Linear.Matrix:fromQuaternion from linear-1.19.1.3, A

Percentage Accurate: 95.1% → 100.0%

Time: 6.1s

Alternatives: 3

Speedup: 1.3×

• 28.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \left(x \cdot x - x \cdot y\right) \end{array} \]

FPCore

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

C

double code(double x, double y) {
	return 2.0 * ((x * 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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(x \cdot x - x \cdot y\right) \end{array} \]

FPCore

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

C

double code(double x, double y) {
	return 2.0 * ((x * 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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(x \cdot \left(x - y\right)\right) \end{array} \]

FPCore

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

C

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 - y))
end function

Java

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

Python

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

Julia

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 - y));
end

Wolfram

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

Derivation

1. Initial program 94.5%

   \[2 \cdot \left(x \cdot x - x \cdot y\right) \]
2. Step-by-step derivation

   1. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto 2 \cdot \left(x \cdot \left(x - y\right)\right) \]
6. Add Preprocessing

Alternative 2: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+26} \lor \neg \left(y \leq 5.7 \cdot 10^{-92}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.5e+26) (not (<= y 5.7e-92)))
   (* (* x y) (- 2.0))
   (* 2.0 (* x x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.5e+26) || !(y <= 5.7e-92)) {
		tmp = (x * y) * -2.0;
	} else {
		tmp = 2.0 * (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-7.5d+26)) .or. (.not. (y <= 5.7d-92))) then
        tmp = (x * y) * -2.0d0
    else
        tmp = 2.0d0 * (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -7.5e+26) || !(y <= 5.7e-92)) {
		tmp = (x * y) * -2.0;
	} else {
		tmp = 2.0 * (x * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.5e+26) or not (y <= 5.7e-92):
		tmp = (x * y) * -2.0
	else:
		tmp = 2.0 * (x * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.5e+26) || !(y <= 5.7e-92))
		tmp = Float64(Float64(x * y) * Float64(-2.0));
	else
		tmp = Float64(2.0 * Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -7.5e+26) || ~((y <= 5.7e-92)))
		tmp = (x * y) * -2.0;
	else
		tmp = 2.0 * (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.5e+26], N[Not[LessEqual[y, 5.7e-92]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * (-2.0)), $MachinePrecision], N[(2.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999941e26 or 5.70000000000000009e-92 < y

   1. Initial program 88.5%

      \[2 \cdot \left(x \cdot x - x \cdot y\right) \]
   2. Step-by-step derivation

      1. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 78.8%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(x \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 78.8%

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

      2. *-commutative 78.8%

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

      3. distribute-rgt-neg-in 78.8%

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

   7. Simplified 78.8%

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

   if -7.49999999999999941e26 < y < 5.70000000000000009e-92

   1. Initial program 100.0%

      \[2 \cdot \left(x \cdot x - x \cdot y\right) \]
   2. Step-by-step derivation

      1. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(x - y\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. distribute-lft-out-- 100.0%

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

      2. fma-neg 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(x, x, x \cdot \left(-y\right)\right)} \]
   7. Step-by-step derivation

      1. fma-undefine 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

      3. unsub-neg 100.0%

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

      4. add-sqr-sqrt 38.1%

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

      5. sqrt-unprod 89.3%

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

      6. sqr-neg 89.3%

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

      7. sqrt-unprod 51.2%

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

      8. add-sqr-sqrt 88.6%

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

      9. distribute-rgt-neg-out 88.6%

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

      10. neg-mul-1 88.6%

          \[\leadsto 2 \cdot \left(x \cdot x - \color{blue}{-1 \cdot \left(x \cdot y\right)}\right) \]

      11. *-commutative 88.6%

          \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

      12. *-commutative 88.6%

          \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

      13. add-sqr-sqrt 37.4%

          \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \left(x \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right)\right) \]

      14. sqrt-unprod 99.3%

          \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \left(x \cdot \color{blue}{\sqrt{y \cdot y}}\right)\right) \]

      15. sqr-neg 99.3%

          \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \left(x \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right)\right) \]

      16. sqrt-unprod 61.8%

          \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \left(x \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right)\right) \]

      17. add-sqr-sqrt 100.0%

          \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \left(x \cdot \color{blue}{\left(-y\right)}\right)\right) \]

      18. prod-diff 100.0%

          \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, x, -\left(x \cdot \left(-y\right)\right) \cdot -1\right) + \mathsf{fma}\left(-x \cdot \left(-y\right), -1, \left(x \cdot \left(-y\right)\right) \cdot -1\right)\right)} \]

   8. Applied egg-rr 100.0%

      \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, x, -\left(y \cdot x\right) \cdot -1\right) + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right)} \]
   9. Step-by-step derivation

      1. fma-undefine 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot x + \left(-\left(y \cdot x\right) \cdot -1\right)\right)} + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right) \]

      2. distribute-rgt-neg-in 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot x + \color{blue}{\left(y \cdot x\right) \cdot \left(--1\right)}\right) + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right) \]

      3. metadata-eval 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot x + \left(y \cdot x\right) \cdot \color{blue}{1}\right) + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right) \]

      4. *-rgt-identity 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot x + \color{blue}{y \cdot x}\right) + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right) \]

      5. distribute-rgt-in 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{x \cdot \left(x + y\right)} + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right) \]

      6. fma-undefine 100.0%

         \[\leadsto 2 \cdot \left(x \cdot \left(x + y\right) + \color{blue}{\left(\left(y \cdot x\right) \cdot -1 + \left(y \cdot x\right) \cdot -1\right)}\right) \]

