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

Average Error: 0.0 → 0.0

Time: 6.6s

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	13.3
Cost	917

\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+211}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -15500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+173} \lor \neg \left(z \leq 2.3 \cdot 10^{+241}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	13.2
Cost	916

\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{+201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -30000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+254}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	12.9
Cost	916

\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+202}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	12.9
Cost	916

\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+199}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-6}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+233}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	2.1
Cost	905

\[\begin{array}{l} \mathbf{if}\;1 - z \leq -20000000000000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	13.4
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -15500 \lor \neg \left(z \leq 21000000000000\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	0.0
Cost	448

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

Alternative 8
Error	38.6
Cost	196

\[\begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9
Error	24.0
Cost	192

\[x + y \]

Alternative 10
Error	43.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023066 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))