Result for (yx - xx)*(zy - xy) - (zx - xx)*(yy

Alternative 1: 96.2% accurate, 0.9× speedup?

\[\begin{array}{l} \\ \mathsf{fma}\left(zy - yy, -xx, \mathsf{fma}\left(xy - yy, zx, \left(zy - xy\right) \cdot yx\right)\right) \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (fma (- zy yy) (- xx) (fma (- xy yy) zx (* (- zy xy) yx))))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	return fma((zy - yy), -xx, fma((xy - yy), zx, ((zy - xy) * yx)));
}

function code(yx, xx, zy, xy, zx, yy)
	return fma(Float64(zy - yy), Float64(-xx), fma(Float64(xy - yy), zx, Float64(Float64(zy - xy) * yx)))
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := N[(N[(zy - yy), $MachinePrecision] * (-xx) + N[(N[(xy - yy), $MachinePrecision] * zx + N[(N[(zy - xy), $MachinePrecision] * yx), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\mathsf{fma}\left(zy - yy, -xx, \mathsf{fma}\left(xy - yy, zx, \left(zy - xy\right) \cdot yx\right)\right)
\end{array}

Derivation

Initial program 82.6%
\[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
Add Preprocessing
Taylor expanded in xx around -inf
\[\leadsto \color{blue}{-1 \cdot \left(xx \cdot \left(\left(zy + -1 \cdot \frac{yx \cdot \left(zy - xy\right) - zx \cdot \left(yy - xy\right)}{xx}\right) - yy\right)\right)} \]
Step-by-step derivation
1. associate-*r*N/A
  \[\leadsto \color{blue}{\left(-1 \cdot xx\right) \cdot \left(\left(zy + -1 \cdot \frac{yx \cdot \left(zy - xy\right) - zx \cdot \left(yy - xy\right)}{xx}\right) - yy\right)} \]
2. mul-1-negN/A
  \[\leadsto \color{blue}{\left(\mathsf{neg}\left(xx\right)\right)} \cdot \left(\left(zy + -1 \cdot \frac{yx \cdot \left(zy - xy\right) - zx \cdot \left(yy - xy\right)}{xx}\right) - yy\right) \]
3. lower-*.f64N/A
  \[\leadsto \color{blue}{\left(\mathsf{neg}\left(xx\right)\right) \cdot \left(\left(zy + -1 \cdot \frac{yx \cdot \left(zy - xy\right) - zx \cdot \left(yy - xy\right)}{xx}\right) - yy\right)} \]
4. lower-neg.f64N/A
  \[\leadsto \color{blue}{\left(-xx\right)} \cdot \left(\left(zy + -1 \cdot \frac{yx \cdot \left(zy - xy\right) - zx \cdot \left(yy - xy\right)}{xx}\right) - yy\right) \]
5. lower--.f64N/A
  \[\leadsto \left(-xx\right) \cdot \color{blue}{\left(\left(zy + -1 \cdot \frac{yx \cdot \left(zy - xy\right) - zx \cdot \left(yy - xy\right)}{xx}\right) - yy\right)} \]
Applied rewrites83.7%
\[\leadsto \color{blue}{\left(-xx\right) \cdot \left(\left(zy - \frac{\mathsf{fma}\left(xy - yy, zx, \left(zy - xy\right) \cdot yx\right)}{xx}\right) - yy\right)} \]
Taylor expanded in xx around 0
\[\leadsto -1 \cdot \left(xx \cdot \left(zy - yy\right)\right) + \color{blue}{\left(yx \cdot \left(zy - xy\right) + zx \cdot \left(xy - yy\right)\right)} \]
Step-by-step derivation
Applied rewrites96.9%
\[\leadsto \mathsf{fma}\left(zy - yy, \color{blue}{-xx}, \mathsf{fma}\left(xy - yy, zx, \left(zy - xy\right) \cdot yx\right)\right) \]
Add Preprocessing

Alternative 2: 89.2% accurate, 0.5× speedup?

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

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

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

public static double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double t_0 = ((yx - xx) * (zy - xy)) - ((zx - xx) * (yy - xy));
	double tmp;
	if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = t_0;
	} else {
		tmp = (zx - yx) * xy;
	}
	return tmp;
}

def code(yx, xx, zy, xy, zx, yy):
	t_0 = ((yx - xx) * (zy - xy)) - ((zx - xx) * (yy - xy))
	tmp = 0
	if t_0 <= math.inf:
		tmp = t_0
	else:
		tmp = (zx - yx) * xy
	return tmp

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

function tmp_2 = code(yx, xx, zy, xy, zx, yy)
	t_0 = ((yx - xx) * (zy - xy)) - ((zx - xx) * (yy - xy));
	tmp = 0.0;
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = (zx - yx) * xy;
	end
	tmp_2 = tmp;
end

