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

Average Error: 0.0 → 0.0

Time: 10.5s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

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 + 1.0);
}

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 + 1.0d0)
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 + 1.0);
}

Python

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

↓

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

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(z + 1.0))
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 + 1.0);
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[(z + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	40.2
Cost	1116

\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+22}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-49}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-150}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-239}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 2
Error	12.9
Cost	1112

\[\begin{array}{l} t_0 := \left(1 + z\right) \cdot x\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+185}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+68}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -0.0002:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-20}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(1 + z\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+70}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 3
Error	13.1
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+189}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+68}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-20}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(1 + z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+76}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 4
Error	13.2
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+187}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+69}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+15}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+73}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 5
Error	39.3
Cost	724

\[\begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{+18}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-50}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6
Error	1.6
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 7
Error	38.2
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Error	42.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023077 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))