\[\left(\frac{x}{2} + y \cdot x\right) + z \]

↓

\[\mathsf{fma}\left(x, y + 0.5, z\right) \]

(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))

↓

(FPCore (x y z) :precision binary64 (fma x (+ y 0.5) z))

double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

↓

double code(double x, double y, double z) {
	return fma(x, (y + 0.5), z);
}

function code(x, y, z)
	return Float64(Float64(Float64(x / 2.0) + Float64(y * x)) + z)
end

↓

function code(x, y, z)
	return fma(x, Float64(y + 0.5), z)
end

code[x_, y_, z_] := N[(N[(N[(x / 2.0), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

↓

code[x_, y_, z_] := N[(x * N[(y + 0.5), $MachinePrecision] + z), $MachinePrecision]

\left(\frac{x}{2} + y \cdot x\right) + z

↓

\mathsf{fma}\left(x, y + 0.5, z\right)

Derivation

Initial program 0.0
\[\left(\frac{x}{2} + y \cdot x\right) + z \]
Applied egg-rr0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(x, y + 0.5, z\right)} \]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(x, y + 0.5, z\right) \]

Alternatives

Alternative 1
Error	29.0
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1579974111594026 \cdot 10^{-88}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7.194918048588965 \cdot 10^{-194}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;z \leq 5.712248937390512 \cdot 10^{-149}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 4.664629525171111 \cdot 10^{-134}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;z \leq 5.134227242420965 \cdot 10^{-119}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.100189012993165 \cdot 10^{+81}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 2
Error	11.5
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+114}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3.2097596329413378 \cdot 10^{+63}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -190000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+88}:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3
Error	11.8
Cost	584

\[\begin{array}{l} t_0 := z + x \cdot 0.5\\ \mathbf{if}\;z \leq -1.1579974111594026 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.100189012993165 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.0
Cost	584

\[\begin{array}{l} t_0 := z + x \cdot y\\ \mathbf{if}\;y \leq -190000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0003449627705008839:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	0.0
Cost	576

\[z + \left(\frac{x}{2} + x \cdot y\right) \]

Alternative 6
Error	27.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1579974111594026 \cdot 10^{-88}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.664629525171111 \cdot 10^{-134}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7
Error	34.6
Cost	64

\[z \]

Reproduce

herbie shell --seed 2022295 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2.0) (* y x)) z))

Error

Derivation

Alternatives

Error

Reproduce