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

\begin{array}{l}

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

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if (-.f64 (*.f64 (-.f64 yx xx) (-.f64 zy xy)) (*.f64 (-.f64 zx xx) (-.f64 yy xy))) < +inf.0
1. Initial program 94.4%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
if +inf.0 < (-.f64 (*.f64 (-.f64 yx xx) (-.f64 zy xy)) (*.f64 (-.f64 zx xx) (-.f64 yy xy)))
1. Initial program 0.0%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
3. Taylor expanded in xy around inf
  \[\leadsto \color{blue}{xy \cdot \left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  3. cancel-sign-sub-invN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(zx - xx\right)\right)} \cdot xy \]
  4. metadata-evalN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{1} \cdot \left(zx - xx\right)\right) \cdot xy \]
  5. *-lft-identityN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{\left(zx - xx\right)}\right) \cdot xy \]
  6. associate-+r-N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  7. lower--.f64N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  8. lower-+.f64N/A
    \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(yx - xx\right) + zx\right)} - xx\right) \cdot xy \]
  9. mul-1-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\mathsf{neg}\left(\left(yx - xx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  10. sub-negN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(yx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  11. +-commutativeN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + yx\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  12. distribute-neg-inN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  13. unsub-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) - yx\right)} + zx\right) - xx\right) \cdot xy \]
  14. remove-double-negN/A
    \[\leadsto \left(\left(\left(\color{blue}{xx} - yx\right) + zx\right) - xx\right) \cdot xy \]
  15. lower--.f6420.1
    \[\leadsto \left(\left(\color{blue}{\left(xx - yx\right)} + zx\right) - xx\right) \cdot xy \]
5. Applied rewrites20.1%
  \[\leadsto \color{blue}{\left(\left(\left(xx - yx\right) + zx\right) - xx\right) \cdot xy} \]
6. Taylor expanded in yx around 0
  \[\leadsto \left(zx + -1 \cdot yx\right) \cdot xy \]
7. Step-by-step derivation
8. Applied rewrites59.8%
  \[\leadsto \left(zx - yx\right) \cdot xy \]
Recombined 2 regimes into one program.
Add Preprocessing

Alternative 3: 81.1% accurate, 0.9× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;xy \leq -1.9 \cdot 10^{+24} \lor \neg \left(xy \leq 6 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{fma}\left(xy - yy, zx, \left(zy - xy\right) \cdot yx\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(xx - zx, yy, \left(yx - xx\right) \cdot zy\right)\\ \end{array} \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (if (or (<= xy -1.9e+24) (not (<= xy 6e+69)))
   (fma (- xy yy) zx (* (- zy xy) yx))
   (fma (- xx zx) yy (* (- yx xx) zy))))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((xy <= -1.9e+24) || !(xy <= 6e+69)) {
		tmp = fma((xy - yy), zx, ((zy - xy) * yx));
	} else {
		tmp = fma((xx - zx), yy, ((yx - xx) * zy));
	}
	return tmp;
}

function code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0
	if ((xy <= -1.9e+24) || !(xy <= 6e+69))
		tmp = fma(Float64(xy - yy), zx, Float64(Float64(zy - xy) * yx));
	else
		tmp = fma(Float64(xx - zx), yy, Float64(Float64(yx - xx) * zy));
	end
	return tmp
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := If[Or[LessEqual[xy, -1.9e+24], N[Not[LessEqual[xy, 6e+69]], $MachinePrecision]], N[(N[(xy - yy), $MachinePrecision] * zx + N[(N[(zy - xy), $MachinePrecision] * yx), $MachinePrecision]), $MachinePrecision], N[(N[(xx - zx), $MachinePrecision] * yy + N[(N[(yx - xx), $MachinePrecision] * zy), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;xy \leq -1.9 \cdot 10^{+24} \lor \neg \left(xy \leq 6 \cdot 10^{+69}\right):\\
\;\;\;\;\mathsf{fma}\left(xy - yy, zx, \left(zy - xy\right) \cdot yx\right)\\

