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

Average Error: 0.0 → 0.0

Time: 15.9s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

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 * ((y + x) * z)) + (y + x);
}

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) * ((y + x) * z)) + (y + x)
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 * ((y + x) * z)) + (y + x);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Taylor expanded in z around 0 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	12.6
Cost	840

\[\begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;1 - z \leq 0.95:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 1.05:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	1.7
Cost	780

\[\begin{array}{l} t_0 := \left(y + x\right) \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-7}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 480000000:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	25.9
Cost	716

\[\begin{array}{l} t_0 := \left(1 - z\right) \cdot x\\ t_1 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-161}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	26.0
Cost	716

\[\begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-15}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-161}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	25.9
Cost	716

\[\begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-12}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-161}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot y\\ \end{array} \]

Alternative 6
Error	13.3
Cost	520

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	13.1
Cost	520

\[\begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -27:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	0.0
Cost	448

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

Alternative 9
Error	39.1
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10
Error	23.7
Cost	192

\[y + x \]

Alternative 11
Error	43.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023068 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))