Result for xx*yy + yx*zy + zx*xy - xx*zy - yx*xy

Alternative 1: 95.2% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy\\ \mathbf{if}\;t\_0 \leq \infty:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(zx - yx, xy, \left(xx - zx\right) \cdot yy\right)\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (let* ((t_0
         (-
          (- (- (+ (+ (* xx yy) (* yx zy)) (* zx xy)) (* xx zy)) (* yx xy))
          (* zx yy))))
   (if (<= t_0 INFINITY) t_0 (fma (- zx yx) xy (* (- xx zx) yy)))))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double t_0 = (((((xx * yy) + (yx * zy)) + (zx * xy)) - (xx * zy)) - (yx * xy)) - (zx * yy);
	double tmp;
	if (t_0 <= ((double) INFINITY)) {
		tmp = t_0;
	} else {
		tmp = fma((zx - yx), xy, ((xx - zx) * yy));
	}
	return tmp;
}

function code(xx, yy, yx, zy, zx, xy)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(xx * yy) + Float64(yx * zy)) + Float64(zx * xy)) - Float64(xx * zy)) - Float64(yx * xy)) - Float64(zx * yy))
	tmp = 0.0
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = fma(Float64(zx - yx), xy, Float64(Float64(xx - zx) * yy));
	end
	return tmp
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(xx * yy), $MachinePrecision] + N[(yx * zy), $MachinePrecision]), $MachinePrecision] + N[(zx * xy), $MachinePrecision]), $MachinePrecision] - N[(xx * zy), $MachinePrecision]), $MachinePrecision] - N[(yx * xy), $MachinePrecision]), $MachinePrecision] - N[(zx * yy), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, Infinity], t$95$0, N[(N[(zx - yx), $MachinePrecision] * xy + N[(N[(xx - zx), $MachinePrecision] * yy), $MachinePrecision]), $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy\\
\mathbf{if}\;t\_0 \leq \infty:\\
\;\;\;\;t\_0\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(zx - yx, xy, \left(xx - zx\right) \cdot yy\right)\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if (-.f64 (-.f64 (-.f64 (+.f64 (+.f64 (*.f64 xx yy) (*.f64 yx zy)) (*.f64 zx xy)) (*.f64 xx zy)) (*.f64 yx xy)) (*.f64 zx yy)) < +inf.0
1. Initial program 100.0%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
if +inf.0 < (-.f64 (-.f64 (-.f64 (+.f64 (+.f64 (*.f64 xx yy) (*.f64 yx zy)) (*.f64 zx xy)) (*.f64 xx zy)) (*.f64 yx xy)) (*.f64 zx yy))
1. Initial program 0.0%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
4. Step-by-step derivation
  1. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xy \cdot zx + xx \cdot yy\right)} - \left(xy \cdot yx + yy \cdot zx\right) \]
  2. associate--l+N/A
    \[\leadsto \color{blue}{xy \cdot zx + \left(xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  3. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  4. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{xx \cdot yy + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)}\right) \]
  5. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\mathsf{neg}\left(\color{blue}{\left(yy \cdot zx + xy \cdot yx\right)}\right)\right)\right) \]
  6. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \color{blue}{\left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(xy \cdot yx\right)\right)\right)}\right) \]
  7. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(\color{blue}{yx \cdot xy}\right)\right)\right)\right) \]
  8. distribute-lft-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \color{blue}{\left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right)\right) \]
  9. associate-+r+N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right) \]
  10. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(\color{blue}{yy \cdot xx} + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  11. distribute-rgt-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + \color{blue}{yy \cdot \left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  12. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + yy \cdot \color{blue}{\left(-1 \cdot zx\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  13. distribute-lft-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{yy \cdot \left(xx + -1 \cdot zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  14. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \left(xx + \color{blue}{\left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  15. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \color{blue}{\left(xx - zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  16. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx - zx\right) \cdot yy} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  17. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)}\right) \]
  18. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \mathsf{fma}\left(\color{blue}{xx - zx}, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)\right) \]
5. Applied rewrites56.4%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, \mathsf{fma}\left(xx - zx, yy, \left(-yx\right) \cdot xy\right)\right)} \]
6. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
7. Step-by-step derivation
  1. sub-negN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)} \]
  2. neg-mul-1N/A
    \[\leadsto \left(xx \cdot yy + xy \cdot zx\right) + \color{blue}{-1 \cdot \left(xy \cdot yx + yy \cdot zx\right)} \]
  3. distribute-lft-outN/A
    \[\leadsto \left(xx \cdot yy + xy \cdot zx\right) + \color{blue}{\left(-1 \cdot \left(xy \cdot yx\right) + -1 \cdot \left(yy \cdot zx\right)\right)} \]
  4. +-commutativeN/A
    \[\leadsto \left(xx \cdot yy + xy \cdot zx\right) + \color{blue}{\left(-1 \cdot \left(yy \cdot zx\right) + -1 \cdot \left(xy \cdot yx\right)\right)} \]
  5. associate-+l+N/A
    \[\leadsto \color{blue}{\left(\left(xx \cdot yy + xy \cdot zx\right) + -1 \cdot \left(yy \cdot zx\right)\right) + -1 \cdot \left(xy \cdot yx\right)} \]
  6. +-commutativeN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yy \cdot zx\right) + \left(xx \cdot yy + xy \cdot zx\right)\right)} + -1 \cdot \left(xy \cdot yx\right) \]
  7. associate-+r+N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yy \cdot zx\right) + xx \cdot yy\right) + xy \cdot zx\right)} + -1 \cdot \left(xy \cdot yx\right) \]
  8. associate-+l+N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yy \cdot zx\right) + xx \cdot yy\right) + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right)} \]
  9. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy + -1 \cdot \left(yy \cdot zx\right)\right)} + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  10. mul-1-negN/A
    \[\leadsto \left(xx \cdot yy + \color{blue}{\left(\mathsf{neg}\left(yy \cdot zx\right)\right)}\right) + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  11. unsub-negN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy - yy \cdot zx\right)} + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  12. *-commutativeN/A
    \[\leadsto \left(\color{blue}{yy \cdot xx} - yy \cdot zx\right) + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  13. distribute-lft-out--N/A
    \[\leadsto \color{blue}{yy \cdot \left(xx - zx\right)} + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  14. mul-1-negN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \left(xy \cdot zx + \color{blue}{\left(\mathsf{neg}\left(xy \cdot yx\right)\right)}\right) \]
  15. distribute-rgt-neg-inN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \left(xy \cdot zx + \color{blue}{xy \cdot \left(\mathsf{neg}\left(yx\right)\right)}\right) \]
  16. mul-1-negN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \left(xy \cdot zx + xy \cdot \color{blue}{\left(-1 \cdot yx\right)}\right) \]
  17. distribute-lft-inN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \color{blue}{xy \cdot \left(zx + -1 \cdot yx\right)} \]
  18. +-commutativeN/A
    \[\leadsto \color{blue}{xy \cdot \left(zx + -1 \cdot yx\right) + yy \cdot \left(xx - zx\right)} \]
8. Applied rewrites66.2%
  \[\leadsto \color{blue}{\mathsf{fma}\left(zx - yx, xy, \left(xx - zx\right) \cdot yy\right)} \]
Recombined 2 regimes into one program.
Add Preprocessing

Alternative 2: 80.9% accurate, 1.1× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(zy, yx, \mathsf{fma}\left(xx - zx, yy, \left(-xx\right) \cdot zy\right)\right)\\ \mathbf{if}\;zy \leq -1.5 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;zy \leq 4 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(zx - yx, xy, \left(xx - zx\right) \cdot yy\right)\\ \mathbf{elif}\;zy \leq 2.5 \cdot 10^{+199}:\\ \;\;\;\;\mathsf{fma}\left(yy - zy, xx, \left(xy - yy\right) \cdot zx\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (let* ((t_0 (fma zy yx (fma (- xx zx) yy (* (- xx) zy)))))
   (if (<= zy -1.5e-26)
     t_0
     (if (<= zy 4e+33)
       (fma (- zx yx) xy (* (- xx zx) yy))
       (if (<= zy 2.5e+199) (fma (- yy zy) xx (* (- xy yy) zx)) t_0)))))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double t_0 = fma(zy, yx, fma((xx - zx), yy, (-xx * zy)));
	double tmp;
	if (zy <= -1.5e-26) {
		tmp = t_0;
	} else if (zy <= 4e+33) {
		tmp = fma((zx - yx), xy, ((xx - zx) * yy));
	} else if (zy <= 2.5e+199) {
		tmp = fma((yy - zy), xx, ((xy - yy) * zx));
	} else {
		tmp = t_0;
	}
	return tmp;
}

function code(xx, yy, yx, zy, zx, xy)
	t_0 = fma(zy, yx, fma(Float64(xx - zx), yy, Float64(Float64(-xx) * zy)))
	tmp = 0.0
	if (zy <= -1.5e-26)
		tmp = t_0;
	elseif (zy <= 4e+33)
		tmp = fma(Float64(zx - yx), xy, Float64(Float64(xx - zx) * yy));
	elseif (zy <= 2.5e+199)
		tmp = fma(Float64(yy - zy), xx, Float64(Float64(xy - yy) * zx));
	else
		tmp = t_0;
	end
	return tmp
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := Block[{t$95$0 = N[(zy * yx + N[(N[(xx - zx), $MachinePrecision] * yy + N[((-xx) * zy), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[zy, -1.5e-26], t$95$0, If[LessEqual[zy, 4e+33], N[(N[(zx - yx), $MachinePrecision] * xy + N[(N[(xx - zx), $MachinePrecision] * yy), $MachinePrecision]), $MachinePrecision], If[LessEqual[zy, 2.5e+199], N[(N[(yy - zy), $MachinePrecision] * xx + N[(N[(xy - yy), $MachinePrecision] * zx), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \mathsf{fma}\left(zy, yx, \mathsf{fma}\left(xx - zx, yy, \left(-xx\right) \cdot zy\right)\right)\\
\mathbf{if}\;zy \leq -1.5 \cdot 10^{-26}:\\
\;\;\;\;t\_0\\

\mathbf{elif}\;zy \leq 4 \cdot 10^{+33}:\\
\;\;\;\;\mathsf{fma}\left(zx - yx, xy, \left(xx - zx\right) \cdot yy\right)\\

\mathbf{elif}\;zy \leq 2.5 \cdot 10^{+199}:\\
\;\;\;\;\mathsf{fma}\left(yy - zy, xx, \left(xy - yy\right) \cdot zx\right)\\