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if xy < -1.90000000000000008e24 or 5.99999999999999967e69 < xy
1. Initial program 67.6%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
3. Taylor expanded in xx around 0
  \[\leadsto \color{blue}{yx \cdot \left(zy - xy\right) - zx \cdot \left(yy - xy\right)} \]
4. Step-by-step derivation
  1. sub-negN/A
    \[\leadsto \color{blue}{yx \cdot \left(zy - xy\right) + \left(\mathsf{neg}\left(zx \cdot \left(yy - xy\right)\right)\right)} \]
  2. +-commutativeN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(zx \cdot \left(yy - xy\right)\right)\right) + yx \cdot \left(zy - xy\right)} \]
  3. *-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(yy - xy\right) \cdot zx}\right)\right) + yx \cdot \left(zy - xy\right) \]
  4. distribute-lft-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(yy - xy\right)\right)\right) \cdot zx} + yx \cdot \left(zy - xy\right) \]
  5. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yy - xy\right)\right)} \cdot zx + yx \cdot \left(zy - xy\right) \]
  6. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(yy - xy\right), zx, yx \cdot \left(zy - xy\right)\right)} \]
  7. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(yy - xy\right)\right)}, zx, yx \cdot \left(zy - xy\right)\right) \]
  8. sub-negN/A
    \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(yy + \left(\mathsf{neg}\left(xy\right)\right)\right)}\right), zx, yx \cdot \left(zy - xy\right)\right) \]
  9. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xy\right)\right) + yy\right)}\right), zx, yx \cdot \left(zy - xy\right)\right) \]
  10. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xy\right)\right)\right)\right) + \left(\mathsf{neg}\left(yy\right)\right)}, zx, yx \cdot \left(zy - xy\right)\right) \]
  11. remove-double-negN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{xy} + \left(\mathsf{neg}\left(yy\right)\right), zx, yx \cdot \left(zy - xy\right)\right) \]
  12. sub-negN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{xy - yy}, zx, yx \cdot \left(zy - xy\right)\right) \]
  13. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{xy - yy}, zx, yx \cdot \left(zy - xy\right)\right) \]
  14. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xy - yy, zx, \color{blue}{\left(zy - xy\right) \cdot yx}\right) \]
  15. lower-*.f64N/A
    \[\leadsto \mathsf{fma}\left(xy - yy, zx, \color{blue}{\left(zy - xy\right) \cdot yx}\right) \]
  16. lower--.f6483.0
    \[\leadsto \mathsf{fma}\left(xy - yy, zx, \color{blue}{\left(zy - xy\right)} \cdot yx\right) \]
5. Applied rewrites83.0%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xy - yy, zx, \left(zy - xy\right) \cdot yx\right)} \]
if -1.90000000000000008e24 < xy < 5.99999999999999967e69
1. Initial program 94.5%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
3. Taylor expanded in xy around 0
  \[\leadsto \color{blue}{zy \cdot \left(yx - xx\right) - yy \cdot \left(zx - xx\right)} \]
4. Step-by-step derivation
  1. sub-negN/A
    \[\leadsto \color{blue}{zy \cdot \left(yx - xx\right) + \left(\mathsf{neg}\left(yy \cdot \left(zx - xx\right)\right)\right)} \]
  2. +-commutativeN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(yy \cdot \left(zx - xx\right)\right)\right) + zy \cdot \left(yx - xx\right)} \]
  3. *-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right) \cdot yy}\right)\right) + zy \cdot \left(yx - xx\right) \]
  4. distribute-lft-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right) \cdot yy} + zy \cdot \left(yx - xx\right) \]
  5. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy + zy \cdot \left(yx - xx\right) \]
  6. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(zx - xx\right), yy, zy \cdot \left(yx - xx\right)\right)} \]
  7. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(zx - xx\right)\right)}, yy, zy \cdot \left(yx - xx\right)\right) \]
  8. sub-negN/A
    \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right), yy, zy \cdot \left(yx - xx\right)\right) \]
  9. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right), yy, zy \cdot \left(yx - xx\right)\right) \]
  10. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)}, yy, zy \cdot \left(yx - xx\right)\right) \]
  11. remove-double-negN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right), yy, zy \cdot \left(yx - xx\right)\right) \]
  12. sub-negN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{xx - zx}, yy, zy \cdot \left(yx - xx\right)\right) \]
  13. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{xx - zx}, yy, zy \cdot \left(yx - xx\right)\right) \]
  14. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xx - zx, yy, \color{blue}{\left(yx - xx\right) \cdot zy}\right) \]
  15. lower-*.f64N/A
    \[\leadsto \mathsf{fma}\left(xx - zx, yy, \color{blue}{\left(yx - xx\right) \cdot zy}\right) \]
  16. lower--.f6491.2
    \[\leadsto \mathsf{fma}\left(xx - zx, yy, \color{blue}{\left(yx - xx\right)} \cdot zy\right) \]
5. Applied rewrites91.2%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(yx - xx\right) \cdot zy\right)} \]
Recombined 2 regimes into one program.
Final simplification87.6%
\[\leadsto \begin{array}{l} \mathbf{if}\;xy \leq -1.9 \cdot 10^{+24} \lor \neg \left(xy \leq 6 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{fma}\left(xy - yy, zx, \left(zy - xy\right) \cdot yx\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(xx - zx, yy, \left(yx - xx\right) \cdot zy\right)\\ \end{array} \]
Add Preprocessing

Alternative 4: 77.7% accurate, 0.9× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;xy \leq -1 \cdot 10^{+97} \lor \neg \left(xy \leq 5.2 \cdot 10^{+86}\right):\\ \;\;\;\;\left(zx - yx\right) \cdot xy\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(xx - zx, yy, \left(yx - xx\right) \cdot zy\right)\\ \end{array} \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (if (or (<= xy -1e+97) (not (<= xy 5.2e+86)))
   (* (- zx yx) xy)
   (fma (- xx zx) yy (* (- yx xx) zy))))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((xy <= -1e+97) || !(xy <= 5.2e+86)) {
		tmp = (zx - yx) * xy;
	} else {
		tmp = fma((xx - zx), yy, ((yx - xx) * zy));
	}
	return tmp;
}

function code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0
	if ((xy <= -1e+97) || !(xy <= 5.2e+86))
		tmp = Float64(Float64(zx - yx) * xy);
	else
		tmp = fma(Float64(xx - zx), yy, Float64(Float64(yx - xx) * zy));
	end
	return tmp
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := If[Or[LessEqual[xy, -1e+97], N[Not[LessEqual[xy, 5.2e+86]], $MachinePrecision]], N[(N[(zx - yx), $MachinePrecision] * xy), $MachinePrecision], N[(N[(xx - zx), $MachinePrecision] * yy + N[(N[(yx - xx), $MachinePrecision] * zy), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;xy \leq -1 \cdot 10^{+97} \lor \neg \left(xy \leq 5.2 \cdot 10^{+86}\right):\\
\;\;\;\;\left(zx - yx\right) \cdot xy\\

