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

Average Error: 0.0 → 0.0

Time: 11.2s

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 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	35.8
Cost	1376

\[\begin{array}{l} t_1 := \frac{-0.5}{\frac{t}{z}}\\ t_2 := \frac{x \cdot 0.5}{t}\\ t_3 := \frac{y \cdot 0.5}{t}\\ \mathbf{if}\;x \leq -4.361299013214296 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -0.0011620768576852626:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.6659128887533902 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.2099350274059515 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.389299769456452 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.747932259324724 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.620119436775503 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.061861310051913 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	35.7
Cost	1376

\[\begin{array}{l} t_1 := z \cdot \frac{-0.5}{t}\\ t_2 := \frac{x \cdot 0.5}{t}\\ t_3 := \frac{y \cdot 0.5}{t}\\ \mathbf{if}\;x \leq -4.361299013214296 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -0.0011620768576852626:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.6659128887533902 \cdot 10^{-34}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -1.2099350274059515 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.389299769456452 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.0829898245218201 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.620119436775503 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.061861310051913 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	35.7
Cost	1376

\[\begin{array}{l} t_1 := -0.5 \cdot \frac{z}{t}\\ t_2 := \frac{x \cdot 0.5}{t}\\ t_3 := \frac{y \cdot 0.5}{t}\\ \mathbf{if}\;x \leq -4.361299013214296 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -0.0011620768576852626:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.6659128887533902 \cdot 10^{-34}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -1.2099350274059515 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.389299769456452 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.0829898245218201 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.620119436775503 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.061861310051913 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	14.9
Cost	844

\[\begin{array}{l} t_1 := 0.5 \cdot \frac{x - z}{t}\\ \mathbf{if}\;y \leq 1.4009320111895204 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.345850346240369 \cdot 10^{-39}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \mathbf{elif}\;y \leq 454228894.6735435:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x + y}}\\ \end{array} \]

Alternative 5
Error	14.9
Cost	844

\[\begin{array}{l} t_1 := 0.5 \cdot \frac{x - z}{t}\\ \mathbf{if}\;y \leq 1.4009320111895204 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.345850346240369 \cdot 10^{-39}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \mathbf{elif}\;y \leq 454228894.6735435:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]

Alternative 6
Error	14.3
Cost	712

\[\begin{array}{l} t_1 := -0.5 \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+188}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	14.3
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 454228894.6735435:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x + y}}\\ \end{array} \]

Alternative 8
Error	0.3
Cost	576

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

Alternative 9
Error	35.9
Cost	452

\[\begin{array}{l} \mathbf{if}\;x \leq -4.361299013214296 \cdot 10^{+31}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]

Alternative 10
Error	35.9
Cost	452

\[\begin{array}{l} \mathbf{if}\;x \leq -4.361299013214296 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]

Alternative 11
Error	35.9
Cost	452

\[\begin{array}{l} \mathbf{if}\;x \leq -4.361299013214296 \cdot 10^{+31}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]

Alternative 12
Error	41.6
Cost	320

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

Reproduce

herbie shell --seed 2022318 
(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)))