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

Average Error: 0.0 → 0.0

Time: 6.2s

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	35.1
Cost	1112

\[\begin{array}{l} t_1 := \frac{0.5}{\frac{t}{x}}\\ t_2 := y \cdot \frac{0.5}{t}\\ t_3 := \frac{-0.5}{\frac{t}{z}}\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -0.075:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-179}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-303}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	35.1
Cost	1112

\[\begin{array}{l} t_1 := \frac{0.5}{\frac{t}{x}}\\ t_2 := y \cdot \frac{0.5}{t}\\ t_3 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+24}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -0.025:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-177}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-303}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	35.1
Cost	1112

\[\begin{array}{l} t_1 := \frac{x \cdot 0.5}{t}\\ t_2 := y \cdot \frac{0.5}{t}\\ t_3 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -0.00172:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-178}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-303}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	35.1
Cost	1112

\[\begin{array}{l} t_1 := \frac{x \cdot 0.5}{t}\\ t_2 := \frac{y \cdot 0.5}{t}\\ t_3 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{+23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -0.00095:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-178}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-303}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	29.9
Cost	584

\[\begin{array}{l} t_1 := z \cdot \frac{-0.5}{t}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	18.0
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{-24}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]

Alternative 7
Error	14.6
Cost	580

\[\begin{array}{l} \mathbf{if}\;x \leq -0.037:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 8
Error	14.5
Cost	580

\[\begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{-5}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 9
Error	0.3
Cost	576

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

Alternative 10
Error	40.4
Cost	320

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

Reproduce

herbie shell --seed 2022337 
(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)))