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

Average Error: 0.0 → 0.0

Time: 10.9s

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	40.7
Cost	1512

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+106}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-81}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-145}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-210}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-289}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-222}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 2
Error	12.2
Cost	984

\[\begin{array}{l} t_0 := y \cdot \left(z - -1\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+52}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.00145:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+49}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+81}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3
Error	32.0
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-99}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 11200:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 4
Error	12.7
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 11200:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 5
Error	1.7
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 6
Error	24.3
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-102}:\\ \;\;\;\;\left(1 + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - -1\right)\\ \end{array} \]

Alternative 7
Error	38.7
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 9.6 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Error	42.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023075 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))