\mathbf{else}:\\
\;\;\;\;t\_0\\


\end{array}
\end{array}

Derivation

Split input into 3 regimes
if zy < -1.50000000000000006e-26 or 2.4999999999999999e199 < zy
1. Initial program 71.1%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in xy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + yx \cdot zy\right) - \left(xx \cdot zy + yy \cdot zx\right)} \]
4. Step-by-step derivation
  1. +-commutativeN/A
    \[\leadsto \color{blue}{\left(yx \cdot zy + xx \cdot yy\right)} - \left(xx \cdot zy + yy \cdot zx\right) \]
  2. associate--l+N/A
    \[\leadsto \color{blue}{yx \cdot zy + \left(xx \cdot yy - \left(xx \cdot zy + yy \cdot zx\right)\right)} \]
  3. *-commutativeN/A
    \[\leadsto \color{blue}{zy \cdot yx} + \left(xx \cdot yy - \left(xx \cdot zy + yy \cdot zx\right)\right) \]
  4. sub-negN/A
    \[\leadsto zy \cdot yx + \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(\left(xx \cdot zy + yy \cdot zx\right)\right)\right)\right)} \]
  5. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(zy, yx, xx \cdot yy + \left(\mathsf{neg}\left(\left(xx \cdot zy + yy \cdot zx\right)\right)\right)\right)} \]
  6. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(zy, yx, xx \cdot yy + \left(\mathsf{neg}\left(\color{blue}{\left(yy \cdot zx + xx \cdot zy\right)}\right)\right)\right) \]
  7. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(zy, yx, xx \cdot yy + \color{blue}{\left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(xx \cdot zy\right)\right)\right)}\right) \]
  8. distribute-lft-neg-inN/A
    \[\leadsto \mathsf{fma}\left(zy, yx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \color{blue}{\left(\mathsf{neg}\left(xx\right)\right) \cdot zy}\right)\right) \]
  9. associate-+r+N/A
    \[\leadsto \mathsf{fma}\left(zy, yx, \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(xx\right)\right) \cdot zy}\right) \]
  10. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(zy, yx, \left(\color{blue}{yy \cdot xx} + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(xx\right)\right) \cdot zy\right) \]
  11. distribute-rgt-neg-inN/A
    \[\leadsto \mathsf{fma}\left(zy, yx, \left(yy \cdot xx + \color{blue}{yy \cdot \left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(xx\right)\right) \cdot zy\right) \]
  12. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(zy, yx, \left(yy \cdot xx + yy \cdot \color{blue}{\left(-1 \cdot zx\right)}\right) + \left(\mathsf{neg}\left(xx\right)\right) \cdot zy\right) \]
  13. distribute-lft-inN/A
    \[\leadsto \mathsf{fma}\left(zy, yx, \color{blue}{yy \cdot \left(xx + -1 \cdot zx\right)} + \left(\mathsf{neg}\left(xx\right)\right) \cdot zy\right) \]
  14. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(zy, yx, yy \cdot \left(xx + \color{blue}{\left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(xx\right)\right) \cdot zy\right) \]
  15. sub-negN/A
    \[\leadsto \mathsf{fma}\left(zy, yx, yy \cdot \color{blue}{\left(xx - zx\right)} + \left(\mathsf{neg}\left(xx\right)\right) \cdot zy\right) \]
  16. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(zy, yx, \color{blue}{\left(xx - zx\right) \cdot yy} + \left(\mathsf{neg}\left(xx\right)\right) \cdot zy\right) \]
  17. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(zy, yx, \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(\mathsf{neg}\left(xx\right)\right) \cdot zy\right)}\right) \]
  18. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(zy, yx, \mathsf{fma}\left(\color{blue}{xx - zx}, yy, \left(\mathsf{neg}\left(xx\right)\right) \cdot zy\right)\right) \]
5. Applied rewrites79.4%
  \[\leadsto \color{blue}{\mathsf{fma}\left(zy, yx, \mathsf{fma}\left(xx - zx, yy, \left(-xx\right) \cdot zy\right)\right)} \]
if -1.50000000000000006e-26 < zy < 3.9999999999999998e33
1. Initial program 92.2%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
4. Step-by-step derivation
  1. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xy \cdot zx + xx \cdot yy\right)} - \left(xy \cdot yx + yy \cdot zx\right) \]
  2. associate--l+N/A
    \[\leadsto \color{blue}{xy \cdot zx + \left(xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  3. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  4. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{xx \cdot yy + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)}\right) \]
  5. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\mathsf{neg}\left(\color{blue}{\left(yy \cdot zx + xy \cdot yx\right)}\right)\right)\right) \]
  6. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \color{blue}{\left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(xy \cdot yx\right)\right)\right)}\right) \]
  7. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(\color{blue}{yx \cdot xy}\right)\right)\right)\right) \]
  8. distribute-lft-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \color{blue}{\left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right)\right) \]
  9. associate-+r+N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right) \]
  10. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(\color{blue}{yy \cdot xx} + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  11. distribute-rgt-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + \color{blue}{yy \cdot \left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  12. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + yy \cdot \color{blue}{\left(-1 \cdot zx\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  13. distribute-lft-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{yy \cdot \left(xx + -1 \cdot zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  14. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \left(xx + \color{blue}{\left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  15. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \color{blue}{\left(xx - zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  16. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx - zx\right) \cdot yy} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  17. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)}\right) \]
  18. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \mathsf{fma}\left(\color{blue}{xx - zx}, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)\right) \]
5. Applied rewrites88.9%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, \mathsf{fma}\left(xx - zx, yy, \left(-yx\right) \cdot xy\right)\right)} \]
6. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
7. Step-by-step derivation
  1. sub-negN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)} \]
  2. neg-mul-1N/A
    \[\leadsto \left(xx \cdot yy + xy \cdot zx\right) + \color{blue}{-1 \cdot \left(xy \cdot yx + yy \cdot zx\right)} \]
  3. distribute-lft-outN/A
    \[\leadsto \left(xx \cdot yy + xy \cdot zx\right) + \color{blue}{\left(-1 \cdot \left(xy \cdot yx\right) + -1 \cdot \left(yy \cdot zx\right)\right)} \]
  4. +-commutativeN/A
    \[\leadsto \left(xx \cdot yy + xy \cdot zx\right) + \color{blue}{\left(-1 \cdot \left(yy \cdot zx\right) + -1 \cdot \left(xy \cdot yx\right)\right)} \]
  5. associate-+l+N/A
    \[\leadsto \color{blue}{\left(\left(xx \cdot yy + xy \cdot zx\right) + -1 \cdot \left(yy \cdot zx\right)\right) + -1 \cdot \left(xy \cdot yx\right)} \]
  6. +-commutativeN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yy \cdot zx\right) + \left(xx \cdot yy + xy \cdot zx\right)\right)} + -1 \cdot \left(xy \cdot yx\right) \]
  7. associate-+r+N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yy \cdot zx\right) + xx \cdot yy\right) + xy \cdot zx\right)} + -1 \cdot \left(xy \cdot yx\right) \]
  8. associate-+l+N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yy \cdot zx\right) + xx \cdot yy\right) + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right)} \]
  9. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy + -1 \cdot \left(yy \cdot zx\right)\right)} + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  10. mul-1-negN/A
    \[\leadsto \left(xx \cdot yy + \color{blue}{\left(\mathsf{neg}\left(yy \cdot zx\right)\right)}\right) + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  11. unsub-negN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy - yy \cdot zx\right)} + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  12. *-commutativeN/A
    \[\leadsto \left(\color{blue}{yy \cdot xx} - yy \cdot zx\right) + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  13. distribute-lft-out--N/A
    \[\leadsto \color{blue}{yy \cdot \left(xx - zx\right)} + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  14. mul-1-negN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \left(xy \cdot zx + \color{blue}{\left(\mathsf{neg}\left(xy \cdot yx\right)\right)}\right) \]
  15. distribute-rgt-neg-inN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \left(xy \cdot zx + \color{blue}{xy \cdot \left(\mathsf{neg}\left(yx\right)\right)}\right) \]
  16. mul-1-negN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \left(xy \cdot zx + xy \cdot \color{blue}{\left(-1 \cdot yx\right)}\right) \]
  17. distribute-lft-inN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \color{blue}{xy \cdot \left(zx + -1 \cdot yx\right)} \]
  18. +-commutativeN/A
    \[\leadsto \color{blue}{xy \cdot \left(zx + -1 \cdot yx\right) + yy \cdot \left(xx - zx\right)} \]
8. Applied rewrites89.7%
  \[\leadsto \color{blue}{\mathsf{fma}\left(zx - yx, xy, \left(xx - zx\right) \cdot yy\right)} \]
if 3.9999999999999998e33 < zy < 2.4999999999999999e199
1. Initial program 86.4%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
4. Step-by-step derivation
  1. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xy \cdot zx + xx \cdot yy\right)} - \left(xy \cdot yx + yy \cdot zx\right) \]
  2. associate--l+N/A
    \[\leadsto \color{blue}{xy \cdot zx + \left(xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  3. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  4. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{xx \cdot yy + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)}\right) \]
  5. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\mathsf{neg}\left(\color{blue}{\left(yy \cdot zx + xy \cdot yx\right)}\right)\right)\right) \]
  6. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \color{blue}{\left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(xy \cdot yx\right)\right)\right)}\right) \]
  7. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(\color{blue}{yx \cdot xy}\right)\right)\right)\right) \]
  8. distribute-lft-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \color{blue}{\left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right)\right) \]
  9. associate-+r+N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right) \]
  10. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(\color{blue}{yy \cdot xx} + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  11. distribute-rgt-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + \color{blue}{yy \cdot \left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  12. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + yy \cdot \color{blue}{\left(-1 \cdot zx\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  13. distribute-lft-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{yy \cdot \left(xx + -1 \cdot zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  14. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \left(xx + \color{blue}{\left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  15. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \color{blue}{\left(xx - zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  16. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx - zx\right) \cdot yy} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  17. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)}\right) \]
  18. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \mathsf{fma}\left(\color{blue}{xx - zx}, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)\right) \]
5. Applied rewrites60.4%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, \mathsf{fma}\left(xx - zx, yy, \left(-yx\right) \cdot xy\right)\right)} \]
6. Taylor expanded in yx around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xx \cdot zy + yy \cdot zx\right)} \]
7. Step-by-step derivation
  1. associate--r+N/A
    \[\leadsto \color{blue}{\left(\left(xx \cdot yy + xy \cdot zx\right) - xx \cdot zy\right) - yy \cdot zx} \]
  2. sub-negN/A
    \[\leadsto \color{blue}{\left(\left(xx \cdot yy + xy \cdot zx\right) + \left(\mathsf{neg}\left(xx \cdot zy\right)\right)\right)} - yy \cdot zx \]
  3. +-commutativeN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(xx \cdot zy\right)\right) + \left(xx \cdot yy + xy \cdot zx\right)\right)} - yy \cdot zx \]
  4. associate-+r+N/A
    \[\leadsto \color{blue}{\left(\left(\left(\mathsf{neg}\left(xx \cdot zy\right)\right) + xx \cdot yy\right) + xy \cdot zx\right)} - yy \cdot zx \]
  5. associate--l+N/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(xx \cdot zy\right)\right) + xx \cdot yy\right) + \left(xy \cdot zx - yy \cdot zx\right)} \]
  6. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(xx \cdot zy\right)\right)\right)} + \left(xy \cdot zx - yy \cdot zx\right) \]
  7. unsub-negN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy - xx \cdot zy\right)} + \left(xy \cdot zx - yy \cdot zx\right) \]
  8. distribute-lft-out--N/A
    \[\leadsto \color{blue}{xx \cdot \left(yy - zy\right)} + \left(xy \cdot zx - yy \cdot zx\right) \]
  9. *-commutativeN/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} + \left(xy \cdot zx - yy \cdot zx\right) \]
  10. distribute-rgt-out--N/A
    \[\leadsto \left(yy - zy\right) \cdot xx + \color{blue}{zx \cdot \left(xy - yy\right)} \]
  11. sub-negN/A
    \[\leadsto \left(yy - zy\right) \cdot xx + zx \cdot \color{blue}{\left(xy + \left(\mathsf{neg}\left(yy\right)\right)\right)} \]
  12. mul-1-negN/A
    \[\leadsto \left(yy - zy\right) \cdot xx + zx \cdot \left(xy + \color{blue}{-1 \cdot yy}\right) \]
  13. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(yy - zy, xx, zx \cdot \left(xy + -1 \cdot yy\right)\right)} \]
  14. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{yy - zy}, xx, zx \cdot \left(xy + -1 \cdot yy\right)\right) \]
  15. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy + -1 \cdot yy\right) \cdot zx}\right) \]
  16. lower-*.f64N/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy + -1 \cdot yy\right) \cdot zx}\right) \]
  17. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \left(xy + \color{blue}{\left(\mathsf{neg}\left(yy\right)\right)}\right) \cdot zx\right) \]
  18. sub-negN/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy - yy\right)} \cdot zx\right) \]
  19. lower--.f6487.1
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy - yy\right)} \cdot zx\right) \]
8. Applied rewrites87.1%
  \[\leadsto \color{blue}{\mathsf{fma}\left(yy - zy, xx, \left(xy - yy\right) \cdot zx\right)} \]
Recombined 3 regimes into one program.
Add Preprocessing

