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

Average Error: 0.0 → 0.0

Time: 5.1s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (* (+ z 1.0) (+ 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 (z + 1.0) * (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 = (z + 1.0d0) * (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 (z + 1.0) * (x + y);
}

Python

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

↓

def code(x, y, z):
	return (z + 1.0) * (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(z + 1.0) * 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 = (z + 1.0) * (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[(z + 1.0), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	32.5
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+35}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1569656.80020315:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.721504924031365 \cdot 10^{-152}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.317552863928842 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5427622629783687 \cdot 10^{-57}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3458.740052376808:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 2
Error	32.8
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -1569656.80020315:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.721504924031365 \cdot 10^{-152}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.317552863928842 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5427622629783687 \cdot 10^{-57}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4.4552649754634 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3
Error	12.8
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+35}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1569656.80020315:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.922054069000986 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 137918518.19776228:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4
Error	12.5
Cost	716

\[\begin{array}{l} t_0 := y + y \cdot z\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+35}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -0.0010153119489744239:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.4552649754634 \cdot 10^{-6}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	1.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1569656.80020315:\\ \;\;\;\;z \cdot \left(x + y\right)\\ \mathbf{elif}\;z \leq 0.31326431225840107:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + x \cdot z\\ \end{array} \]

Alternative 6
Error	13.1
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+35}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1569656.80020315:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 137918518.19776228:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7
Error	1.8
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(x + y\right)\\ \mathbf{if}\;z \leq -1569656.80020315:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.31326431225840107:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	38.8
Cost	460

\[\begin{array}{l} \mathbf{if}\;x \leq -0.0021538445002805186:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.736361427816829 \cdot 10^{-55}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.0437138918385737 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9
Error	43.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022297 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))