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

Average Error: 0.0 → 0.0

Time: 4.1s

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	1644

\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+179}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+101}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1522577718.922361:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.0814655738550956 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6887373226864847 \cdot 10^{-286}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.366556451162404 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.551762614963485 \cdot 10^{-154}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6.42736473523191 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.844224016686107 \cdot 10^{-112}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 0.24206959902655423:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+149}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 2
Error	32.4
Cost	1248

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4061406499523838 \cdot 10^{-11}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.0814655738550956 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6887373226864847 \cdot 10^{-286}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.366556451162404 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.551762614963485 \cdot 10^{-154}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6.42736473523191 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.844224016686107 \cdot 10^{-112}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 0.24206959902655423:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3
Error	13.5
Cost	980

\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+179}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+101}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1522577718.922361:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.509890152510585 \cdot 10^{-32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+149}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4
Error	13.2
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+179}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+101}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1522577718.922361:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 0.24206959902655423:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+149}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Error	1.9
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(x + y\right)\\ \mathbf{if}\;z \leq -1522577718.922361:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.24206959902655423:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	38.5
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 4.601476677276083 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Error	43.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022295 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))