Alternative 3: 78.0% accurate, 1.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(zy - xy\right) \cdot yx\\ \mathbf{if}\;yx \leq -2.1 \cdot 10^{+188}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;yx \leq -6 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(zx - yx, xy, \left(xx - zx\right) \cdot yy\right)\\ \mathbf{elif}\;yx \leq 2.2 \cdot 10^{+167}:\\ \;\;\;\;\mathsf{fma}\left(yy - zy, xx, \left(xy - yy\right) \cdot zx\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (let* ((t_0 (* (- zy xy) yx)))
   (if (<= yx -2.1e+188)
     t_0
     (if (<= yx -6e-111)
       (fma (- zx yx) xy (* (- xx zx) yy))
       (if (<= yx 2.2e+167) (fma (- yy zy) xx (* (- xy yy) zx)) t_0)))))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double t_0 = (zy - xy) * yx;
	double tmp;
	if (yx <= -2.1e+188) {
		tmp = t_0;
	} else if (yx <= -6e-111) {
		tmp = fma((zx - yx), xy, ((xx - zx) * yy));
	} else if (yx <= 2.2e+167) {
		tmp = fma((yy - zy), xx, ((xy - yy) * zx));
	} else {
		tmp = t_0;
	}
	return tmp;
}

function code(xx, yy, yx, zy, zx, xy)
	t_0 = Float64(Float64(zy - xy) * yx)
	tmp = 0.0
	if (yx <= -2.1e+188)
		tmp = t_0;
	elseif (yx <= -6e-111)
		tmp = fma(Float64(zx - yx), xy, Float64(Float64(xx - zx) * yy));
	elseif (yx <= 2.2e+167)
		tmp = fma(Float64(yy - zy), xx, Float64(Float64(xy - yy) * zx));
	else
		tmp = t_0;
	end
	return tmp
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := Block[{t$95$0 = N[(N[(zy - xy), $MachinePrecision] * yx), $MachinePrecision]}, If[LessEqual[yx, -2.1e+188], t$95$0, If[LessEqual[yx, -6e-111], N[(N[(zx - yx), $MachinePrecision] * xy + N[(N[(xx - zx), $MachinePrecision] * yy), $MachinePrecision]), $MachinePrecision], If[LessEqual[yx, 2.2e+167], N[(N[(yy - zy), $MachinePrecision] * xx + N[(N[(xy - yy), $MachinePrecision] * zx), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \left(zy - xy\right) \cdot yx\\
\mathbf{if}\;yx \leq -2.1 \cdot 10^{+188}:\\
\;\;\;\;t\_0\\

\mathbf{elif}\;yx \leq -6 \cdot 10^{-111}:\\
\;\;\;\;\mathsf{fma}\left(zx - yx, xy, \left(xx - zx\right) \cdot yy\right)\\

\mathbf{elif}\;yx \leq 2.2 \cdot 10^{+167}:\\
\;\;\;\;\mathsf{fma}\left(yy - zy, xx, \left(xy - yy\right) \cdot zx\right)\\

\mathbf{else}:\\
\;\;\;\;t\_0\\


\end{array}
\end{array}

Derivation

Split input into 3 regimes
if yx < -2.09999999999999986e188 or 2.20000000000000003e167 < yx
1. Initial program 72.3%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in yx around inf
  \[\leadsto \color{blue}{yx \cdot \left(zy - xy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  3. lower--.f6487.7
    \[\leadsto \color{blue}{\left(zy - xy\right)} \cdot yx \]
5. Applied rewrites87.7%
  \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
if -2.09999999999999986e188 < yx < -6.00000000000000016e-111
1. Initial program 85.4%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
4. Step-by-step derivation
  1. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xy \cdot zx + xx \cdot yy\right)} - \left(xy \cdot yx + yy \cdot zx\right) \]
  2. associate--l+N/A
    \[\leadsto \color{blue}{xy \cdot zx + \left(xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  3. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  4. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{xx \cdot yy + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)}\right) \]
  5. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\mathsf{neg}\left(\color{blue}{\left(yy \cdot zx + xy \cdot yx\right)}\right)\right)\right) \]
  6. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \color{blue}{\left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(xy \cdot yx\right)\right)\right)}\right) \]
  7. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(\color{blue}{yx \cdot xy}\right)\right)\right)\right) \]
  8. distribute-lft-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \color{blue}{\left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right)\right) \]
  9. associate-+r+N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right) \]
  10. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(\color{blue}{yy \cdot xx} + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  11. distribute-rgt-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + \color{blue}{yy \cdot \left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  12. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + yy \cdot \color{blue}{\left(-1 \cdot zx\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  13. distribute-lft-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{yy \cdot \left(xx + -1 \cdot zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  14. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \left(xx + \color{blue}{\left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  15. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \color{blue}{\left(xx - zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  16. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx - zx\right) \cdot yy} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  17. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)}\right) \]
  18. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \mathsf{fma}\left(\color{blue}{xx - zx}, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)\right) \]
5. Applied rewrites76.7%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, \mathsf{fma}\left(xx - zx, yy, \left(-yx\right) \cdot xy\right)\right)} \]
6. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
7. Step-by-step derivation
  1. sub-negN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)} \]
  2. neg-mul-1N/A
    \[\leadsto \left(xx \cdot yy + xy \cdot zx\right) + \color{blue}{-1 \cdot \left(xy \cdot yx + yy \cdot zx\right)} \]
  3. distribute-lft-outN/A
    \[\leadsto \left(xx \cdot yy + xy \cdot zx\right) + \color{blue}{\left(-1 \cdot \left(xy \cdot yx\right) + -1 \cdot \left(yy \cdot zx\right)\right)} \]
  4. +-commutativeN/A
    \[\leadsto \left(xx \cdot yy + xy \cdot zx\right) + \color{blue}{\left(-1 \cdot \left(yy \cdot zx\right) + -1 \cdot \left(xy \cdot yx\right)\right)} \]
  5. associate-+l+N/A
    \[\leadsto \color{blue}{\left(\left(xx \cdot yy + xy \cdot zx\right) + -1 \cdot \left(yy \cdot zx\right)\right) + -1 \cdot \left(xy \cdot yx\right)} \]
  6. +-commutativeN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yy \cdot zx\right) + \left(xx \cdot yy + xy \cdot zx\right)\right)} + -1 \cdot \left(xy \cdot yx\right) \]
  7. associate-+r+N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yy \cdot zx\right) + xx \cdot yy\right) + xy \cdot zx\right)} + -1 \cdot \left(xy \cdot yx\right) \]
  8. associate-+l+N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yy \cdot zx\right) + xx \cdot yy\right) + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right)} \]
  9. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy + -1 \cdot \left(yy \cdot zx\right)\right)} + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  10. mul-1-negN/A
    \[\leadsto \left(xx \cdot yy + \color{blue}{\left(\mathsf{neg}\left(yy \cdot zx\right)\right)}\right) + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  11. unsub-negN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy - yy \cdot zx\right)} + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  12. *-commutativeN/A
    \[\leadsto \left(\color{blue}{yy \cdot xx} - yy \cdot zx\right) + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  13. distribute-lft-out--N/A
    \[\leadsto \color{blue}{yy \cdot \left(xx - zx\right)} + \left(xy \cdot zx + -1 \cdot \left(xy \cdot yx\right)\right) \]
  14. mul-1-negN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \left(xy \cdot zx + \color{blue}{\left(\mathsf{neg}\left(xy \cdot yx\right)\right)}\right) \]
  15. distribute-rgt-neg-inN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \left(xy \cdot zx + \color{blue}{xy \cdot \left(\mathsf{neg}\left(yx\right)\right)}\right) \]
  16. mul-1-negN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \left(xy \cdot zx + xy \cdot \color{blue}{\left(-1 \cdot yx\right)}\right) \]
  17. distribute-lft-inN/A
    \[\leadsto yy \cdot \left(xx - zx\right) + \color{blue}{xy \cdot \left(zx + -1 \cdot yx\right)} \]
  18. +-commutativeN/A
    \[\leadsto \color{blue}{xy \cdot \left(zx + -1 \cdot yx\right) + yy \cdot \left(xx - zx\right)} \]
8. Applied rewrites79.9%
  \[\leadsto \color{blue}{\mathsf{fma}\left(zx - yx, xy, \left(xx - zx\right) \cdot yy\right)} \]
if -6.00000000000000016e-111 < yx < 2.20000000000000003e167
1. Initial program 87.0%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
4. Step-by-step derivation
  1. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xy \cdot zx + xx \cdot yy\right)} - \left(xy \cdot yx + yy \cdot zx\right) \]
  2. associate--l+N/A
    \[\leadsto \color{blue}{xy \cdot zx + \left(xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  3. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  4. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{xx \cdot yy + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)}\right) \]
  5. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\mathsf{neg}\left(\color{blue}{\left(yy \cdot zx + xy \cdot yx\right)}\right)\right)\right) \]
  6. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \color{blue}{\left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(xy \cdot yx\right)\right)\right)}\right) \]
  7. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(\color{blue}{yx \cdot xy}\right)\right)\right)\right) \]
  8. distribute-lft-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \color{blue}{\left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right)\right) \]
  9. associate-+r+N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right) \]
  10. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(\color{blue}{yy \cdot xx} + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  11. distribute-rgt-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + \color{blue}{yy \cdot \left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  12. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + yy \cdot \color{blue}{\left(-1 \cdot zx\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  13. distribute-lft-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{yy \cdot \left(xx + -1 \cdot zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  14. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \left(xx + \color{blue}{\left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  15. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \color{blue}{\left(xx - zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  16. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx - zx\right) \cdot yy} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  17. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)}\right) \]
  18. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \mathsf{fma}\left(\color{blue}{xx - zx}, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)\right) \]
5. Applied rewrites66.9%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, \mathsf{fma}\left(xx - zx, yy, \left(-yx\right) \cdot xy\right)\right)} \]
6. Taylor expanded in yx around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xx \cdot zy + yy \cdot zx\right)} \]
7. Step-by-step derivation
  1. associate--r+N/A
    \[\leadsto \color{blue}{\left(\left(xx \cdot yy + xy \cdot zx\right) - xx \cdot zy\right) - yy \cdot zx} \]
  2. sub-negN/A
    \[\leadsto \color{blue}{\left(\left(xx \cdot yy + xy \cdot zx\right) + \left(\mathsf{neg}\left(xx \cdot zy\right)\right)\right)} - yy \cdot zx \]
  3. +-commutativeN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(xx \cdot zy\right)\right) + \left(xx \cdot yy + xy \cdot zx\right)\right)} - yy \cdot zx \]
  4. associate-+r+N/A
    \[\leadsto \color{blue}{\left(\left(\left(\mathsf{neg}\left(xx \cdot zy\right)\right) + xx \cdot yy\right) + xy \cdot zx\right)} - yy \cdot zx \]
  5. associate--l+N/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(xx \cdot zy\right)\right) + xx \cdot yy\right) + \left(xy \cdot zx - yy \cdot zx\right)} \]
  6. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(xx \cdot zy\right)\right)\right)} + \left(xy \cdot zx - yy \cdot zx\right) \]
  7. unsub-negN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy - xx \cdot zy\right)} + \left(xy \cdot zx - yy \cdot zx\right) \]
  8. distribute-lft-out--N/A
    \[\leadsto \color{blue}{xx \cdot \left(yy - zy\right)} + \left(xy \cdot zx - yy \cdot zx\right) \]
  9. *-commutativeN/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} + \left(xy \cdot zx - yy \cdot zx\right) \]
  10. distribute-rgt-out--N/A
    \[\leadsto \left(yy - zy\right) \cdot xx + \color{blue}{zx \cdot \left(xy - yy\right)} \]
  11. sub-negN/A
    \[\leadsto \left(yy - zy\right) \cdot xx + zx \cdot \color{blue}{\left(xy + \left(\mathsf{neg}\left(yy\right)\right)\right)} \]
  12. mul-1-negN/A
    \[\leadsto \left(yy - zy\right) \cdot xx + zx \cdot \left(xy + \color{blue}{-1 \cdot yy}\right) \]
  13. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(yy - zy, xx, zx \cdot \left(xy + -1 \cdot yy\right)\right)} \]
  14. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{yy - zy}, xx, zx \cdot \left(xy + -1 \cdot yy\right)\right) \]
  15. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy + -1 \cdot yy\right) \cdot zx}\right) \]
  16. lower-*.f64N/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy + -1 \cdot yy\right) \cdot zx}\right) \]
  17. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \left(xy + \color{blue}{\left(\mathsf{neg}\left(yy\right)\right)}\right) \cdot zx\right) \]
  18. sub-negN/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy - yy\right)} \cdot zx\right) \]
  19. lower--.f6485.2
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy - yy\right)} \cdot zx\right) \]
8. Applied rewrites85.2%
  \[\leadsto \color{blue}{\mathsf{fma}\left(yy - zy, xx, \left(xy - yy\right) \cdot zx\right)} \]
Recombined 3 regimes into one program.
Add Preprocessing

