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

Average Accuracy: 100.0% → 100.0%

Time: 3.7s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (+ (+ (* y z) (+ x y)) (* 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 ((y * z) + (x + y)) + (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 = ((y * z) + (x + y)) + (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 ((y * z) + (x + y)) + (x * z);
}

Python

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

↓

def code(x, y, z):
	return ((y * z) + (x + y)) + (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(y * z) + Float64(x + y)) + 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 = ((y * z) + (x + y)) + (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[(y * z), $MachinePrecision] + N[(x + y), $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%

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

   [Start] 100.0	\[ \left(x + y\right) \cdot \left(z + 1\right) \]
   *-commutative [=>] 100.0	\[ \color{blue}{\left(z + 1\right) \cdot \left(x + y\right)} \]
   distribute-lft1-in [<=] 100.0	\[ \color{blue}{z \cdot \left(x + y\right) + \left(x + y\right)} \]
   +-commutative [=>] 100.0	\[ \color{blue}{\left(x + y\right) + z \cdot \left(x + y\right)} \]
   +-commutative [=>] 100.0	\[ \left(x + y\right) + z \cdot \color{blue}{\left(y + x\right)} \]
   distribute-lft-in [=>] 100.0	\[ \left(x + y\right) + \color{blue}{\left(z \cdot y + z \cdot x\right)} \]
   *-commutative [<=] 100.0	\[ \left(x + y\right) + \left(\color{blue}{y \cdot z} + z \cdot x\right) \]
   associate-+r+ [=>] 100.0	\[ \color{blue}{\left(\left(x + y\right) + y \cdot z\right) + z \cdot x} \]
   *-commutative [=>] 100.0	\[ \left(\left(x + y\right) + y \cdot z\right) + \color{blue}{x \cdot z} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	38.6%
Cost	988

\[\begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-97}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-298}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{-281}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-227}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 2
Accuracy	80.0%
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-15}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3
Accuracy	61.6%
Cost	717

\[\begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 108000000000 \lor \neg \left(y \leq 3.6 \cdot 10^{+95}\right):\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Accuracy	79.5%
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 430000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+91}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 5
Accuracy	97.4%
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 6
Accuracy	100.0%
Cost	448

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

Alternative 7
Accuracy	40.5%
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 1.22 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Accuracy	32.6%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))