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

Average Error: 0.0 → 0.0

Time: 5.5s

Precision: binary64

Cost: 704

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

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	31.7
Cost	1881

\[\begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;z + 1 \leq -2 \cdot 10^{+50}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z + 1 \leq 1.00000005:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 10^{+82} \lor \neg \left(z + 1 \leq 1.5 \cdot 10^{+219}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 2
Error	13.4
Cost	1752

\[\begin{array}{l} \mathbf{if}\;z + 1 \leq -2 \cdot 10^{+50}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq -400:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq 50000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 10^{+82}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq 1.5 \cdot 10^{+219}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3
Error	32.7
Cost	1644

\[\begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+50}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-215}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-284}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 48000000:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+84}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+219}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 4
Error	32.9
Cost	1116

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-215}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-285}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 48000000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 5
Error	1.8
Cost	841

\[\begin{array}{l} \mathbf{if}\;z + 1 \leq -400 \lor \neg \left(z + 1 \leq 2\right):\\ \;\;\;\;\left(x + y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	0.0
Cost	576

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

Alternative 7
Error	0.0
Cost	448

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

Alternative 8
Error	31.4
Cost	196

\[\begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9
Error	43.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023060 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))