?

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

↓

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

(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	25.5
Cost	984

\[\begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+27}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-47}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-86}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{-164}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-29}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+44}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 2
Error	14.2
Cost	848

\[\begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-86}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{-164}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	14.3
Cost	848

\[\begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{-47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{5 + x}{\frac{1}{z}}\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{-164}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	25.8
Cost	721

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-51}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-86} \lor \neg \left(x \leq -6.7 \cdot 10^{-164}\right) \land x \leq 2.8 \cdot 10^{-30}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5
Error	16.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-204} \lor \neg \left(z \leq 2.05 \cdot 10^{-106}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6
Error	0.1
Cost	576

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

Alternative 7
Error	0.1
Cost	576

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

Alternative 8
Error	35.0
Cost	192

\[z \cdot 5 \]

Reproduce?

herbie shell --seed 2023125 
(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?