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

Average Error: 0.03% → 0.03%

Time: 5.7s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (- (+ x y) (* 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 (x + y) - (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 = (x + y) - (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 (x + y) - (z * (x + y));
}

Python

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

↓

def code(x, y, z):
	return (x + y) - (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(x + y) - Float64(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 = (x + y) - (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[(x + y), $MachinePrecision] - N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.03

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

2. Applied egg-rr 0.03

   \[\leadsto \color{blue}{\left(x + y\right) + \left(x + y\right) \cdot \left(-z\right)} \]

3. Final simplification 0.03

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

Alternatives

Alternative 1
Error	19.92%
Cost	1880

\[\begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ t_1 := z \cdot \left(-x\right)\\ \mathbf{if}\;1 - z \leq -5 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;1 - z \leq 0.9999998:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 10^{+190}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	19.93%
Cost	1880

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;1 - z \leq -5 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 0.9999998:\\ \;\;\;\;y - y \cdot z\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 10^{+190}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	20.48%
Cost	1296

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;1 - z \leq -5 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 0.9999998:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	3.68%
Cost	905

\[\begin{array}{l} \mathbf{if}\;1 - z \leq -2 \cdot 10^{+15} \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	21.04%
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -45 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	20.81%
Cost	520

\[\begin{array}{l} \mathbf{if}\;z \leq -180:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 7
Error	0.03%
Cost	448

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

Alternative 8
Error	60.13%
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9
Error	37.22%
Cost	192

\[x + y \]

Alternative 10
Error	67.92%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023103 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))