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

Average Error: 0.0 → 0.0

Time: 3.6s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

↓

double code(double x, double y, double z) {
	return (1.0 - z) * (x + y);
}

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) * (1.0d0 - z)
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 = (1.0d0 - z) * (x + y)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

↓

public static double code(double x, double y, double z) {
	return (1.0 - z) * (x + y);
}

Python

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

↓

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

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

↓

function code(x, y, z)
	return Float64(Float64(1.0 - z) * Float64(x + y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

↓

function tmp = code(x, y, z)
	tmp = (1.0 - z) * (x + y);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	12.6
Cost	1360

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;1 - z \leq -8 \cdot 10^{+205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -20:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 1.000000000001:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 2
Error	31.3
Cost	1360

\[\begin{array}{l} \mathbf{if}\;1 - z \leq -8 \cdot 10^{+205}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;1 - z \leq 1.000000000001:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 3
Error	1.7
Cost	904

\[\begin{array}{l} t_0 := z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{if}\;1 - z \leq -20:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	12.8
Cost	784

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -432.59138076847006:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.01988196549529779:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+205}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	12.8
Cost	520

\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -432.59138076847006:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.01988196549529779:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	39.1
Cost	460

\[\begin{array}{l} \mathbf{if}\;x \leq -62147770860.630646:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.1724524457345529 \cdot 10^{-32}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.3571155631350517 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Error	23.7
Cost	192

\[x + y \]

Alternative 8
Error	43.2
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022291 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))