Numeric.Log:$clog1p from log-domain-0.10.2.1, A

Average Error: 0.0 → 0.0

Time: 4.5s

Precision: binary64

Cost: 704

Math

\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y \]

↓

\[y \cdot y + \left(x \cdot x + x \cdot 2\right) \]

FPCore

(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))

↓

(FPCore (x y) :precision binary64 (+ (* y y) (+ (* x x) (* x 2.0))))

C

double code(double x, double y) {
	return ((x * 2.0) + (x * x)) + (y * y);
}

↓

double code(double x, double y) {
	return (y * y) + ((x * x) + (x * 2.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) + (x * x)) + (y * y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y * y) + ((x * x) + (x * 2.0d0))
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) + (x * x)) + (y * y);
}

↓

public static double code(double x, double y) {
	return (y * y) + ((x * x) + (x * 2.0));
}

Python

def code(x, y):
	return ((x * 2.0) + (x * x)) + (y * y)

↓

def code(x, y):
	return (y * y) + ((x * x) + (x * 2.0))

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) + Float64(x * x)) + Float64(y * y))
end

↓

function code(x, y)
	return Float64(Float64(y * y) + Float64(Float64(x * x) + Float64(x * 2.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) + (x * x)) + (y * y);
end

↓

function tmp = code(x, y)
	tmp = (y * y) + ((x * x) + (x * 2.0));
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(y * y), $MachinePrecision] + N[(N[(x * x), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

\[y \cdot y + \left(2 \cdot x + x \cdot x\right) \]

Derivation

1. Initial program 0.0

   \[\left(x \cdot 2 + x \cdot x\right) + y \cdot y \]

2. Final simplification 0.0

   \[\leadsto y \cdot y + \left(x \cdot x + x \cdot 2\right) \]

Alternatives

Alternative 1
Error	22.3
Cost	1232

\[\begin{array}{l} \mathbf{if}\;y \cdot y \leq 4.87003390152761 \cdot 10^{-308}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \cdot y \leq 2.554087250060537 \cdot 10^{-270}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;y \cdot y \leq 2.762706390561362 \cdot 10^{-245}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \cdot y \leq 9.20407117788922 \cdot 10^{-140}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 2
Error	9.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.9639238159190677 \cdot 10^{-58}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 6.580643267745813 \cdot 10^{-43}:\\ \;\;\;\;x \cdot x + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 3
Error	4.5
Cost	712

\[\begin{array}{l} t_0 := x \cdot x + y \cdot y\\ \mathbf{if}\;y \leq -2.050568675011294 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.580643267745813 \cdot 10^{-43}:\\ \;\;\;\;x \cdot x + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.4
Cost	712

\[\begin{array}{l} t_0 := x \cdot x + y \cdot y\\ \mathbf{if}\;x \leq -16023655.39004206:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.309380535345464:\\ \;\;\;\;y \cdot y + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	9.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.9639238159190677 \cdot 10^{-58}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 6.580643267745813 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 6
Error	0.0
Cost	576

\[y \cdot y + x \cdot \left(x + 2\right) \]

Alternative 7
Error	21.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.050568675011294 \cdot 10^{-100}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 6.580643267745813 \cdot 10^{-43}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 8
Error	42.2
Cost	192

\[x \cdot 2 \]

Reproduce

herbie shell --seed 2022294 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (+ (* y y) (+ (* 2.0 x) (* x x)))

  (+ (+ (* x 2.0) (* x x)) (* y y)))