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

Average Error: 0.0 → 0.0

Time: 4.4s

Precision: binary64

Cost: 704

Math

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

↓

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

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(x + y) + Float64(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[(x + y), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	32.1
Cost	1512

\[\begin{array}{l} \mathbf{if}\;z \leq -175000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.12 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-146}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-196}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-106}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 2
Error	39.5
Cost	1512

\[\begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-302}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-139}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-115}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-115}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1000000000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+22}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3
Error	12.1
Cost	716

\[\begin{array}{l} t_0 := y \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+50}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -0.0024:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.00046:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	24.8
Cost	716

\[\begin{array}{l} t_0 := y \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq 10^{-172}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-141}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-46}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	12.6
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+48}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.4:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6
Error	1.6
Cost	584

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

Alternative 7
Error	0.0
Cost	576

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

Alternative 8
Error	38.5
Cost	460

\[\begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-115}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9
Error	0.0
Cost	448

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

Alternative 10
Error	42.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022329 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))