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

Average Error: 0.0 → 0.0

Time: 4.7s

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	32.1
Cost	1644

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+162}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+124}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+81}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-166}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-144}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 0.061:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+61}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+157}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 2
Error	12.2
Cost	1244

\[\begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+163}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+124}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+83}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.053:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+151}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3
Error	12.7
Cost	1116

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+162}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+124}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+82}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 780:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+61}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+162}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4
Error	12.4
Cost	1116

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+163}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+124}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+81}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 0.053:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+163}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Error	32.4
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-165}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-146}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6.8:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 6
Error	1.7
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 7
Error	38.8
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 3.9 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Error	43.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023016 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))