Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G

Average Error: 0.0 → 0.0

Time: 51.0s

Precision: binary64

Cost: 6976

Math

\[\left(x + y\right) \cdot \left(z + 1\right) \]

↓

\[\mathsf{fma}\left(1 + z, y, x \cdot \left(1 + z\right)\right) \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))

↓

(FPCore (x y z) :precision binary64 (fma (+ 1.0 z) y (* x (+ 1.0 z))))

C

double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

↓

double code(double x, double y, double z) {
	return fma((1.0 + z), y, (x * (1.0 + z)));
}

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(z + 1.0))
end

↓

function code(x, y, z)
	return fma(Float64(1.0 + z), y, Float64(x * Float64(1.0 + z)))
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(1.0 + z), $MachinePrecision] * y + N[(x * N[(1.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\left(x + y\right) \cdot \left(z + 1\right) \]

2. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(1 + z, y, x \cdot \left(1 + z\right)\right)} \]

Alternatives

Alternative 1
Error	32.8
Cost	1776

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+86}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+21}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-37}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-127}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-155}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-299}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-181}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00145:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 2
Error	32.7
Cost	1512

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-37}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-127}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-155}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-299}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-181}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3
Error	13.3
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+86}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 19.5:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 4
Error	12.8
Cost	716

\[\begin{array}{l} t_0 := \left(1 + z\right) \cdot x\\ \mathbf{if}\;z \leq -9 \cdot 10^{+85}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -0.0098:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-9}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	34.4
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-91}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-77}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	1.7
Cost	584

\[\begin{array}{l} t_0 := \left(y + x\right) \cdot z\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	0.0
Cost	448

\[\left(x + y\right) \cdot \left(z + 1\right) \]

Alternative 8
Error	42.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))