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

Average Error: 0.1 → 0.1

Time: 6.9s

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	9.2
Cost	844

\[\begin{array}{l} t_1 := \frac{-0.5 \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;z \leq -3.75 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-33}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 2
Error	14.1
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+35} \lor \neg \left(z \leq 9.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]

Alternative 3
Error	8.9
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+34} \lor \neg \left(z \leq 7.6 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]

Alternative 4
Error	29.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+19} \lor \neg \left(z \leq 1.16 \cdot 10^{-32}\right):\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]

Alternative 5
Error	36.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{t}{0.5}}\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{-196}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]

Alternative 6
Error	36.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{t}{0.5}}\\ \mathbf{elif}\;x \leq -4.15 \cdot 10^{-196}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{0.5}}\\ \end{array} \]

Alternative 7
Error	36.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{t}{0.5}}\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{-195}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{0.5}}\\ \end{array} \]

Alternative 8
Error	0.3
Cost	576

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

Alternative 9
Error	40.9
Cost	320

\[z \cdot \frac{-0.5}{t} \]

Reproduce

herbie shell --seed 2023018 
(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)))