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

Average Error: 0.09% → 0.09%

Time: 7.9s

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 0.09

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

2. Final simplification 0.09

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

Alternatives

Alternative 1
Error	22.41%
Cost	978

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+100} \lor \neg \left(z \leq 5 \cdot 10^{-51}\right) \land \left(z \leq 52000000 \lor \neg \left(z \leq 7.8 \cdot 10^{+108}\right)\right):\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]

Alternative 2
Error	47.18%
Cost	850

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+28} \lor \neg \left(z \leq 10^{-54} \lor \neg \left(z \leq 750000000\right) \land z \leq 5.3 \cdot 10^{+60}\right):\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]

Alternative 3
Error	55.66%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{\frac{t}{0.5}}\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-266} \lor \neg \left(x \leq 2.5 \cdot 10^{-242}\right) \land x \leq 8.5 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]

Alternative 4
Error	55.57%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{\frac{t}{0.5}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-266} \lor \neg \left(x \leq 2.8 \cdot 10^{-242}\right) \land x \leq 1.76 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{0.5}}\\ \end{array} \]

Alternative 5
Error	55.52%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{\frac{t}{0.5}}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-266} \lor \neg \left(x \leq 2.5 \cdot 10^{-242}\right) \land x \leq 3.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{0.5}}\\ \end{array} \]

Alternative 6
Error	23.51%
Cost	845

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+64} \lor \neg \left(x \leq -12.2\right) \land x \leq -1.55 \cdot 10^{-39}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 7
Error	24.51%
Cost	844

\[\begin{array}{l} t_1 := \frac{-0.5}{t} \cdot \left(z - x\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-32}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 8
Error	0.42%
Cost	576

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

Alternative 9
Error	64.36%
Cost	320

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

Reproduce

herbie shell --seed 2023088 
(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)))