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

Average Error: 0.0 → 0.0

Time: 6.5s

Precision: binary64

Cost: 704

Math

\[\left(x + y\right) \cdot \left(1 - z\right) \]

↓

\[\left(1 - z\right) \cdot x + \left(1 - z\right) \cdot y \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

↓

(FPCore (x y z) :precision binary64 (+ (* (- 1.0 z) x) (* (- 1.0 z) y)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

↓

double code(double x, double y, double z) {
	return ((1.0 - z) * x) + ((1.0 - z) * y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((1.0d0 - z) * x) + ((1.0d0 - z) * y)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

↓

public static double code(double x, double y, double z) {
	return ((1.0 - z) * x) + ((1.0 - z) * y);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

↓

def code(x, y, z):
	return ((1.0 - z) * x) + ((1.0 - z) * y)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

↓

function code(x, y, z)
	return Float64(Float64(Float64(1.0 - z) * x) + Float64(Float64(1.0 - z) * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

↓

function tmp = code(x, y, z)
	tmp = ((1.0 - z) * x) + ((1.0 - z) * y);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision] + N[(N[(1.0 - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\left(x + y\right) \cdot \left(1 - z\right) \]

2. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{\left(1 - z\right) \cdot x + y \cdot \left(1 - z\right)} \]

3. Final simplification 0.0

   \[\leadsto \left(1 - z\right) \cdot x + \left(1 - z\right) \cdot y \]

Alternatives

Alternative 1
Error	12.6
Cost	1113

\[\begin{array}{l} t_0 := \left(1 - z\right) \cdot x\\ t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-8}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+81} \lor \neg \left(z \leq 1.3 \cdot 10^{+219}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	12.7
Cost	1113

\[\begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-16}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-8}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+81} \lor \neg \left(z \leq 1.4 \cdot 10^{+219}\right):\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	13.1
Cost	1049

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.8:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+84} \lor \neg \left(z \leq 1.32 \cdot 10^{+219}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	13.0
Cost	917

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -490:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+81} \lor \neg \left(z \leq 1.4 \cdot 10^{+219}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 5
Error	1.8
Cost	905

\[\begin{array}{l} \mathbf{if}\;1 - z \leq -1000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	13.5
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -120 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	0.0
Cost	448

\[\left(1 - z\right) \cdot \left(x + y\right) \]

Alternative 8
Error	40.2
Cost	196

\[\begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9
Error	24.1
Cost	192

\[x + y \]

Alternative 10
Error	43.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023060 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))