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

Average Accuracy: 99.9% → 99.9%

Time: 8.9s

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 99.9%

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

2. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	44.9%
Cost	1112

\[\begin{array}{l} t_1 := z \cdot \frac{-0.5}{t}\\ t_2 := y \cdot \frac{0.5}{t}\\ t_3 := \frac{x}{\frac{t}{0.5}}\\ \mathbf{if}\;y \leq 10^{-245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 27:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	44.9%
Cost	1112

\[\begin{array}{l} t_1 := z \cdot \frac{-0.5}{t}\\ t_2 := \frac{y}{\frac{t}{0.5}}\\ t_3 := \frac{x}{\frac{t}{0.5}}\\ \mathbf{if}\;y \leq 2.25 \cdot 10^{-243}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.102:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+57}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	45.0%
Cost	1112

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{0.5}}\\ t_2 := \frac{x}{\frac{t}{0.5}}\\ \mathbf{if}\;y \leq 1.3 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-37}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;y \leq 0.85:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.22 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	75.2%
Cost	845

\[\begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-58} \lor \neg \left(y \leq 39\right) \land y \leq 5.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 5
Accuracy	75.5%
Cost	845

\[\begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-58} \lor \neg \left(y \leq 0.46\right) \land y \leq 1.6 \cdot 10^{+55}:\\ \;\;\;\;\frac{-0.5 \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 6
Accuracy	73.8%
Cost	580

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{t}{0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 7
Accuracy	99.6%
Cost	576

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

Alternative 8
Accuracy	43.8%
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-37}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 9
Accuracy	36.3%
Cost	320

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

Reproduce

herbie shell --seed 2023137 
(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)))