Alternative 4: 52.8% accurate, 1.4× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(zx - yx\right) \cdot xy\\ \mathbf{if}\;xy \leq -1.85 \cdot 10^{+60}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;xy \leq -6.2 \cdot 10^{-215}:\\ \;\;\;\;\left(xx - zx\right) \cdot yy\\ \mathbf{elif}\;xy \leq -5.2 \cdot 10^{-251}:\\ \;\;\;\;zy \cdot yx\\ \mathbf{elif}\;xy \leq 7 \cdot 10^{+37}:\\ \;\;\;\;\left(yy - zy\right) \cdot xx\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (let* ((t_0 (* (- zx yx) xy)))
   (if (<= xy -1.85e+60)
     t_0
     (if (<= xy -6.2e-215)
       (* (- xx zx) yy)
       (if (<= xy -5.2e-251)
         (* zy yx)
         (if (<= xy 7e+37) (* (- yy zy) xx) t_0))))))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double t_0 = (zx - yx) * xy;
	double tmp;
	if (xy <= -1.85e+60) {
		tmp = t_0;
	} else if (xy <= -6.2e-215) {
		tmp = (xx - zx) * yy;
	} else if (xy <= -5.2e-251) {
		tmp = zy * yx;
	} else if (xy <= 7e+37) {
		tmp = (yy - zy) * xx;
	} else {
		tmp = t_0;
	}
	return tmp;
}

real(8) function code(xx, yy, yx, zy, zx, xy)
    real(8), intent (in) :: xx
    real(8), intent (in) :: yy
    real(8), intent (in) :: yx
    real(8), intent (in) :: zy
    real(8), intent (in) :: zx
    real(8), intent (in) :: xy
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (zx - yx) * xy
    if (xy <= (-1.85d+60)) then
        tmp = t_0
    else if (xy <= (-6.2d-215)) then
        tmp = (xx - zx) * yy
    else if (xy <= (-5.2d-251)) then
        tmp = zy * yx
    else if (xy <= 7d+37) then
        tmp = (yy - zy) * xx
    else
        tmp = t_0
    end if
    code = tmp
end function

public static double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double t_0 = (zx - yx) * xy;
	double tmp;
	if (xy <= -1.85e+60) {
		tmp = t_0;
	} else if (xy <= -6.2e-215) {
		tmp = (xx - zx) * yy;
	} else if (xy <= -5.2e-251) {
		tmp = zy * yx;
	} else if (xy <= 7e+37) {
		tmp = (yy - zy) * xx;
	} else {
		tmp = t_0;
	}
	return tmp;
}

def code(xx, yy, yx, zy, zx, xy):
	t_0 = (zx - yx) * xy
	tmp = 0
	if xy <= -1.85e+60:
		tmp = t_0
	elif xy <= -6.2e-215:
		tmp = (xx - zx) * yy
	elif xy <= -5.2e-251:
		tmp = zy * yx
	elif xy <= 7e+37:
		tmp = (yy - zy) * xx
	else:
		tmp = t_0
	return tmp

function code(xx, yy, yx, zy, zx, xy)
	t_0 = Float64(Float64(zx - yx) * xy)
	tmp = 0.0
	if (xy <= -1.85e+60)
		tmp = t_0;
	elseif (xy <= -6.2e-215)
		tmp = Float64(Float64(xx - zx) * yy);
	elseif (xy <= -5.2e-251)
		tmp = Float64(zy * yx);
	elseif (xy <= 7e+37)
		tmp = Float64(Float64(yy - zy) * xx);
	else
		tmp = t_0;
	end
	return tmp
end

function tmp_2 = code(xx, yy, yx, zy, zx, xy)
	t_0 = (zx - yx) * xy;
	tmp = 0.0;
	if (xy <= -1.85e+60)
		tmp = t_0;
	elseif (xy <= -6.2e-215)
		tmp = (xx - zx) * yy;
	elseif (xy <= -5.2e-251)
		tmp = zy * yx;
	elseif (xy <= 7e+37)
		tmp = (yy - zy) * xx;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := Block[{t$95$0 = N[(N[(zx - yx), $MachinePrecision] * xy), $MachinePrecision]}, If[LessEqual[xy, -1.85e+60], t$95$0, If[LessEqual[xy, -6.2e-215], N[(N[(xx - zx), $MachinePrecision] * yy), $MachinePrecision], If[LessEqual[xy, -5.2e-251], N[(zy * yx), $MachinePrecision], If[LessEqual[xy, 7e+37], N[(N[(yy - zy), $MachinePrecision] * xx), $MachinePrecision], t$95$0]]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \left(zx - yx\right) \cdot xy\\
\mathbf{if}\;xy \leq -1.85 \cdot 10^{+60}:\\
\;\;\;\;t\_0\\

\mathbf{elif}\;xy \leq -6.2 \cdot 10^{-215}:\\
\;\;\;\;\left(xx - zx\right) \cdot yy\\

\mathbf{elif}\;xy \leq -5.2 \cdot 10^{-251}:\\
\;\;\;\;zy \cdot yx\\

\mathbf{elif}\;xy \leq 7 \cdot 10^{+37}:\\
\;\;\;\;\left(yy - zy\right) \cdot xx\\

\mathbf{else}:\\
\;\;\;\;t\_0\\


\end{array}
\end{array}

Derivation

Split input into 4 regimes
if xy < -1.84999999999999994e60 or 7e37 < xy
1. Initial program 77.7%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in xy around inf
  \[\leadsto \color{blue}{xy \cdot \left(zx - yx\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(zx - yx\right) \cdot xy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(zx - yx\right) \cdot xy} \]
  3. lower--.f6470.7
    \[\leadsto \color{blue}{\left(zx - yx\right)} \cdot xy \]
5. Applied rewrites70.7%
  \[\leadsto \color{blue}{\left(zx - yx\right) \cdot xy} \]
if -1.84999999999999994e60 < xy < -6.19999999999999987e-215
1. Initial program 91.5%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in yy around inf
  \[\leadsto \color{blue}{yy \cdot \left(xx - zx\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
  3. lower--.f6452.6
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites52.6%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
if -6.19999999999999987e-215 < xy < -5.1999999999999998e-251
1. Initial program 85.7%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in yx around inf
  \[\leadsto \color{blue}{yx \cdot \left(zy - xy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  3. lower--.f64100.0
    \[\leadsto \color{blue}{\left(zy - xy\right)} \cdot yx \]
5. Applied rewrites100.0%
  \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
6. Taylor expanded in zy around inf
  \[\leadsto yx \cdot \color{blue}{zy} \]
7. Step-by-step derivation
8. Applied rewrites100.0%
  \[\leadsto zy \cdot \color{blue}{yx} \]
if -5.1999999999999998e-251 < xy < 7e37
1. Initial program 86.6%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in xx around inf
  \[\leadsto \color{blue}{xx \cdot \left(yy - zy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
  3. lower--.f6461.2
    \[\leadsto \color{blue}{\left(yy - zy\right)} \cdot xx \]
5. Applied rewrites61.2%
  \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
Recombined 4 regimes into one program.
Add Preprocessing

Alternative 5: 29.8% accurate, 1.4× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;yy \leq -1.75 \cdot 10^{+161}:\\ \;\;\;\;yy \cdot xx\\ \mathbf{elif}\;yy \leq -9.5 \cdot 10^{-77}:\\ \;\;\;\;zy \cdot yx\\ \mathbf{elif}\;yy \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;\left(-zy\right) \cdot xx\\ \mathbf{elif}\;yy \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;\left(-zx\right) \cdot yy\\ \mathbf{else}:\\ \;\;\;\;yy \cdot xx\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (if (<= yy -1.75e+161)
   (* yy xx)
   (if (<= yy -9.5e-77)
     (* zy yx)
     (if (<= yy 1.6e+28)
       (* (- zy) xx)
       (if (<= yy 3.8e+147) (* (- zx) yy) (* yy xx))))))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double tmp;
	if (yy <= -1.75e+161) {
		tmp = yy * xx;
	} else if (yy <= -9.5e-77) {
		tmp = zy * yx;
	} else if (yy <= 1.6e+28) {
		tmp = -zy * xx;
	} else if (yy <= 3.8e+147) {
		tmp = -zx * yy;
	} else {
		tmp = yy * xx;
	}
	return tmp;
}

real(8) function code(xx, yy, yx, zy, zx, xy)
    real(8), intent (in) :: xx
    real(8), intent (in) :: yy
    real(8), intent (in) :: yx
    real(8), intent (in) :: zy
    real(8), intent (in) :: zx
    real(8), intent (in) :: xy
    real(8) :: tmp
    if (yy <= (-1.75d+161)) then
        tmp = yy * xx
    else if (yy <= (-9.5d-77)) then
        tmp = zy * yx
    else if (yy <= 1.6d+28) then
        tmp = -zy * xx
    else if (yy <= 3.8d+147) then
        tmp = -zx * yy
    else
        tmp = yy * xx
    end if
    code = tmp
end function

public static double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double tmp;
	if (yy <= -1.75e+161) {
		tmp = yy * xx;
	} else if (yy <= -9.5e-77) {
		tmp = zy * yx;
	} else if (yy <= 1.6e+28) {
		tmp = -zy * xx;
	} else if (yy <= 3.8e+147) {
		tmp = -zx * yy;
	} else {
		tmp = yy * xx;
	}
	return tmp;
}

