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

Average Error: 0.0 → 0.0

Time: 6.3s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

↓

double code(double x, double y, double z) {
	return ((y + x) - (y * z)) - (z * x);
}

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 = ((y + x) - (y * z)) - (z * x)
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 ((y + x) - (y * z)) - (z * x);
}

Python

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

↓

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

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

↓

function code(x, y, z)
	return Float64(Float64(Float64(y + x) - Float64(y * z)) - Float64(z * x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

↓

function tmp = code(x, y, z)
	tmp = ((y + x) - (y * z)) - (z * x);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(N[(y + x), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(z * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Simplified 0.0

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

   [Start] 0.0	\[ \left(y - y \cdot z\right) + \left(x - x \cdot z\right) \]
   rational_best_oopsla_all_46_json_45_simplify-107 [<=] 0.0	\[ \color{blue}{\left(x + \left(y - y \cdot z\right)\right) - x \cdot z} \]
   rational_best_oopsla_all_46_json_45_simplify-108 [=>] 0.0	\[ \color{blue}{\left(\left(y + x\right) - y \cdot z\right)} - x \cdot z \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.0	\[ \left(\left(y + x\right) - y \cdot z\right) - \color{blue}{z \cdot x} \]

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	13.0
Cost	1360

\[\begin{array}{l} t_0 := \left(-z\right) \cdot x\\ t_1 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;1 - z \leq -2 \cdot 10^{+111}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 0.999:\\ \;\;\;\;t_1\\ \mathbf{elif}\;1 - z \leq 1.005:\\ \;\;\;\;y + x\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	12.7
Cost	980

\[\begin{array}{l} t_0 := \left(1 - z\right) \cdot x\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+171}:\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-6}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	12.7
Cost	980

\[\begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+170}:\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{elif}\;z \leq -3.95 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-10}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-6}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \end{array} \]

Alternative 4
Error	13.1
Cost	916

\[\begin{array}{l} t_0 := \left(-z\right) \cdot x\\ t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -230:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	1.7
Cost	648

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

Alternative 6
Error	0.0
Cost	576

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

Alternative 7
Error	13.7
Cost	520

\[\begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	39.4
Cost	460

\[\begin{array}{l} \mathbf{if}\;y \leq 3.85 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.00172:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 102000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9
Error	0.0
Cost	448

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

Alternative 10
Error	24.2
Cost	192

\[y + x \]

Alternative 11
Error	44.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))