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

Average Error: 0.1 → 0.1

Time: 9.2s

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	15.7
Cost	1240

\[\begin{array}{l} t_1 := \frac{z \cdot -0.5}{t}\\ t_2 := 0.5 \cdot \frac{x + y}{t}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+267}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	36.0
Cost	981

\[\begin{array}{l} t_1 := \frac{0.5}{\frac{t}{x}}\\ t_2 := z \cdot \frac{-0.5}{t}\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{-230} \lor \neg \left(x \leq 1.16 \cdot 10^{-279}\right):\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	35.9
Cost	981

\[\begin{array}{l} t_1 := \frac{x}{\frac{t}{0.5}}\\ t_2 := z \cdot \frac{-0.5}{t}\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-231} \lor \neg \left(x \leq 2.65 \cdot 10^{-281}\right):\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	35.9
Cost	981

\[\begin{array}{l} t_1 := \frac{x}{\frac{t}{0.5}}\\ t_2 := z \cdot \frac{-0.5}{t}\\ \mathbf{if}\;x \leq -2 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{-230} \lor \neg \left(x \leq 1.22 \cdot 10^{-275}\right):\\ \;\;\;\;\frac{y}{\frac{t}{0.5}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	35.9
Cost	981

\[\begin{array}{l} t_1 := \frac{x}{\frac{t}{0.5}}\\ t_2 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;x \leq -7 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-231} \lor \neg \left(x \leq 2.3 \cdot 10^{-282}\right):\\ \;\;\;\;\frac{y}{\frac{t}{0.5}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	9.2
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+15} \lor \neg \left(z \leq 3.5 \cdot 10^{+65}\right):\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]

Alternative 7
Error	15.2
Cost	708

\[\begin{array}{l} \mathbf{if}\;y \leq 130:\\ \;\;\;\;\frac{-0.5 \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \end{array} \]

Alternative 8
Error	15.4
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 9
Error	15.3
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{-0.5 \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 10
Error	0.3
Cost	576

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

Alternative 11
Error	36.1
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 160:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 12
Error	41.3
Cost	320

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

Reproduce

herbie shell --seed 2023039 
(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)))