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

Average Error: 0.0 → 0.0

Time: 5.7s

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	12.9
Cost	1880

\[\begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;1 - z \leq -5 \cdot 10^{+234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;1 - z \leq -2 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -10000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;1 - z \leq -500000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 500000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+131}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	2.0
Cost	1424

\[\begin{array}{l} t_0 := z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{if}\;1 - z \leq -500000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 500000000:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;1 - z \leq 2 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	25.0
Cost	980

\[\begin{array}{l} t_0 := x - x \cdot z\\ t_1 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;y \leq 1.5114795816327223 \cdot 10^{-148}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.911858793683972 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.838964024643599 \cdot 10^{-68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 284912895422498100:\\ \;\;\;\;y - y \cdot z\\ \mathbf{elif}\;y \leq 3.1222481688434846 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	12.7
Cost	848

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := y - y \cdot z\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1276315716.0921998:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.09971435489618234:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+234}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	12.9
Cost	784

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1276315716.0921998:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.09971435489618234:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+234}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	13.3
Cost	520

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -232907.12960139074:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.09971435489618234:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	39.5
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 1.5114795816327223 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Error	23.8
Cost	192

\[x + y \]

Alternative 9
Error	43.2
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))