def code(xx, yy, yx, zy, zx, xy):
	tmp = 0
	if yy <= -1.75e+161:
		tmp = yy * xx
	elif yy <= -9.5e-77:
		tmp = zy * yx
	elif yy <= 1.6e+28:
		tmp = -zy * xx
	elif yy <= 3.8e+147:
		tmp = -zx * yy
	else:
		tmp = yy * xx
	return tmp

function code(xx, yy, yx, zy, zx, xy)
	tmp = 0.0
	if (yy <= -1.75e+161)
		tmp = Float64(yy * xx);
	elseif (yy <= -9.5e-77)
		tmp = Float64(zy * yx);
	elseif (yy <= 1.6e+28)
		tmp = Float64(Float64(-zy) * xx);
	elseif (yy <= 3.8e+147)
		tmp = Float64(Float64(-zx) * yy);
	else
		tmp = Float64(yy * xx);
	end
	return tmp
end

function tmp_2 = code(xx, yy, yx, zy, zx, xy)
	tmp = 0.0;
	if (yy <= -1.75e+161)
		tmp = yy * xx;
	elseif (yy <= -9.5e-77)
		tmp = zy * yx;
	elseif (yy <= 1.6e+28)
		tmp = -zy * xx;
	elseif (yy <= 3.8e+147)
		tmp = -zx * yy;
	else
		tmp = yy * xx;
	end
	tmp_2 = tmp;
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := If[LessEqual[yy, -1.75e+161], N[(yy * xx), $MachinePrecision], If[LessEqual[yy, -9.5e-77], N[(zy * yx), $MachinePrecision], If[LessEqual[yy, 1.6e+28], N[((-zy) * xx), $MachinePrecision], If[LessEqual[yy, 3.8e+147], N[((-zx) * yy), $MachinePrecision], N[(yy * xx), $MachinePrecision]]]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;yy \leq -1.75 \cdot 10^{+161}:\\
\;\;\;\;yy \cdot xx\\

\mathbf{elif}\;yy \leq -9.5 \cdot 10^{-77}:\\
\;\;\;\;zy \cdot yx\\

\mathbf{elif}\;yy \leq 1.6 \cdot 10^{+28}:\\
\;\;\;\;\left(-zy\right) \cdot xx\\

\mathbf{elif}\;yy \leq 3.8 \cdot 10^{+147}:\\
\;\;\;\;\left(-zx\right) \cdot yy\\

\mathbf{else}:\\
\;\;\;\;yy \cdot xx\\


\end{array}
\end{array}

Derivation

Split input into 4 regimes
if yy < -1.74999999999999994e161 or 3.7999999999999997e147 < yy
1. Initial program 69.9%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
4. Step-by-step derivation
  1. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xy \cdot zx + xx \cdot yy\right)} - \left(xy \cdot yx + yy \cdot zx\right) \]
  2. associate--l+N/A
    \[\leadsto \color{blue}{xy \cdot zx + \left(xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  3. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  4. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{xx \cdot yy + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)}\right) \]
  5. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\mathsf{neg}\left(\color{blue}{\left(yy \cdot zx + xy \cdot yx\right)}\right)\right)\right) \]
  6. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \color{blue}{\left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(xy \cdot yx\right)\right)\right)}\right) \]
  7. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(\color{blue}{yx \cdot xy}\right)\right)\right)\right) \]
  8. distribute-lft-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \color{blue}{\left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right)\right) \]
  9. associate-+r+N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right) \]
  10. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(\color{blue}{yy \cdot xx} + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  11. distribute-rgt-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + \color{blue}{yy \cdot \left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  12. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + yy \cdot \color{blue}{\left(-1 \cdot zx\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  13. distribute-lft-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{yy \cdot \left(xx + -1 \cdot zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  14. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \left(xx + \color{blue}{\left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  15. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \color{blue}{\left(xx - zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  16. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx - zx\right) \cdot yy} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  17. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)}\right) \]
  18. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \mathsf{fma}\left(\color{blue}{xx - zx}, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)\right) \]
5. Applied rewrites85.1%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, \mathsf{fma}\left(xx - zx, yy, \left(-yx\right) \cdot xy\right)\right)} \]
6. Taylor expanded in xx around inf
  \[\leadsto xx \cdot \color{blue}{yy} \]
7. Step-by-step derivation
8. Applied rewrites55.3%
  \[\leadsto yy \cdot \color{blue}{xx} \]
if -1.74999999999999994e161 < yy < -9.5000000000000005e-77
1. Initial program 88.3%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in yx around inf
  \[\leadsto \color{blue}{yx \cdot \left(zy - xy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  3. lower--.f6445.0
    \[\leadsto \color{blue}{\left(zy - xy\right)} \cdot yx \]
5. Applied rewrites45.0%
  \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
6. Taylor expanded in zy around inf
  \[\leadsto yx \cdot \color{blue}{zy} \]
7. Step-by-step derivation
8. Applied rewrites28.5%
  \[\leadsto zy \cdot \color{blue}{yx} \]
if -9.5000000000000005e-77 < yy < 1.6e28
1. Initial program 91.8%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in xx around inf
  \[\leadsto \color{blue}{xx \cdot \left(yy - zy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
  3. lower--.f6438.6
    \[\leadsto \color{blue}{\left(yy - zy\right)} \cdot xx \]
5. Applied rewrites38.6%
  \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
6. Taylor expanded in yy around 0
  \[\leadsto \left(-1 \cdot zy\right) \cdot xx \]
7. Step-by-step derivation
8. Applied rewrites33.1%
  \[\leadsto \left(-zy\right) \cdot xx \]
if 1.6e28 < yy < 3.7999999999999997e147
1. Initial program 77.8%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in yy around inf
  \[\leadsto \color{blue}{yy \cdot \left(xx - zx\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
  3. lower--.f6461.7
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites61.7%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
6. Taylor expanded in xx around 0
  \[\leadsto \left(-1 \cdot zx\right) \cdot yy \]
7. Step-by-step derivation
8. Applied rewrites45.1%
  \[\leadsto \left(-zx\right) \cdot yy \]
Recombined 4 regimes into one program.
Add Preprocessing

Alternative 6: 77.7% accurate, 1.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;yx \leq -1.7 \cdot 10^{+148} \lor \neg \left(yx \leq 2.2 \cdot 10^{+167}\right):\\ \;\;\;\;\left(zy - xy\right) \cdot yx\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(yy - zy, xx, \left(xy - yy\right) \cdot zx\right)\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (if (or (<= yx -1.7e+148) (not (<= yx 2.2e+167)))
   (* (- zy xy) yx)
   (fma (- yy zy) xx (* (- xy yy) zx))))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double tmp;
	if ((yx <= -1.7e+148) || !(yx <= 2.2e+167)) {
		tmp = (zy - xy) * yx;
	} else {
		tmp = fma((yy - zy), xx, ((xy - yy) * zx));
	}
	return tmp;
}

function code(xx, yy, yx, zy, zx, xy)
	tmp = 0.0
	if ((yx <= -1.7e+148) || !(yx <= 2.2e+167))
		tmp = Float64(Float64(zy - xy) * yx);
	else
		tmp = fma(Float64(yy - zy), xx, Float64(Float64(xy - yy) * zx));
	end
	return tmp
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := If[Or[LessEqual[yx, -1.7e+148], N[Not[LessEqual[yx, 2.2e+167]], $MachinePrecision]], N[(N[(zy - xy), $MachinePrecision] * yx), $MachinePrecision], N[(N[(yy - zy), $MachinePrecision] * xx + N[(N[(xy - yy), $MachinePrecision] * zx), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;yx \leq -1.7 \cdot 10^{+148} \lor \neg \left(yx \leq 2.2 \cdot 10^{+167}\right):\\
\;\;\;\;\left(zy - xy\right) \cdot yx\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(yy - zy, xx, \left(xy - yy\right) \cdot zx\right)\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if yx < -1.7000000000000001e148 or 2.20000000000000003e167 < yx
1. Initial program 76.4%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in yx around inf
  \[\leadsto \color{blue}{yx \cdot \left(zy - xy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  3. lower--.f6487.6
    \[\leadsto \color{blue}{\left(zy - xy\right)} \cdot yx \]
5. Applied rewrites87.6%
  \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
if -1.7000000000000001e148 < yx < 2.20000000000000003e167
1. Initial program 86.0%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
4. Step-by-step derivation
  1. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xy \cdot zx + xx \cdot yy\right)} - \left(xy \cdot yx + yy \cdot zx\right) \]
  2. associate--l+N/A
    \[\leadsto \color{blue}{xy \cdot zx + \left(xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  3. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  4. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{xx \cdot yy + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)}\right) \]
  5. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\mathsf{neg}\left(\color{blue}{\left(yy \cdot zx + xy \cdot yx\right)}\right)\right)\right) \]
  6. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \color{blue}{\left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(xy \cdot yx\right)\right)\right)}\right) \]
  7. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(\color{blue}{yx \cdot xy}\right)\right)\right)\right) \]
  8. distribute-lft-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \color{blue}{\left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right)\right) \]
  9. associate-+r+N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right) \]
  10. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(\color{blue}{yy \cdot xx} + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  11. distribute-rgt-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + \color{blue}{yy \cdot \left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  12. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + yy \cdot \color{blue}{\left(-1 \cdot zx\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  13. distribute-lft-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{yy \cdot \left(xx + -1 \cdot zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  14. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \left(xx + \color{blue}{\left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  15. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \color{blue}{\left(xx - zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  16. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx - zx\right) \cdot yy} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  17. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)}\right) \]
  18. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \mathsf{fma}\left(\color{blue}{xx - zx}, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)\right) \]
5. Applied rewrites69.1%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, \mathsf{fma}\left(xx - zx, yy, \left(-yx\right) \cdot xy\right)\right)} \]
6. Taylor expanded in yx around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xx \cdot zy + yy \cdot zx\right)} \]
7. Step-by-step derivation
  1. associate--r+N/A
    \[\leadsto \color{blue}{\left(\left(xx \cdot yy + xy \cdot zx\right) - xx \cdot zy\right) - yy \cdot zx} \]
  2. sub-negN/A
    \[\leadsto \color{blue}{\left(\left(xx \cdot yy + xy \cdot zx\right) + \left(\mathsf{neg}\left(xx \cdot zy\right)\right)\right)} - yy \cdot zx \]
  3. +-commutativeN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(xx \cdot zy\right)\right) + \left(xx \cdot yy + xy \cdot zx\right)\right)} - yy \cdot zx \]
  4. associate-+r+N/A
    \[\leadsto \color{blue}{\left(\left(\left(\mathsf{neg}\left(xx \cdot zy\right)\right) + xx \cdot yy\right) + xy \cdot zx\right)} - yy \cdot zx \]
  5. associate--l+N/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(xx \cdot zy\right)\right) + xx \cdot yy\right) + \left(xy \cdot zx - yy \cdot zx\right)} \]
  6. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(xx \cdot zy\right)\right)\right)} + \left(xy \cdot zx - yy \cdot zx\right) \]
  7. unsub-negN/A
    \[\leadsto \color{blue}{\left(xx \cdot yy - xx \cdot zy\right)} + \left(xy \cdot zx - yy \cdot zx\right) \]
  8. distribute-lft-out--N/A
    \[\leadsto \color{blue}{xx \cdot \left(yy - zy\right)} + \left(xy \cdot zx - yy \cdot zx\right) \]
  9. *-commutativeN/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} + \left(xy \cdot zx - yy \cdot zx\right) \]
  10. distribute-rgt-out--N/A
    \[\leadsto \left(yy - zy\right) \cdot xx + \color{blue}{zx \cdot \left(xy - yy\right)} \]
  11. sub-negN/A
    \[\leadsto \left(yy - zy\right) \cdot xx + zx \cdot \color{blue}{\left(xy + \left(\mathsf{neg}\left(yy\right)\right)\right)} \]
  12. mul-1-negN/A
    \[\leadsto \left(yy - zy\right) \cdot xx + zx \cdot \left(xy + \color{blue}{-1 \cdot yy}\right) \]
  13. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(yy - zy, xx, zx \cdot \left(xy + -1 \cdot yy\right)\right)} \]
  14. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{yy - zy}, xx, zx \cdot \left(xy + -1 \cdot yy\right)\right) \]
  15. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy + -1 \cdot yy\right) \cdot zx}\right) \]
  16. lower-*.f64N/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy + -1 \cdot yy\right) \cdot zx}\right) \]
  17. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \left(xy + \color{blue}{\left(\mathsf{neg}\left(yy\right)\right)}\right) \cdot zx\right) \]
  18. sub-negN/A
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy - yy\right)} \cdot zx\right) \]
  19. lower--.f6480.5
    \[\leadsto \mathsf{fma}\left(yy - zy, xx, \color{blue}{\left(xy - yy\right)} \cdot zx\right) \]
8. Applied rewrites80.5%
  \[\leadsto \color{blue}{\mathsf{fma}\left(yy - zy, xx, \left(xy - yy\right) \cdot zx\right)} \]
Recombined 2 regimes into one program.
Final simplification82.0%
\[\leadsto \begin{array}{l} \mathbf{if}\;yx \leq -1.7 \cdot 10^{+148} \lor \neg \left(yx \leq 2.2 \cdot 10^{+167}\right):\\ \;\;\;\;\left(zy - xy\right) \cdot yx\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(yy - zy, xx, \left(xy - yy\right) \cdot zx\right)\\ \end{array} \]
Add Preprocessing

