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

Average Error: 0.02% → 0.02%

Time: 986.0ms

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (x * (x + 2.0d0)) + (y * y)
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 (x * (x + 2.0)) + (y * y);
}

Python

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

↓

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

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(x * Float64(x + 2.0)) + Float64(y * y))
end

MATLAB

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

↓

function tmp = code(x, y)
	tmp = (x * (x + 2.0)) + (y * y);
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[(x * N[(x + 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]

Target

Original	0.02%
Target	0.02%
Herbie	0.02%

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

Derivation

1. Initial program 0.02

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

2. Simplified 0.02

   \[\leadsto \color{blue}{x \cdot \left(2 + x\right) + y \cdot y} \]
   Proof

   [Start] 0.02	\[ \left(x \cdot 2 + x \cdot x\right) + y \cdot y \]
   distribute-lft-out [=>] 0.02	\[ \color{blue}{x \cdot \left(2 + x\right)} + y \cdot y \]

3. Final simplification 0.02

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

Reproduce

herbie shell --seed 2023102 
(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)))