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if xy < -1.0000000000000001e97 or 5.1999999999999995e86 < xy
1. Initial program 65.2%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
3. Taylor expanded in xy around inf
  \[\leadsto \color{blue}{xy \cdot \left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  3. cancel-sign-sub-invN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(zx - xx\right)\right)} \cdot xy \]
  4. metadata-evalN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{1} \cdot \left(zx - xx\right)\right) \cdot xy \]
  5. *-lft-identityN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{\left(zx - xx\right)}\right) \cdot xy \]
  6. associate-+r-N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  7. lower--.f64N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  8. lower-+.f64N/A
    \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(yx - xx\right) + zx\right)} - xx\right) \cdot xy \]
  9. mul-1-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\mathsf{neg}\left(\left(yx - xx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  10. sub-negN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(yx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  11. +-commutativeN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + yx\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  12. distribute-neg-inN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  13. unsub-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) - yx\right)} + zx\right) - xx\right) \cdot xy \]
  14. remove-double-negN/A
    \[\leadsto \left(\left(\left(\color{blue}{xx} - yx\right) + zx\right) - xx\right) \cdot xy \]
  15. lower--.f6457.8
    \[\leadsto \left(\left(\color{blue}{\left(xx - yx\right)} + zx\right) - xx\right) \cdot xy \]
5. Applied rewrites57.8%
  \[\leadsto \color{blue}{\left(\left(\left(xx - yx\right) + zx\right) - xx\right) \cdot xy} \]
6. Taylor expanded in yx around 0
  \[\leadsto \left(zx + -1 \cdot yx\right) \cdot xy \]
7. Step-by-step derivation
8. Applied rewrites76.2%
  \[\leadsto \left(zx - yx\right) \cdot xy \]
if -1.0000000000000001e97 < xy < 5.1999999999999995e86
1. Initial program 93.5%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
3. Taylor expanded in xy around 0
  \[\leadsto \color{blue}{zy \cdot \left(yx - xx\right) - yy \cdot \left(zx - xx\right)} \]
4. Step-by-step derivation
  1. sub-negN/A
    \[\leadsto \color{blue}{zy \cdot \left(yx - xx\right) + \left(\mathsf{neg}\left(yy \cdot \left(zx - xx\right)\right)\right)} \]
  2. +-commutativeN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(yy \cdot \left(zx - xx\right)\right)\right) + zy \cdot \left(yx - xx\right)} \]
  3. *-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right) \cdot yy}\right)\right) + zy \cdot \left(yx - xx\right) \]
  4. distribute-lft-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right) \cdot yy} + zy \cdot \left(yx - xx\right) \]
  5. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy + zy \cdot \left(yx - xx\right) \]
  6. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(zx - xx\right), yy, zy \cdot \left(yx - xx\right)\right)} \]
  7. mul-1-negN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(zx - xx\right)\right)}, yy, zy \cdot \left(yx - xx\right)\right) \]
  8. sub-negN/A
    \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right), yy, zy \cdot \left(yx - xx\right)\right) \]
  9. +-commutativeN/A
    \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right), yy, zy \cdot \left(yx - xx\right)\right) \]
  10. distribute-neg-inN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)}, yy, zy \cdot \left(yx - xx\right)\right) \]
  11. remove-double-negN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right), yy, zy \cdot \left(yx - xx\right)\right) \]
  12. sub-negN/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{xx - zx}, yy, zy \cdot \left(yx - xx\right)\right) \]
  13. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{xx - zx}, yy, zy \cdot \left(yx - xx\right)\right) \]
  14. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(xx - zx, yy, \color{blue}{\left(yx - xx\right) \cdot zy}\right) \]
  15. lower-*.f64N/A
    \[\leadsto \mathsf{fma}\left(xx - zx, yy, \color{blue}{\left(yx - xx\right) \cdot zy}\right) \]
  16. lower--.f6488.9
    \[\leadsto \mathsf{fma}\left(xx - zx, yy, \color{blue}{\left(yx - xx\right)} \cdot zy\right) \]
5. Applied rewrites88.9%
  \[\leadsto \color{blue}{\mathsf{fma}\left(xx - zx, yy, \left(yx - xx\right) \cdot zy\right)} \]
Recombined 2 regimes into one program.
Final simplification84.0%
\[\leadsto \begin{array}{l} \mathbf{if}\;xy \leq -1 \cdot 10^{+97} \lor \neg \left(xy \leq 5.2 \cdot 10^{+86}\right):\\ \;\;\;\;\left(zx - yx\right) \cdot xy\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(xx - zx, yy, \left(yx - xx\right) \cdot zy\right)\\ \end{array} \]
Add Preprocessing

