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

Average Accuracy: 100.0% → 100.0%

Time: 7.3s

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 100.0%

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

2. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ \left(x + y\right) \cdot \left(1 - z\right) \]
   sub-neg [=>] 100.0	\[ \left(x + y\right) \cdot \color{blue}{\left(1 + \left(-z\right)\right)} \]
   distribute-lft-in [=>] 100.0	\[ \color{blue}{\left(x + y\right) \cdot 1 + \left(x + y\right) \cdot \left(-z\right)} \]
   *-commutative [<=] 100.0	\[ \color{blue}{1 \cdot \left(x + y\right)} + \left(x + y\right) \cdot \left(-z\right) \]
   *-un-lft-identity [<=] 100.0	\[ \color{blue}{\left(x + y\right)} + \left(x + y\right) \cdot \left(-z\right) \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	60.9%
Cost	1246

\[\begin{array}{l} t_0 := x - x \cdot z\\ \mathbf{if}\;y \leq 1.7 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-94} \lor \neg \left(y \leq 7.5 \cdot 10^{-57}\right) \land \left(y \leq 1.2 \cdot 10^{-37} \lor \neg \left(y \leq 1.3 \cdot 10^{+27}\right) \land y \leq 6 \cdot 10^{+48}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 2
Accuracy	97.4%
Cost	905

\[\begin{array}{l} \mathbf{if}\;1 - z \leq -500 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Accuracy	79.1%
Cost	784

\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	79.4%
Cost	784

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.0069:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Accuracy	79.0%
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -3900000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Accuracy	38.1%
Cost	460

\[\begin{array}{l} \mathbf{if}\;x \leq -62:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-61}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Accuracy	100.0%
Cost	448

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

Alternative 8
Accuracy	62.1%
Cost	192

\[x + y \]

Alternative 9
Accuracy	32.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023147 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))