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

Average Error: 0.0 → 0.0

Time: 6.0s

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 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	1.7
Cost	905

\[\begin{array}{l} \mathbf{if}\;1 - z \leq -50000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Error	12.1
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-8}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+130}:\\ \;\;\;\;y - y \cdot z\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 3
Error	12.3
Cost	784

\[\begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;z \leq -8.8:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 4
Error	12.7
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -2000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	12.6
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -35 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	38.9
Cost	460

\[\begin{array}{l} \mathbf{if}\;y \leq 5.8 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-59}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Error	25.2
Cost	452

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 8
Error	25.2
Cost	452

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-124}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 9
Error	0.0
Cost	448

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

Alternative 10
Error	23.0
Cost	192

\[x + y \]

Alternative 11
Error	42.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022364 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))