Alternative 5: 64.9% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;zx \leq -9.2 \cdot 10^{+69} \lor \neg \left(zx \leq 3.7 \cdot 10^{+80}\right):\\ \;\;\;\;\left(xy - yy\right) \cdot zx\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(yx - xx, zy, yy \cdot xx\right)\\ \end{array} \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (if (or (<= zx -9.2e+69) (not (<= zx 3.7e+80)))
   (* (- xy yy) zx)
   (fma (- yx xx) zy (* yy xx))))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((zx <= -9.2e+69) || !(zx <= 3.7e+80)) {
		tmp = (xy - yy) * zx;
	} else {
		tmp = fma((yx - xx), zy, (yy * xx));
	}
	return tmp;
}

function code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0
	if ((zx <= -9.2e+69) || !(zx <= 3.7e+80))
		tmp = Float64(Float64(xy - yy) * zx);
	else
		tmp = fma(Float64(yx - xx), zy, Float64(yy * xx));
	end
	return tmp
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := If[Or[LessEqual[zx, -9.2e+69], N[Not[LessEqual[zx, 3.7e+80]], $MachinePrecision]], N[(N[(xy - yy), $MachinePrecision] * zx), $MachinePrecision], N[(N[(yx - xx), $MachinePrecision] * zy + N[(yy * xx), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;zx \leq -9.2 \cdot 10^{+69} \lor \neg \left(zx \leq 3.7 \cdot 10^{+80}\right):\\
\;\;\;\;\left(xy - yy\right) \cdot zx\\

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if zx < -9.20000000000000067e69 or 3.69999999999999996e80 < zx
1. Initial program 88.4%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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. sub-negN/A
    \[\leadsto \color{blue}{\left(xy + \left(\mathsf{neg}\left(yy\right)\right)\right)} \cdot zx \]
  3. remove-double-negN/A
    \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xy\right)\right)\right)\right)} + \left(\mathsf{neg}\left(yy\right)\right)\right) \cdot zx \]
  4. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(xy\right)\right) + yy\right)\right)\right)} \cdot zx \]
  5. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(yy + \left(\mathsf{neg}\left(xy\right)\right)\right)}\right)\right) \cdot zx \]
  6. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(yy - xy\right)}\right)\right) \cdot zx \]
  7. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yy - xy\right)\right)} \cdot zx \]
  8. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yy - xy\right)\right) \cdot zx} \]
  9. mul-1-negN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(yy - xy\right)\right)\right)} \cdot zx \]
  10. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(yy + \left(\mathsf{neg}\left(xy\right)\right)\right)}\right)\right) \cdot zx \]
  11. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xy\right)\right) + yy\right)}\right)\right) \cdot zx \]
  12. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xy\right)\right)\right)\right) + \left(\mathsf{neg}\left(yy\right)\right)\right)} \cdot zx \]
  13. remove-double-negN/A
    \[\leadsto \left(\color{blue}{xy} + \left(\mathsf{neg}\left(yy\right)\right)\right) \cdot zx \]
  14. sub-negN/A
    \[\leadsto \color{blue}{\left(xy - yy\right)} \cdot zx \]
  15. lower--.f6478.5
    \[\leadsto \color{blue}{\left(xy - yy\right)} \cdot zx \]
5. Applied rewrites78.5%
  \[\leadsto \color{blue}{\left(xy - yy\right) \cdot zx} \]
if -9.20000000000000067e69 < zx < 3.69999999999999996e80
1. Initial program 79.2%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
3. Taylor expanded in zx around 0
  \[\leadsto \color{blue}{\left(yx - xx\right) \cdot \left(zy - xy\right) - -1 \cdot \left(xx \cdot \left(yy - xy\right)\right)} \]
4. Step-by-step derivation
  1. associate-*r*N/A
    \[\leadsto \left(yx - xx\right) \cdot \left(zy - xy\right) - \color{blue}{\left(-1 \cdot xx\right) \cdot \left(yy - xy\right)} \]
  2. mul-1-negN/A
    \[\leadsto \left(yx - xx\right) \cdot \left(zy - xy\right) - \color{blue}{\left(\mathsf{neg}\left(xx\right)\right)} \cdot \left(yy - xy\right) \]
  3. cancel-sign-subN/A
    \[\leadsto \color{blue}{\left(yx - xx\right) \cdot \left(zy - xy\right) + xx \cdot \left(yy - xy\right)} \]
  4. lower-fma.f64N/A
    \[\leadsto \color{blue}{\mathsf{fma}\left(yx - xx, zy - xy, xx \cdot \left(yy - xy\right)\right)} \]
  5. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(\color{blue}{yx - xx}, zy - xy, xx \cdot \left(yy - xy\right)\right) \]
  6. lower--.f64N/A
    \[\leadsto \mathsf{fma}\left(yx - xx, \color{blue}{zy - xy}, xx \cdot \left(yy - xy\right)\right) \]
  7. *-commutativeN/A
    \[\leadsto \mathsf{fma}\left(yx - xx, zy - xy, \color{blue}{\left(yy - xy\right) \cdot xx}\right) \]
  8. lower-*.f64N/A
    \[\leadsto \mathsf{fma}\left(yx - xx, zy - xy, \color{blue}{\left(yy - xy\right) \cdot xx}\right) \]
  9. lower--.f6470.4
    \[\leadsto \mathsf{fma}\left(yx - xx, zy - xy, \color{blue}{\left(yy - xy\right)} \cdot xx\right) \]
5. Applied rewrites70.4%
  \[\leadsto \color{blue}{\mathsf{fma}\left(yx - xx, zy - xy, \left(yy - xy\right) \cdot xx\right)} \]
6. Taylor expanded in xy around 0
  \[\leadsto xx \cdot yy + \color{blue}{zy \cdot \left(yx - xx\right)} \]
7. Step-by-step derivation
8. Applied rewrites65.2%
  \[\leadsto \mathsf{fma}\left(yx - xx, \color{blue}{zy}, yy \cdot xx\right) \]
Recombined 2 regimes into one program.
Final simplification70.1%
\[\leadsto \begin{array}{l} \mathbf{if}\;zx \leq -9.2 \cdot 10^{+69} \lor \neg \left(zx \leq 3.7 \cdot 10^{+80}\right):\\ \;\;\;\;\left(xy - yy\right) \cdot zx\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(yx - xx, zy, yy \cdot xx\right)\\ \end{array} \]
Add Preprocessing