Alternative 7: 64.0% accurate, 1.7× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;yx \leq -1.7 \cdot 10^{+148} \lor \neg \left(yx \leq 1.3 \cdot 10^{+103}\right):\\ \;\;\;\;\left(zy - xy\right) \cdot yx\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(xx - zx, yy, zx \cdot xy\right)\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (if (or (<= yx -1.7e+148) (not (<= yx 1.3e+103)))
   (* (- zy xy) yx)
   (fma (- xx zx) yy (* zx xy))))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double tmp;
	if ((yx <= -1.7e+148) || !(yx <= 1.3e+103)) {
		tmp = (zy - xy) * yx;
	} else {
		tmp = fma((xx - zx), yy, (zx * xy));
	}
	return tmp;
}

function code(xx, yy, yx, zy, zx, xy)
	tmp = 0.0
	if ((yx <= -1.7e+148) || !(yx <= 1.3e+103))
		tmp = Float64(Float64(zy - xy) * yx);
	else
		tmp = fma(Float64(xx - zx), yy, Float64(zx * xy));
	end
	return tmp
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := If[Or[LessEqual[yx, -1.7e+148], N[Not[LessEqual[yx, 1.3e+103]], $MachinePrecision]], N[(N[(zy - xy), $MachinePrecision] * yx), $MachinePrecision], N[(N[(xx - zx), $MachinePrecision] * yy + N[(zx * xy), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;yx \leq -1.7 \cdot 10^{+148} \lor \neg \left(yx \leq 1.3 \cdot 10^{+103}\right):\\
\;\;\;\;\left(zy - xy\right) \cdot yx\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(xx - zx, yy, zx \cdot xy\right)\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if yx < -1.7000000000000001e148 or 1.3000000000000001e103 < yx
1. Initial program 75.0%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in yx around inf
  \[\leadsto \color{blue}{yx \cdot \left(zy - xy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  3. lower--.f6480.0
    \[\leadsto \color{blue}{\left(zy - xy\right)} \cdot yx \]
5. Applied rewrites80.0%
  \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
if -1.7000000000000001e148 < yx < 1.3000000000000001e103
1. Initial program 87.2%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
4. Step-by-step derivation
  1. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xy \cdot zx + xx \cdot yy\right)} - \left(xy \cdot yx + yy \cdot zx\right) \]
  2. associate--l+N/A
    \[\leadsto \color{blue}{xy \cdot zx + \left(xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  3. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  4. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{xx \cdot yy + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)}\right) \]
  5. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\mathsf{neg}\left(\color{blue}{\left(yy \cdot zx + xy \cdot yx\right)}\right)\right)\right) \]
  6. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \color{blue}{\left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(xy \cdot yx\right)\right)\right)}\right) \]
  7. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(\color{blue}{yx \cdot xy}\right)\right)\right)\right) \]
  8. distribute-lft-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \color{blue}{\left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right)\right) \]
  9. associate-+r+N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right) \]
  10. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(\color{blue}{yy \cdot xx} + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  11. distribute-rgt-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + \color{blue}{yy \cdot \left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  12. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + yy \cdot \color{blue}{\left(-1 \cdot zx\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  13. distribute-lft-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{yy \cdot \left(xx + -1 \cdot zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  14. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \left(xx + \color{blue}{\left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  15. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \color{blue}{\left(xx - zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  16. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx - zx\right) \cdot yy} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  17. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)}\right) \]
  18. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \mathsf{fma}\left(\color{blue}{xx - zx}, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)\right) \]
5. Applied rewrites71.1%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, \mathsf{fma}\left(xx - zx, yy, \left(-yx\right) \cdot xy\right)\right)} \]
6. Taylor expanded in yx around 0
  \[\leadsto xy \cdot zx + \color{blue}{yy \cdot \left(xx - zx\right)} \]
7. Step-by-step derivation
8. Applied rewrites62.5%
  \[\leadsto \mathsf{fma}\left(xx - zx, \color{blue}{yy}, zx \cdot xy\right) \]
Recombined 2 regimes into one program.
Final simplification67.1%
\[\leadsto \begin{array}{l} \mathbf{if}\;yx \leq -1.7 \cdot 10^{+148} \lor \neg \left(yx \leq 1.3 \cdot 10^{+103}\right):\\ \;\;\;\;\left(zy - xy\right) \cdot yx\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(xx - zx, yy, zx \cdot xy\right)\\ \end{array} \]
Add Preprocessing

Alternative 8: 44.7% accurate, 1.7× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(xx - zx\right) \cdot yy\\ \mathbf{if}\;yy \leq -1.75 \cdot 10^{+70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;yy \leq -3.2 \cdot 10^{-78}:\\ \;\;\;\;\left(xy - yy\right) \cdot zx\\ \mathbf{elif}\;yy \leq 1.2 \cdot 10^{-64}:\\ \;\;\;\;\left(-zy\right) \cdot xx\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (let* ((t_0 (* (- xx zx) yy)))
   (if (<= yy -1.75e+70)
     t_0
     (if (<= yy -3.2e-78)
       (* (- xy yy) zx)
       (if (<= yy 1.2e-64) (* (- zy) xx) t_0)))))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double t_0 = (xx - zx) * yy;
	double tmp;
	if (yy <= -1.75e+70) {
		tmp = t_0;
	} else if (yy <= -3.2e-78) {
		tmp = (xy - yy) * zx;
	} else if (yy <= 1.2e-64) {
		tmp = -zy * xx;
	} else {
		tmp = t_0;
	}
	return tmp;
}

real(8) function code(xx, yy, yx, zy, zx, xy)
    real(8), intent (in) :: xx
    real(8), intent (in) :: yy
    real(8), intent (in) :: yx
    real(8), intent (in) :: zy
    real(8), intent (in) :: zx
    real(8), intent (in) :: xy
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (xx - zx) * yy
    if (yy <= (-1.75d+70)) then
        tmp = t_0
    else if (yy <= (-3.2d-78)) then
        tmp = (xy - yy) * zx
    else if (yy <= 1.2d-64) then
        tmp = -zy * xx
    else
        tmp = t_0
    end if
    code = tmp
end function

public static double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double t_0 = (xx - zx) * yy;
	double tmp;
	if (yy <= -1.75e+70) {
		tmp = t_0;
	} else if (yy <= -3.2e-78) {
		tmp = (xy - yy) * zx;
	} else if (yy <= 1.2e-64) {
		tmp = -zy * xx;
	} else {
		tmp = t_0;
	}
	return tmp;
}

def code(xx, yy, yx, zy, zx, xy):
	t_0 = (xx - zx) * yy
	tmp = 0
	if yy <= -1.75e+70:
		tmp = t_0
	elif yy <= -3.2e-78:
		tmp = (xy - yy) * zx
	elif yy <= 1.2e-64:
		tmp = -zy * xx
	else:
		tmp = t_0
	return tmp

function code(xx, yy, yx, zy, zx, xy)
	t_0 = Float64(Float64(xx - zx) * yy)
	tmp = 0.0
	if (yy <= -1.75e+70)
		tmp = t_0;
	elseif (yy <= -3.2e-78)
		tmp = Float64(Float64(xy - yy) * zx);
	elseif (yy <= 1.2e-64)
		tmp = Float64(Float64(-zy) * xx);
	else
		tmp = t_0;
	end
	return tmp
end

function tmp_2 = code(xx, yy, yx, zy, zx, xy)
	t_0 = (xx - zx) * yy;
	tmp = 0.0;
	if (yy <= -1.75e+70)
		tmp = t_0;
	elseif (yy <= -3.2e-78)
		tmp = (xy - yy) * zx;
	elseif (yy <= 1.2e-64)
		tmp = -zy * xx;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := Block[{t$95$0 = N[(N[(xx - zx), $MachinePrecision] * yy), $MachinePrecision]}, If[LessEqual[yy, -1.75e+70], t$95$0, If[LessEqual[yy, -3.2e-78], N[(N[(xy - yy), $MachinePrecision] * zx), $MachinePrecision], If[LessEqual[yy, 1.2e-64], N[((-zy) * xx), $MachinePrecision], t$95$0]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \left(xx - zx\right) \cdot yy\\
\mathbf{if}\;yy \leq -1.75 \cdot 10^{+70}:\\
\;\;\;\;t\_0\\

\mathbf{elif}\;yy \leq -3.2 \cdot 10^{-78}:\\
\;\;\;\;\left(xy - yy\right) \cdot zx\\

\mathbf{elif}\;yy \leq 1.2 \cdot 10^{-64}:\\
\;\;\;\;\left(-zy\right) \cdot xx\\

\mathbf{else}:\\
\;\;\;\;t\_0\\


\end{array}
\end{array}

Derivation

Split input into 3 regimes
if yy < -1.75000000000000001e70 or 1.19999999999999999e-64 < yy
1. Initial program 76.7%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in yy around inf
  \[\leadsto \color{blue}{yy \cdot \left(xx - zx\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
  3. lower--.f6465.5
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites65.5%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
if -1.75000000000000001e70 < yy < -3.2e-78
1. Initial program 91.9%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zx around inf
  \[\leadsto \color{blue}{zx \cdot \left(xy - yy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(xy - yy\right) \cdot zx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(xy - yy\right) \cdot zx} \]
  3. lower--.f6445.4
    \[\leadsto \color{blue}{\left(xy - yy\right)} \cdot zx \]
5. Applied rewrites45.4%
  \[\leadsto \color{blue}{\left(xy - yy\right) \cdot zx} \]
if -3.2e-78 < yy < 1.19999999999999999e-64
1. Initial program 91.1%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in xx around inf
  \[\leadsto \color{blue}{xx \cdot \left(yy - zy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
  3. lower--.f6436.2
    \[\leadsto \color{blue}{\left(yy - zy\right)} \cdot xx \]
5. Applied rewrites36.2%
  \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
6. Taylor expanded in yy around 0
  \[\leadsto \left(-1 \cdot zy\right) \cdot xx \]
7. Step-by-step derivation
8. Applied rewrites35.3%
  \[\leadsto \left(-zy\right) \cdot xx \]
Recombined 3 regimes into one program.
Add Preprocessing

