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

Average Error: 0.0 → 0.0

Time: 5.6s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

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) + (y * z)) + (x * z);
}

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) + (y * z)) + (x * z)
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) + (y * z)) + (x * z);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	32.6
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-297}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-221}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.078:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 2
Error	32.8
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -0.000226:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-293}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-221}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.095:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3
Error	12.5
Cost	716

\[\begin{array}{l} t_0 := y \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -0.00032:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+134}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 4
Error	24.5
Cost	716

\[\begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-91}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-132}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 5
Error	13.0
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 190000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+135}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 6
Error	1.8
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	38.1
Cost	460

\[\begin{array}{l} \mathbf{if}\;x \leq -118000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Error	0.0
Cost	448

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

Alternative 9
Error	43.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022343 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))