Alternative 6: 53.1% accurate, 1.2× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;yy \leq -3.6 \cdot 10^{-12} \lor \neg \left(yy \leq 6.8 \cdot 10^{+37}\right):\\ \;\;\;\;\left(xx - zx\right) \cdot yy\\ \mathbf{else}:\\ \;\;\;\;\left(zy - xy\right) \cdot yx\\ \end{array} \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (if (or (<= yy -3.6e-12) (not (<= yy 6.8e+37)))
   (* (- xx zx) yy)
   (* (- zy xy) yx)))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((yy <= -3.6e-12) || !(yy <= 6.8e+37)) {
		tmp = (xx - zx) * yy;
	} else {
		tmp = (zy - xy) * yx;
	}
	return tmp;
}

real(8) function code(yx, xx, zy, xy, zx, yy)
    real(8), intent (in) :: yx
    real(8), intent (in) :: xx
    real(8), intent (in) :: zy
    real(8), intent (in) :: xy
    real(8), intent (in) :: zx
    real(8), intent (in) :: yy
    real(8) :: tmp
    if ((yy <= (-3.6d-12)) .or. (.not. (yy <= 6.8d+37))) then
        tmp = (xx - zx) * yy
    else
        tmp = (zy - xy) * yx
    end if
    code = tmp
end function

public static double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((yy <= -3.6e-12) || !(yy <= 6.8e+37)) {
		tmp = (xx - zx) * yy;
	} else {
		tmp = (zy - xy) * yx;
	}
	return tmp;
}

def code(yx, xx, zy, xy, zx, yy):
	tmp = 0
	if (yy <= -3.6e-12) or not (yy <= 6.8e+37):
		tmp = (xx - zx) * yy
	else:
		tmp = (zy - xy) * yx
	return tmp

function code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0
	if ((yy <= -3.6e-12) || !(yy <= 6.8e+37))
		tmp = Float64(Float64(xx - zx) * yy);
	else
		tmp = Float64(Float64(zy - xy) * yx);
	end
	return tmp
end

function tmp_2 = code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0;
	if ((yy <= -3.6e-12) || ~((yy <= 6.8e+37)))
		tmp = (xx - zx) * yy;
	else
		tmp = (zy - xy) * yx;
	end
	tmp_2 = tmp;
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := If[Or[LessEqual[yy, -3.6e-12], N[Not[LessEqual[yy, 6.8e+37]], $MachinePrecision]], N[(N[(xx - zx), $MachinePrecision] * yy), $MachinePrecision], N[(N[(zy - xy), $MachinePrecision] * yx), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;yy \leq -3.6 \cdot 10^{-12} \lor \neg \left(yy \leq 6.8 \cdot 10^{+37}\right):\\
\;\;\;\;\left(xx - zx\right) \cdot yy\\

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if yy < -3.6e-12 or 6.80000000000000011e37 < yy
1. Initial program 86.4%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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. sub-negN/A
    \[\leadsto \color{blue}{\left(xx + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  3. remove-double-negN/A
    \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right)} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  4. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)\right)\right)} \cdot yy \]
  5. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  6. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right)}\right)\right) \cdot yy \]
  7. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy \]
  8. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right) \cdot yy} \]
  9. mul-1-negN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right)} \cdot yy \]
  10. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  11. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right)\right) \cdot yy \]
  12. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  13. remove-double-negN/A
    \[\leadsto \left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  14. sub-negN/A
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
  15. lower--.f6471.7
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites71.7%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
if -3.6e-12 < yy < 6.80000000000000011e37
1. Initial program 79.0%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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--.f6456.4
    \[\leadsto \color{blue}{\left(zy - xy\right)} \cdot yx \]
5. Applied rewrites56.4%
  \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
Recombined 2 regimes into one program.
Final simplification63.9%
\[\leadsto \begin{array}{l} \mathbf{if}\;yy \leq -3.6 \cdot 10^{-12} \lor \neg \left(yy \leq 6.8 \cdot 10^{+37}\right):\\ \;\;\;\;\left(xx - zx\right) \cdot yy\\ \mathbf{else}:\\ \;\;\;\;\left(zy - xy\right) \cdot yx\\ \end{array} \]
Add Preprocessing