Alternative 9: 54.5% accurate, 2.2× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;xx \leq -5.4 \cdot 10^{+28} \lor \neg \left(xx \leq 1.15 \cdot 10^{-9}\right):\\ \;\;\;\;\left(yy - zy\right) \cdot xx\\ \mathbf{else}:\\ \;\;\;\;\left(xy - yy\right) \cdot zx\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (if (or (<= xx -5.4e+28) (not (<= xx 1.15e-9)))
   (* (- yy zy) xx)
   (* (- xy yy) zx)))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double tmp;
	if ((xx <= -5.4e+28) || !(xx <= 1.15e-9)) {
		tmp = (yy - zy) * xx;
	} else {
		tmp = (xy - yy) * zx;
	}
	return tmp;
}

real(8) function code(xx, yy, yx, zy, zx, xy)
    real(8), intent (in) :: xx
    real(8), intent (in) :: yy
    real(8), intent (in) :: yx
    real(8), intent (in) :: zy
    real(8), intent (in) :: zx
    real(8), intent (in) :: xy
    real(8) :: tmp
    if ((xx <= (-5.4d+28)) .or. (.not. (xx <= 1.15d-9))) then
        tmp = (yy - zy) * xx
    else
        tmp = (xy - yy) * zx
    end if
    code = tmp
end function

public static double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double tmp;
	if ((xx <= -5.4e+28) || !(xx <= 1.15e-9)) {
		tmp = (yy - zy) * xx;
	} else {
		tmp = (xy - yy) * zx;
	}
	return tmp;
}

def code(xx, yy, yx, zy, zx, xy):
	tmp = 0
	if (xx <= -5.4e+28) or not (xx <= 1.15e-9):
		tmp = (yy - zy) * xx
	else:
		tmp = (xy - yy) * zx
	return tmp

function code(xx, yy, yx, zy, zx, xy)
	tmp = 0.0
	if ((xx <= -5.4e+28) || !(xx <= 1.15e-9))
		tmp = Float64(Float64(yy - zy) * xx);
	else
		tmp = Float64(Float64(xy - yy) * zx);
	end
	return tmp
end

function tmp_2 = code(xx, yy, yx, zy, zx, xy)
	tmp = 0.0;
	if ((xx <= -5.4e+28) || ~((xx <= 1.15e-9)))
		tmp = (yy - zy) * xx;
	else
		tmp = (xy - yy) * zx;
	end
	tmp_2 = tmp;
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := If[Or[LessEqual[xx, -5.4e+28], N[Not[LessEqual[xx, 1.15e-9]], $MachinePrecision]], N[(N[(yy - zy), $MachinePrecision] * xx), $MachinePrecision], N[(N[(xy - yy), $MachinePrecision] * zx), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;xx \leq -5.4 \cdot 10^{+28} \lor \neg \left(xx \leq 1.15 \cdot 10^{-9}\right):\\
\;\;\;\;\left(yy - zy\right) \cdot xx\\

\mathbf{else}:\\
\;\;\;\;\left(xy - yy\right) \cdot zx\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if xx < -5.4000000000000003e28 or 1.15e-9 < xx
1. Initial program 75.5%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in xx around inf
  \[\leadsto \color{blue}{xx \cdot \left(yy - zy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
  3. lower--.f6465.5
    \[\leadsto \color{blue}{\left(yy - zy\right)} \cdot xx \]
5. Applied rewrites65.5%
  \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
if -5.4000000000000003e28 < xx < 1.15e-9
1. Initial program 92.8%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zx around inf
  \[\leadsto \color{blue}{zx \cdot \left(xy - yy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(xy - yy\right) \cdot zx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(xy - yy\right) \cdot zx} \]
  3. lower--.f6445.5
    \[\leadsto \color{blue}{\left(xy - yy\right)} \cdot zx \]
5. Applied rewrites45.5%
  \[\leadsto \color{blue}{\left(xy - yy\right) \cdot zx} \]
Recombined 2 regimes into one program.
Final simplification55.7%
\[\leadsto \begin{array}{l} \mathbf{if}\;xx \leq -5.4 \cdot 10^{+28} \lor \neg \left(xx \leq 1.15 \cdot 10^{-9}\right):\\ \;\;\;\;\left(yy - zy\right) \cdot xx\\ \mathbf{else}:\\ \;\;\;\;\left(xy - yy\right) \cdot zx\\ \end{array} \]
Add Preprocessing

Alternative 10: 44.2% accurate, 2.2× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;yy \leq -2.1 \cdot 10^{-77} \lor \neg \left(yy \leq 1.2 \cdot 10^{-64}\right):\\ \;\;\;\;\left(xx - zx\right) \cdot yy\\ \mathbf{else}:\\ \;\;\;\;\left(-zy\right) \cdot xx\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (if (or (<= yy -2.1e-77) (not (<= yy 1.2e-64)))
   (* (- xx zx) yy)
   (* (- zy) xx)))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double tmp;
	if ((yy <= -2.1e-77) || !(yy <= 1.2e-64)) {
		tmp = (xx - zx) * yy;
	} else {
		tmp = -zy * xx;
	}
	return tmp;
}

real(8) function code(xx, yy, yx, zy, zx, xy)
    real(8), intent (in) :: xx
    real(8), intent (in) :: yy
    real(8), intent (in) :: yx
    real(8), intent (in) :: zy
    real(8), intent (in) :: zx
    real(8), intent (in) :: xy
    real(8) :: tmp
    if ((yy <= (-2.1d-77)) .or. (.not. (yy <= 1.2d-64))) then
        tmp = (xx - zx) * yy
    else
        tmp = -zy * xx
    end if
    code = tmp
end function

public static double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double tmp;
	if ((yy <= -2.1e-77) || !(yy <= 1.2e-64)) {
		tmp = (xx - zx) * yy;
	} else {
		tmp = -zy * xx;
	}
	return tmp;
}

def code(xx, yy, yx, zy, zx, xy):
	tmp = 0
	if (yy <= -2.1e-77) or not (yy <= 1.2e-64):
		tmp = (xx - zx) * yy
	else:
		tmp = -zy * xx
	return tmp

function code(xx, yy, yx, zy, zx, xy)
	tmp = 0.0
	if ((yy <= -2.1e-77) || !(yy <= 1.2e-64))
		tmp = Float64(Float64(xx - zx) * yy);
	else
		tmp = Float64(Float64(-zy) * xx);
	end
	return tmp
end

function tmp_2 = code(xx, yy, yx, zy, zx, xy)
	tmp = 0.0;
	if ((yy <= -2.1e-77) || ~((yy <= 1.2e-64)))
		tmp = (xx - zx) * yy;
	else
		tmp = -zy * xx;
	end
	tmp_2 = tmp;
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := If[Or[LessEqual[yy, -2.1e-77], N[Not[LessEqual[yy, 1.2e-64]], $MachinePrecision]], N[(N[(xx - zx), $MachinePrecision] * yy), $MachinePrecision], N[((-zy) * xx), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;yy \leq -2.1 \cdot 10^{-77} \lor \neg \left(yy \leq 1.2 \cdot 10^{-64}\right):\\
\;\;\;\;\left(xx - zx\right) \cdot yy\\

\mathbf{else}:\\
\;\;\;\;\left(-zy\right) \cdot xx\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if yy < -2.10000000000000015e-77 or 1.19999999999999999e-64 < yy
1. Initial program 79.2%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in yy around inf
  \[\leadsto \color{blue}{yy \cdot \left(xx - zx\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
  3. lower--.f6459.4
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites59.4%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
if -2.10000000000000015e-77 < yy < 1.19999999999999999e-64
1. Initial program 91.1%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in xx around inf
  \[\leadsto \color{blue}{xx \cdot \left(yy - zy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
  3. lower--.f6436.2
    \[\leadsto \color{blue}{\left(yy - zy\right)} \cdot xx \]
5. Applied rewrites36.2%
  \[\leadsto \color{blue}{\left(yy - zy\right) \cdot xx} \]
6. Taylor expanded in yy around 0
  \[\leadsto \left(-1 \cdot zy\right) \cdot xx \]
7. Step-by-step derivation
8. Applied rewrites35.3%
  \[\leadsto \left(-zy\right) \cdot xx \]
Recombined 2 regimes into one program.
Final simplification49.8%
\[\leadsto \begin{array}{l} \mathbf{if}\;yy \leq -2.1 \cdot 10^{-77} \lor \neg \left(yy \leq 1.2 \cdot 10^{-64}\right):\\ \;\;\;\;\left(xx - zx\right) \cdot yy\\ \mathbf{else}:\\ \;\;\;\;\left(-zy\right) \cdot xx\\ \end{array} \]
Add Preprocessing

Alternative 11: 28.3% accurate, 2.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;yx \leq -1.1 \cdot 10^{+91} \lor \neg \left(yx \leq 1.85 \cdot 10^{+142}\right):\\ \;\;\;\;zy \cdot yx\\ \mathbf{else}:\\ \;\;\;\;yy \cdot xx\\ \end{array} \end{array} \]

(FPCore (xx yy yx zy zx xy)
 :precision binary64
 (if (or (<= yx -1.1e+91) (not (<= yx 1.85e+142))) (* zy yx) (* yy xx)))

double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double tmp;
	if ((yx <= -1.1e+91) || !(yx <= 1.85e+142)) {
		tmp = zy * yx;
	} else {
		tmp = yy * xx;
	}
	return tmp;
}

real(8) function code(xx, yy, yx, zy, zx, xy)
    real(8), intent (in) :: xx
    real(8), intent (in) :: yy
    real(8), intent (in) :: yx
    real(8), intent (in) :: zy
    real(8), intent (in) :: zx
    real(8), intent (in) :: xy
    real(8) :: tmp
    if ((yx <= (-1.1d+91)) .or. (.not. (yx <= 1.85d+142))) then
        tmp = zy * yx
    else
        tmp = yy * xx
    end if
    code = tmp
end function

public static double code(double xx, double yy, double yx, double zy, double zx, double xy) {
	double tmp;
	if ((yx <= -1.1e+91) || !(yx <= 1.85e+142)) {
		tmp = zy * yx;
	} else {
		tmp = yy * xx;
	}
	return tmp;
}

def code(xx, yy, yx, zy, zx, xy):
	tmp = 0
	if (yx <= -1.1e+91) or not (yx <= 1.85e+142):
		tmp = zy * yx
	else:
		tmp = yy * xx
	return tmp

function code(xx, yy, yx, zy, zx, xy)
	tmp = 0.0
	if ((yx <= -1.1e+91) || !(yx <= 1.85e+142))
		tmp = Float64(zy * yx);
	else
		tmp = Float64(yy * xx);
	end
	return tmp
end

function tmp_2 = code(xx, yy, yx, zy, zx, xy)
	tmp = 0.0;
	if ((yx <= -1.1e+91) || ~((yx <= 1.85e+142)))
		tmp = zy * yx;
	else
		tmp = yy * xx;
	end
	tmp_2 = tmp;
end

code[xx_, yy_, yx_, zy_, zx_, xy_] := If[Or[LessEqual[yx, -1.1e+91], N[Not[LessEqual[yx, 1.85e+142]], $MachinePrecision]], N[(zy * yx), $MachinePrecision], N[(yy * xx), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;yx \leq -1.1 \cdot 10^{+91} \lor \neg \left(yx \leq 1.85 \cdot 10^{+142}\right):\\
\;\;\;\;zy \cdot yx\\

