Linear.Matrix:fromQuaternion from linear-1.19.1.3, A

Average Error: 0.0 → 0.0

Time: 1.9s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	7.4
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(x \cdot -2\right)\\ \mathbf{if}\;y \leq -3.0839489774634305 \cdot 10^{-38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.738509804752915 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	21.7
Cost	320

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

Reproduce

herbie shell --seed 2022228 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

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

  (* 2.0 (- (* x x) (* x y))))