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

Average Error: 0.0 → 0.0

Time: 4.8s

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	1.8
Cost	904

\[\begin{array}{l} t_0 := z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{if}\;1 - z \leq -5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	12.6
Cost	848

\[\begin{array}{l} t_0 := y - y \cdot z\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -0.012463115845917512:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.390823441980683 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	24.3
Cost	716

\[\begin{array}{l} t_0 := y - y \cdot z\\ \mathbf{if}\;y \leq 6.957311779636474 \cdot 10^{-53}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;y \leq 6.559736004616496 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 643127.9441547139:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	13.0
Cost	652

\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.0385822915213954:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 0.004298408226721528:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	13.1
Cost	520

\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -490781.89883970364:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.004298408226721528:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	39.0
Cost	460

\[\begin{array}{l} \mathbf{if}\;y \leq 8.406130577890905 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5736050300217394 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.55946523652633 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Error	23.4
Cost	192

\[x + y \]

Alternative 8
Error	43.2
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022311 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))