\mathbf{else}:\\
\;\;\;\;yy \cdot xx\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if yx < -1.1e91 or 1.8499999999999999e142 < yx
1. Initial program 75.3%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in yx around inf
  \[\leadsto \color{blue}{yx \cdot \left(zy - xy\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
  3. lower--.f6474.6
    \[\leadsto \color{blue}{\left(zy - xy\right)} \cdot yx \]
5. Applied rewrites74.6%
  \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
6. Taylor expanded in zy around inf
  \[\leadsto yx \cdot \color{blue}{zy} \]
7. Step-by-step derivation
8. Applied rewrites41.9%
  \[\leadsto zy \cdot \color{blue}{yx} \]
if -1.1e91 < yx < 1.8499999999999999e142
1. Initial program 87.7%
  \[\left(\left(\left(\left(xx \cdot yy + yx \cdot zy\right) + zx \cdot xy\right) - xx \cdot zy\right) - yx \cdot xy\right) - zx \cdot yy \]
2. Add Preprocessing
3. Taylor expanded in zy around 0
  \[\leadsto \color{blue}{\left(xx \cdot yy + xy \cdot zx\right) - \left(xy \cdot yx + yy \cdot zx\right)} \]
4. Step-by-step derivation
  1. +-commutativeN/A
    \[\leadsto \color{blue}{\left(xy \cdot zx + xx \cdot yy\right)} - \left(xy \cdot yx + yy \cdot zx\right) \]
  2. associate--l+N/A
    \[\leadsto \color{blue}{xy \cdot zx + \left(xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  3. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, xx \cdot yy - \left(xy \cdot yx + yy \cdot zx\right)\right)} \]
  4. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{xx \cdot yy + \left(\mathsf{neg}\left(\left(xy \cdot yx + yy \cdot zx\right)\right)\right)}\right) \]
  5. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\mathsf{neg}\left(\color{blue}{\left(yy \cdot zx + xy \cdot yx\right)}\right)\right)\right) \]
  6. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \color{blue}{\left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(xy \cdot yx\right)\right)\right)}\right) \]
  7. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \left(\mathsf{neg}\left(\color{blue}{yx \cdot xy}\right)\right)\right)\right) \]
  8. distribute-lft-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, xx \cdot yy + \left(\left(\mathsf{neg}\left(yy \cdot zx\right)\right) + \color{blue}{\left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right)\right) \]
  9. associate-+r+N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx \cdot yy + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy}\right) \]
  10. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(\color{blue}{yy \cdot xx} + \left(\mathsf{neg}\left(yy \cdot zx\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  11. distribute-rgt-neg-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + \color{blue}{yy \cdot \left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  12. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \left(yy \cdot xx + yy \cdot \color{blue}{\left(-1 \cdot zx\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  13. distribute-lft-inN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{yy \cdot \left(xx + -1 \cdot zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  14. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \left(xx + \color{blue}{\left(\mathsf{neg}\left(zx\right)\right)}\right) + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  15. sub-negN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, yy \cdot \color{blue}{\left(xx - zx\right)} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  16. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\left(xx - zx\right) \cdot yy} + \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right) \]
  17. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)}\right) \]
  18. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(xy, zx, \mathsf{fma}\left(\color{blue}{xx - zx}, yy, \left(\mathsf{neg}\left(yx\right)\right) \cdot xy\right)\right) \]
5. Applied rewrites70.2%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xy, zx, \mathsf{fma}\left(xx - zx, yy, \left(-yx\right) \cdot xy\right)\right)} \]
6. Taylor expanded in xx around inf
  \[\leadsto xx \cdot \color{blue}{yy} \]
7. Step-by-step derivation
8. Applied rewrites28.0%
  \[\leadsto yy \cdot \color{blue}{xx} \]
Recombined 2 regimes into one program.
Final simplification32.2%
\[\leadsto \begin{array}{l} \mathbf{if}\;yx \leq -1.1 \cdot 10^{+91} \lor \neg \left(yx \leq 1.85 \cdot 10^{+142}\right):\\ \;\;\;\;zy \cdot yx\\ \mathbf{else}:\\ \;\;\;\;yy \cdot xx\\ \end{array} \]
Add Preprocessing

47.2% of points produce a very large (infinite) output. You may want to add a precondition. (more)

Specification

Local Percentage Accuracy vs ?

Accuracy vs Speed?

Initial Program: 88.3% accurate, 1.0× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Alternative 1: 95.2% accurate, 0.5× speedupMathFPCoreCJuliaWolframTeX?

if (-.f64 (-.f64 (-.f64 (+.f64 (+.f64 (*.f64 xx yy) (*.f64 yx zy)) (*.f64 zx xy)) (*.f64 xx zy)) (*.f64 yx xy)) (*.f64 zx yy)) < +inf.0

if +inf.0 < (-.f64 (-.f64 (-.f64 (+.f64 (+.f64 (*.f64 xx yy) (*.f64 yx zy)) (*.f64 zx xy)) (*.f64 xx zy)) (*.f64 yx xy)) (*.f64 zx yy))

Alternative 2: 80.9% accurate, 1.1× speedupMathFPCoreCJuliaWolframTeX?

if zy < -1.50000000000000006e-26 or 2.4999999999999999e199 < zy

if -1.50000000000000006e-26 < zy < 3.9999999999999998e33

if 3.9999999999999998e33 < zy < 2.4999999999999999e199

Alternative 3: 78.0% accurate, 1.3× speedupMathFPCoreCJuliaWolframTeX?

if yx < -2.09999999999999986e188 or 2.20000000000000003e167 < yx

if -2.09999999999999986e188 < yx < -6.00000000000000016e-111

if -6.00000000000000016e-111 < yx < 2.20000000000000003e167

Alternative 4: 52.8% accurate, 1.4× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if xy < -1.84999999999999994e60 or 7e37 < xy

if -1.84999999999999994e60 < xy < -6.19999999999999987e-215

if -6.19999999999999987e-215 < xy < -5.1999999999999998e-251

if -5.1999999999999998e-251 < xy < 7e37

Alternative 5: 29.8% accurate, 1.4× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if yy < -1.74999999999999994e161 or 3.7999999999999997e147 < yy

if -1.74999999999999994e161 < yy < -9.5000000000000005e-77

if -9.5000000000000005e-77 < yy < 1.6e28

if 1.6e28 < yy < 3.7999999999999997e147

Alternative 6: 77.7% accurate, 1.5× speedupMathFPCoreCJuliaWolframTeX?

if yx < -1.7000000000000001e148 or 2.20000000000000003e167 < yx

if -1.7000000000000001e148 < yx < 2.20000000000000003e167

Alternative 7: 64.0% accurate, 1.7× speedupMathFPCoreCJuliaWolframTeX?

if yx < -1.7000000000000001e148 or 1.3000000000000001e103 < yx

if -1.7000000000000001e148 < yx < 1.3000000000000001e103

Alternative 8: 44.7% accurate, 1.7× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if yy < -1.75000000000000001e70 or 1.19999999999999999e-64 < yy

if -1.75000000000000001e70 < yy < -3.2e-78

if -3.2e-78 < yy < 1.19999999999999999e-64

Alternative 9: 54.5% accurate, 2.2× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if xx < -5.4000000000000003e28 or 1.15e-9 < xx

if -5.4000000000000003e28 < xx < 1.15e-9

Alternative 10: 44.2% accurate, 2.2× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if yy < -2.10000000000000015e-77 or 1.19999999999999999e-64 < yy

if -2.10000000000000015e-77 < yy < 1.19999999999999999e-64

Alternative 11: 28.3% accurate, 2.5× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if yx < -1.1e91 or 1.8499999999999999e142 < yx

if -1.1e91 < yx < 1.8499999999999999e142

Alternative 12: 20.5% accurate, 7.7× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Reproduce

Initial Program: 88.3% accurate, 1.0× speedup?

Alternative 1: 95.2% accurate, 0.5× speedup?

`if (-.f64 (-.f64 (-.f64 (+.f64 (+.f64 (.f64 xx yy) (.f64 yx zy)) (.f64 zx xy)) (.f64 xx zy)) (.f64 yx xy)) (.f64 zx yy)) < +inf.0`

`if +inf.0 < (-.f64 (-.f64 (-.f64 (+.f64 (+.f64 (.f64 xx yy) (.f64 yx zy)) (.f64 zx xy)) (.f64 xx zy)) (.f64 yx xy)) (.f64 zx yy))`

Alternative 2: 80.9% accurate, 1.1× speedup?

`if zy < -1.50000000000000006e-26 or 2.4999999999999999e199 < zy`

`if -1.50000000000000006e-26 < zy < 3.9999999999999998e33`

`if 3.9999999999999998e33 < zy < 2.4999999999999999e199`

Alternative 3: 78.0% accurate, 1.3× speedup?

`if yx < -2.09999999999999986e188 or 2.20000000000000003e167 < yx`

`if -2.09999999999999986e188 < yx < -6.00000000000000016e-111`

`if -6.00000000000000016e-111 < yx < 2.20000000000000003e167`

Alternative 4: 52.8% accurate, 1.4× speedup?

`if xy < -1.84999999999999994e60 or 7e37 < xy`

`if -1.84999999999999994e60 < xy < -6.19999999999999987e-215`

`if -6.19999999999999987e-215 < xy < -5.1999999999999998e-251`

`if -5.1999999999999998e-251 < xy < 7e37`

Alternative 5: 29.8% accurate, 1.4× speedup?

`if yy < -1.74999999999999994e161 or 3.7999999999999997e147 < yy`

`if -1.74999999999999994e161 < yy < -9.5000000000000005e-77`

`if -9.5000000000000005e-77 < yy < 1.6e28`

`if 1.6e28 < yy < 3.7999999999999997e147`

Alternative 6: 77.7% accurate, 1.5× speedup?

`if yx < -1.7000000000000001e148 or 2.20000000000000003e167 < yx`

`if -1.7000000000000001e148 < yx < 2.20000000000000003e167`

Alternative 7: 64.0% accurate, 1.7× speedup?

`if yx < -1.7000000000000001e148 or 1.3000000000000001e103 < yx`

`if -1.7000000000000001e148 < yx < 1.3000000000000001e103`

Alternative 8: 44.7% accurate, 1.7× speedup?

`if yy < -1.75000000000000001e70 or 1.19999999999999999e-64 < yy`

`if -1.75000000000000001e70 < yy < -3.2e-78`

`if -3.2e-78 < yy < 1.19999999999999999e-64`

Alternative 9: 54.5% accurate, 2.2× speedup?

`if xx < -5.4000000000000003e28 or 1.15e-9 < xx`

`if -5.4000000000000003e28 < xx < 1.15e-9`

Alternative 10: 44.2% accurate, 2.2× speedup?

`if yy < -2.10000000000000015e-77 or 1.19999999999999999e-64 < yy`

`if -2.10000000000000015e-77 < yy < 1.19999999999999999e-64`

Alternative 11: 28.3% accurate, 2.5× speedup?

`if yx < -1.1e91 or 1.8499999999999999e142 < yx`

`if -1.1e91 < yx < 1.8499999999999999e142`

Alternative 12: 20.5% accurate, 7.7× speedup?