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

Average Error: 0.0 → 0.0

Time: 4.3s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

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 * (y + x)));
}

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

Python

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	32.7
Cost	1248

\[\begin{array}{l} \mathbf{if}\;z \leq -7200000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-198}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-306}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-222}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-60}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 0.0002:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 2
Error	12.8
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-8}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3
Error	1.7
Cost	585

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

Alternative 4
Error	23.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-98}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 5
Error	12.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 78000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	38.6
Cost	196

\[\begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Error	43.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023187 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))