Alternative 7: 53.9% accurate, 1.2× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;xy \leq -4.7 \cdot 10^{+33} \lor \neg \left(xy \leq 6.5 \cdot 10^{+84}\right):\\ \;\;\;\;\left(zx - yx\right) \cdot xy\\ \mathbf{else}:\\ \;\;\;\;\left(xx - zx\right) \cdot yy\\ \end{array} \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (if (or (<= xy -4.7e+33) (not (<= xy 6.5e+84)))
   (* (- zx yx) xy)
   (* (- xx zx) yy)))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((xy <= -4.7e+33) || !(xy <= 6.5e+84)) {
		tmp = (zx - yx) * xy;
	} else {
		tmp = (xx - zx) * yy;
	}
	return tmp;
}

real(8) function code(yx, xx, zy, xy, zx, yy)
    real(8), intent (in) :: yx
    real(8), intent (in) :: xx
    real(8), intent (in) :: zy
    real(8), intent (in) :: xy
    real(8), intent (in) :: zx
    real(8), intent (in) :: yy
    real(8) :: tmp
    if ((xy <= (-4.7d+33)) .or. (.not. (xy <= 6.5d+84))) then
        tmp = (zx - yx) * xy
    else
        tmp = (xx - zx) * yy
    end if
    code = tmp
end function

public static double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((xy <= -4.7e+33) || !(xy <= 6.5e+84)) {
		tmp = (zx - yx) * xy;
	} else {
		tmp = (xx - zx) * yy;
	}
	return tmp;
}

def code(yx, xx, zy, xy, zx, yy):
	tmp = 0
	if (xy <= -4.7e+33) or not (xy <= 6.5e+84):
		tmp = (zx - yx) * xy
	else:
		tmp = (xx - zx) * yy
	return tmp

function code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0
	if ((xy <= -4.7e+33) || !(xy <= 6.5e+84))
		tmp = Float64(Float64(zx - yx) * xy);
	else
		tmp = Float64(Float64(xx - zx) * yy);
	end
	return tmp
end

function tmp_2 = code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0;
	if ((xy <= -4.7e+33) || ~((xy <= 6.5e+84)))
		tmp = (zx - yx) * xy;
	else
		tmp = (xx - zx) * yy;
	end
	tmp_2 = tmp;
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := If[Or[LessEqual[xy, -4.7e+33], N[Not[LessEqual[xy, 6.5e+84]], $MachinePrecision]], N[(N[(zx - yx), $MachinePrecision] * xy), $MachinePrecision], N[(N[(xx - zx), $MachinePrecision] * yy), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;xy \leq -4.7 \cdot 10^{+33} \lor \neg \left(xy \leq 6.5 \cdot 10^{+84}\right):\\
\;\;\;\;\left(zx - yx\right) \cdot xy\\

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if xy < -4.6999999999999998e33 or 6.50000000000000027e84 < xy
1. Initial program 66.6%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
3. Taylor expanded in xy around inf
  \[\leadsto \color{blue}{xy \cdot \left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  3. cancel-sign-sub-invN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(zx - xx\right)\right)} \cdot xy \]
  4. metadata-evalN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{1} \cdot \left(zx - xx\right)\right) \cdot xy \]
  5. *-lft-identityN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{\left(zx - xx\right)}\right) \cdot xy \]
  6. associate-+r-N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  7. lower--.f64N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  8. lower-+.f64N/A
    \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(yx - xx\right) + zx\right)} - xx\right) \cdot xy \]
  9. mul-1-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\mathsf{neg}\left(\left(yx - xx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  10. sub-negN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(yx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  11. +-commutativeN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + yx\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  12. distribute-neg-inN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  13. unsub-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) - yx\right)} + zx\right) - xx\right) \cdot xy \]
  14. remove-double-negN/A
    \[\leadsto \left(\left(\left(\color{blue}{xx} - yx\right) + zx\right) - xx\right) \cdot xy \]
  15. lower--.f6456.0
    \[\leadsto \left(\left(\color{blue}{\left(xx - yx\right)} + zx\right) - xx\right) \cdot xy \]
5. Applied rewrites56.0%
  \[\leadsto \color{blue}{\left(\left(\left(xx - yx\right) + zx\right) - xx\right) \cdot xy} \]
6. Taylor expanded in yx around 0
  \[\leadsto \left(zx + -1 \cdot yx\right) \cdot xy \]
7. Step-by-step derivation
8. Applied rewrites74.1%
  \[\leadsto \left(zx - yx\right) \cdot xy \]
if -4.6999999999999998e33 < xy < 6.50000000000000027e84
1. Initial program 93.9%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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. sub-negN/A
    \[\leadsto \color{blue}{\left(xx + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  3. remove-double-negN/A
    \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right)} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  4. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)\right)\right)} \cdot yy \]
  5. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  6. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right)}\right)\right) \cdot yy \]
  7. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy \]
  8. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right) \cdot yy} \]
  9. mul-1-negN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right)} \cdot yy \]
  10. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  11. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right)\right) \cdot yy \]
  12. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  13. remove-double-negN/A
    \[\leadsto \left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  14. sub-negN/A
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
  15. lower--.f6454.5
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites54.5%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
Recombined 2 regimes into one program.
Final simplification62.6%
\[\leadsto \begin{array}{l} \mathbf{if}\;xy \leq -4.7 \cdot 10^{+33} \lor \neg \left(xy \leq 6.5 \cdot 10^{+84}\right):\\ \;\;\;\;\left(zx - yx\right) \cdot xy\\ \mathbf{else}:\\ \;\;\;\;\left(xx - zx\right) \cdot yy\\ \end{array} \]
Add Preprocessing

