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

Average Accuracy: 100.0% → 100.0%

Time: 6.0s

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 100.0%

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

2. Applied egg-rr 100.0%

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

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	49.5%
Cost	1512

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+141}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6.6:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-270}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-188}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.009:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+211}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 2
Accuracy	49.3%
Cost	1248

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-270}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{-187}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.075:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3
Accuracy	81.6%
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+142}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-6}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4
Accuracy	80.9%
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+142}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 12.6:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+212}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Accuracy	81.3%
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+142}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 21.5:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+212}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6
Accuracy	97.3%
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
Accuracy	39.8%
Cost	460

\[\begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-115}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Accuracy	100.0%
Cost	448

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

Alternative 9
Accuracy	32.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023141 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))