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

Average Error: 0.0 → 0.0

Time: 4.9s

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	31.9
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+170}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+39}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+102}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 2
Error	13.1
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+170}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.95 \cdot 10^{+40}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.35:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+103}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3
Error	1.7
Cost	584

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

Alternative 4
Error	31.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 360000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 5
Error	0.0
Cost	448

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

Alternative 6
Error	43.1
Cost	64

\[y \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))