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

Average Error: 0.0 → 0.0

Time: 4.9s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

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 + 1.0);
}

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 + 1.0d0)
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 + 1.0);
}

Python

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

↓

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

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 + 1.0))
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 + 1.0);
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 + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	32.5
Cost	1248

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-156}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-249}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-33}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 2
Error	33.0
Cost	1248

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-155}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-249}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-34}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3
Error	12.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-7} \lor \neg \left(z \leq 1.9 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Error	1.6
Cost	585

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

Alternative 5
Error	13.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6
Error	38.2
Cost	196

\[\begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Error	42.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))