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

Average Error: 0.1 → 0.1

Time: 8.2s

Precision: binary64

Cost: 576

Math

\[\frac{\left(x + y\right) - z}{t \cdot 2} \]

↓

\[\frac{\left(x + y\right) - z}{t \cdot 2} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

↓

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

↓

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

↓

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

↓

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

↓

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

↓

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.1

   \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

2. Final simplification 0.1

   \[\leadsto \frac{\left(x + y\right) - z}{t \cdot 2} \]

Alternatives

Alternative 1
Error	36.4
Cost	1112

\[\begin{array}{l} t_1 := \frac{x \cdot 0.5}{t}\\ t_2 := y \cdot \frac{0.5}{t}\\ t_3 := z \cdot \frac{-0.5}{t}\\ \mathbf{if}\;x \leq -1.0132732407017941 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -462229.2683675224:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.061788441913674 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.460624122880587 \cdot 10^{-242}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.0037521080965203 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.3889196037009396 \cdot 10^{-98}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	36.4
Cost	1112

\[\begin{array}{l} t_1 := \frac{x \cdot 0.5}{t}\\ t_2 := \frac{y \cdot 0.5}{t}\\ t_3 := z \cdot \frac{-0.5}{t}\\ \mathbf{if}\;x \leq -1.0132732407017941 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -462229.2683675224:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.061788441913674 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.460624122880587 \cdot 10^{-242}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.0037521080965203 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.3889196037009396 \cdot 10^{-98}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	36.2
Cost	1112

\[\begin{array}{l} t_1 := \frac{x \cdot 0.5}{t}\\ t_2 := \frac{y \cdot 0.5}{t}\\ t_3 := -0.5 \cdot \frac{z}{t}\\ \mathbf{if}\;x \leq -1.0132732407017941 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -462229.2683675224:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.061788441913674 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.306902949410521 \cdot 10^{-275}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.0037521080965203 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.3889196037009396 \cdot 10^{-98}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	18.7
Cost	844

\[\begin{array}{l} t_1 := \frac{x \cdot 0.5}{t}\\ t_2 := 0.5 \cdot \frac{y - z}{t}\\ \mathbf{if}\;x \leq -8.58324146914392 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.0439071372700694 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.061788441913674 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	16.4
Cost	844

\[\begin{array}{l} t_1 := \frac{0.5}{t} \cdot \left(x + y\right)\\ \mathbf{if}\;x \leq -1.0132732407017941 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -462229.2683675224:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{elif}\;x \leq -2.061788441913674 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 6
Error	15.9
Cost	844

\[\begin{array}{l} t_1 := 0.5 \cdot \frac{y - z}{t}\\ t_2 := 0.5 \cdot \frac{x - z}{t}\\ \mathbf{if}\;y \leq 1.1455358800208273 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 47444224272882.77:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2168887063111929 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	36.2
Cost	716

\[\begin{array}{l} t_1 := y \cdot \frac{0.5}{t}\\ t_2 := \frac{x \cdot 0.5}{t}\\ \mathbf{if}\;y \leq 1.1455358800208273 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 56228864226914520:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2168887063111929 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	0.3
Cost	576

\[\left(x + \left(y - z\right)\right) \cdot \frac{0.5}{t} \]

Alternative 9
Error	41.2
Cost	320

\[y \cdot \frac{0.5}{t} \]

Reproduce

herbie shell --seed 2022317 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))