      7. distribute-lft-out 100.0%

         \[\leadsto 2 \cdot \left(x \cdot \left(x + y\right) + \color{blue}{\left(y \cdot x\right) \cdot \left(-1 + -1\right)}\right) \]

      8. *-commutative 100.0%

         \[\leadsto 2 \cdot \left(x \cdot \left(x + y\right) + \color{blue}{\left(x \cdot y\right)} \cdot \left(-1 + -1\right)\right) \]

      9. metadata-eval 100.0%

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

   10. Simplified 100.0%

       \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(x + y\right) + \left(x \cdot y\right) \cdot -2\right)} \]
   11. Step-by-step derivation

       1. associate-*l* 100.0%

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

       2. distribute-lft-out 100.0%

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

   12. Applied egg-rr 100.0%

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

   13. Taylor expanded in x around inf 88.9%

       \[\leadsto 2 \cdot \left(x \cdot \color{blue}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+26} \lor \neg \left(y \leq 5.7 \cdot 10^{-92}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(x \cdot x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

   \[2 \cdot \left(x \cdot x - x \cdot y\right) \]
2. Step-by-step derivation

   1. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(x - y\right)\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. distribute-lft-out-- 94.5%

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

   2. fma-neg 94.9%

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

   3. distribute-rgt-neg-in 94.9%

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

6. Applied egg-rr 94.9%

   \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(x, x, x \cdot \left(-y\right)\right)} \]
7. Step-by-step derivation

   1. fma-undefine 94.5%

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

   2. distribute-rgt-neg-out 94.5%

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

   3. unsub-neg 94.5%

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

   4. add-sqr-sqrt 44.4%

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

   5. sqrt-unprod 68.7%

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

   6. sqr-neg 68.7%

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

   7. sqrt-unprod 30.2%

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

   8. add-sqr-sqrt 57.2%

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

   9. distribute-rgt-neg-out 57.2%

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

   10. neg-mul-1 57.2%

       \[\leadsto 2 \cdot \left(x \cdot x - \color{blue}{-1 \cdot \left(x \cdot y\right)}\right) \]

   11. *-commutative 57.2%

       \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   12. *-commutative 57.2%

       \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   13. add-sqr-sqrt 27.0%

       \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \left(x \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right)\right) \]

   14. sqrt-unprod 69.5%

       \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \left(x \cdot \color{blue}{\sqrt{y \cdot y}}\right)\right) \]

   15. sqr-neg 69.5%

       \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \left(x \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right)\right) \]

   16. sqrt-unprod 49.9%

       \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \left(x \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right)\right) \]

   17. add-sqr-sqrt 94.5%

       \[\leadsto 2 \cdot \left(x \cdot x - -1 \cdot \left(x \cdot \color{blue}{\left(-y\right)}\right)\right) \]

   18. prod-diff 87.5%

       \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, x, -\left(x \cdot \left(-y\right)\right) \cdot -1\right) + \mathsf{fma}\left(-x \cdot \left(-y\right), -1, \left(x \cdot \left(-y\right)\right) \cdot -1\right)\right)} \]

8. Applied egg-rr 87.5%

   \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(x, x, -\left(y \cdot x\right) \cdot -1\right) + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right)} \]
9. Step-by-step derivation

   1. fma-undefine 87.5%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot x + \left(-\left(y \cdot x\right) \cdot -1\right)\right)} + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right) \]

   2. distribute-rgt-neg-in 87.5%

      \[\leadsto 2 \cdot \left(\left(x \cdot x + \color{blue}{\left(y \cdot x\right) \cdot \left(--1\right)}\right) + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right) \]

   3. metadata-eval 87.5%

      \[\leadsto 2 \cdot \left(\left(x \cdot x + \left(y \cdot x\right) \cdot \color{blue}{1}\right) + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right) \]

   4. *-rgt-identity 87.5%

      \[\leadsto 2 \cdot \left(\left(x \cdot x + \color{blue}{y \cdot x}\right) + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right) \]

   5. distribute-rgt-in 90.2%

      \[\leadsto 2 \cdot \left(\color{blue}{x \cdot \left(x + y\right)} + \mathsf{fma}\left(y \cdot x, -1, \left(y \cdot x\right) \cdot -1\right)\right) \]

   6. fma-undefine 90.2%

      \[\leadsto 2 \cdot \left(x \cdot \left(x + y\right) + \color{blue}{\left(\left(y \cdot x\right) \cdot -1 + \left(y \cdot x\right) \cdot -1\right)}\right) \]

   7. distribute-lft-out 90.2%

      \[\leadsto 2 \cdot \left(x \cdot \left(x + y\right) + \color{blue}{\left(y \cdot x\right) \cdot \left(-1 + -1\right)}\right) \]

   8. *-commutative 90.2%

      \[\leadsto 2 \cdot \left(x \cdot \left(x + y\right) + \color{blue}{\left(x \cdot y\right)} \cdot \left(-1 + -1\right)\right) \]

   9. metadata-eval 90.2%

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

10. Simplified 90.2%

    \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(x + y\right) + \left(x \cdot y\right) \cdot -2\right)} \]
11. Step-by-step derivation

    1. associate-*l* 90.2%

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

    2. distribute-lft-out 100.0%

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

12. Applied egg-rr 100.0%

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

13. Taylor expanded in x around inf 62.8%

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

14. Final simplification 62.8%

    \[\leadsto 2 \cdot \left(x \cdot x\right) \]
15. Add Preprocessing

Developer target: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 2\right) \cdot \left(x - y\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024066 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (* (* x 2.0) (- x y))

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