Linear.Matrix:fromQuaternion from linear-1.19.1.3, B

Average Error: 0.0 → 0.0

Time: 1.9s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

   \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(x + y\right)\right)} \]
   Proof
   (*.f64 2 (*.f64 x (+.f64 x y))): 0 points increase in error, 0 points decrease in error
   (*.f64 2 (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 x x) (*.f64 x y)))): 1 points increase in error, 0 points decrease in error

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	8.7
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(2 \cdot x\right)\\ \mathbf{if}\;y \leq -6.559520391337449 \cdot 10^{-93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 52.47499184320267:\\ \;\;\;\;x \cdot \left(2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	32.3
Cost	320

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

Reproduce

herbie shell --seed 2022317 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

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

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