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

Average Error: 0.0 → 0.0

Time: 5.9s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (z + 1.0d0)
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) + (z * (x + y))
end function

Java

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

↓

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

Python

def code(x, y, z):
	return (x + y) * (z + 1.0)

↓

def code(x, y, z):
	return (x + y) + (z * (x + y))

Julia

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

↓

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

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (z + 1.0);
end

↓

function tmp = code(x, y, z)
	tmp = (x + y) + (z * (x + y));
end

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	41.2
Cost	1380

\[\begin{array}{l} \mathbf{if}\;y \leq -5.673606075966539 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.8036145574711574 \cdot 10^{-130}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq -1.364880366661958 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.86418918995815 \cdot 10^{-303}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 3.1306350735331903 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3148891024357139 \cdot 10^{-71}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 284912895422498100:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.2372921337502776 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+121}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 2
Error	12.2
Cost	984

\[\begin{array}{l} t_0 := x + x \cdot z\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+131}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1276315716.0921998:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.522133415164985 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.0465143978087564 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.946325292056102 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3
Error	25.0
Cost	980

\[\begin{array}{l} t_0 := x + x \cdot z\\ t_1 := y + y \cdot z\\ \mathbf{if}\;y \leq 1.5114795816327223 \cdot 10^{-148}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.911858793683972 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.838964024643599 \cdot 10^{-68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 284912895422498100:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1222481688434846 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	40.6
Cost	724

\[\begin{array}{l} \mathbf{if}\;y \leq -5.673606075966539 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.8036145574711574 \cdot 10^{-130}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq -1.364880366661958 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.86418918995815 \cdot 10^{-303}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 3.1306350735331903 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5
Error	12.9
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+131}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -232907.12960139074:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 0.09971435489618234:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 6
Error	1.5
Cost	712

\[\begin{array}{l} t_0 := y + z \cdot \left(x + y\right)\\ \mathbf{if}\;z \leq -232907.12960139074:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.09971435489618234:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	1.8
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(x + y\right)\\ \mathbf{if}\;z \leq -232907.12960139074:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.09971435489618234:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	0.0
Cost	448

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

Alternative 9
Error	39.7
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 3.1306350735331903 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10
Error	43.2
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))