15.3
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(5 + x\right)\\ \mathbf{if}\;z \leq -2.12 \cdot 10^{-97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-77}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	0.1
Cost	576

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

Alternative 8
Error	35.0
Cost	192

\[z \cdot 5 \]

Reproduce

herbie shell --seed 2022325 
(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