Alternative 8: 42.2% accurate, 1.2× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;xy \leq -4.1 \cdot 10^{+32} \lor \neg \left(xy \leq 9.2 \cdot 10^{+82}\right):\\ \;\;\;\;\left(zx - yx\right) \cdot xy\\ \mathbf{else}:\\ \;\;\;\;\left(-zx\right) \cdot yy\\ \end{array} \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (if (or (<= xy -4.1e+32) (not (<= xy 9.2e+82)))
   (* (- zx yx) xy)
   (* (- zx) yy)))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((xy <= -4.1e+32) || !(xy <= 9.2e+82)) {
		tmp = (zx - yx) * xy;
	} else {
		tmp = -zx * yy;
	}
	return tmp;
}

real(8) function code(yx, xx, zy, xy, zx, yy)
    real(8), intent (in) :: yx
    real(8), intent (in) :: xx
    real(8), intent (in) :: zy
    real(8), intent (in) :: xy
    real(8), intent (in) :: zx
    real(8), intent (in) :: yy
    real(8) :: tmp
    if ((xy <= (-4.1d+32)) .or. (.not. (xy <= 9.2d+82))) then
        tmp = (zx - yx) * xy
    else
        tmp = -zx * yy
    end if
    code = tmp
end function

public static double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((xy <= -4.1e+32) || !(xy <= 9.2e+82)) {
		tmp = (zx - yx) * xy;
	} else {
		tmp = -zx * yy;
	}
	return tmp;
}

def code(yx, xx, zy, xy, zx, yy):
	tmp = 0
	if (xy <= -4.1e+32) or not (xy <= 9.2e+82):
		tmp = (zx - yx) * xy
	else:
		tmp = -zx * yy
	return tmp

function code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0
	if ((xy <= -4.1e+32) || !(xy <= 9.2e+82))
		tmp = Float64(Float64(zx - yx) * xy);
	else
		tmp = Float64(Float64(-zx) * yy);
	end
	return tmp
end

function tmp_2 = code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0;
	if ((xy <= -4.1e+32) || ~((xy <= 9.2e+82)))
		tmp = (zx - yx) * xy;
	else
		tmp = -zx * yy;
	end
	tmp_2 = tmp;
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := If[Or[LessEqual[xy, -4.1e+32], N[Not[LessEqual[xy, 9.2e+82]], $MachinePrecision]], N[(N[(zx - yx), $MachinePrecision] * xy), $MachinePrecision], N[((-zx) * yy), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;xy \leq -4.1 \cdot 10^{+32} \lor \neg \left(xy \leq 9.2 \cdot 10^{+82}\right):\\
\;\;\;\;\left(zx - yx\right) \cdot xy\\

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if xy < -4.09999999999999981e32 or 9.19999999999999953e82 < xy
1. Initial program 66.6%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
3. Taylor expanded in xy around inf
  \[\leadsto \color{blue}{xy \cdot \left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  3. cancel-sign-sub-invN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(zx - xx\right)\right)} \cdot xy \]
  4. metadata-evalN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{1} \cdot \left(zx - xx\right)\right) \cdot xy \]
  5. *-lft-identityN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{\left(zx - xx\right)}\right) \cdot xy \]
  6. associate-+r-N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  7. lower--.f64N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  8. lower-+.f64N/A
    \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(yx - xx\right) + zx\right)} - xx\right) \cdot xy \]
  9. mul-1-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\mathsf{neg}\left(\left(yx - xx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  10. sub-negN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(yx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  11. +-commutativeN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + yx\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  12. distribute-neg-inN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  13. unsub-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) - yx\right)} + zx\right) - xx\right) \cdot xy \]
  14. remove-double-negN/A
    \[\leadsto \left(\left(\left(\color{blue}{xx} - yx\right) + zx\right) - xx\right) \cdot xy \]
  15. lower--.f6456.0
    \[\leadsto \left(\left(\color{blue}{\left(xx - yx\right)} + zx\right) - xx\right) \cdot xy \]
5. Applied rewrites56.0%
  \[\leadsto \color{blue}{\left(\left(\left(xx - yx\right) + zx\right) - xx\right) \cdot xy} \]
6. Taylor expanded in yx around 0
  \[\leadsto \left(zx + -1 \cdot yx\right) \cdot xy \]
7. Step-by-step derivation
8. Applied rewrites74.1%
  \[\leadsto \left(zx - yx\right) \cdot xy \]
if -4.09999999999999981e32 < xy < 9.19999999999999953e82
1. Initial program 93.9%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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. sub-negN/A
    \[\leadsto \color{blue}{\left(xx + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  3. remove-double-negN/A
    \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right)} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  4. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)\right)\right)} \cdot yy \]
  5. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  6. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right)}\right)\right) \cdot yy \]
  7. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy \]
  8. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right) \cdot yy} \]
  9. mul-1-negN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right)} \cdot yy \]
  10. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  11. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right)\right) \cdot yy \]
  12. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  13. remove-double-negN/A
    \[\leadsto \left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  14. sub-negN/A
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
  15. lower--.f6454.5
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites54.5%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
6. Taylor expanded in xx around 0
  \[\leadsto \left(-1 \cdot zx\right) \cdot yy \]
7. Step-by-step derivation
8. Applied rewrites34.7%
  \[\leadsto \left(-zx\right) \cdot yy \]
Recombined 2 regimes into one program.
Final simplification51.0%
\[\leadsto \begin{array}{l} \mathbf{if}\;xy \leq -4.1 \cdot 10^{+32} \lor \neg \left(xy \leq 9.2 \cdot 10^{+82}\right):\\ \;\;\;\;\left(zx - yx\right) \cdot xy\\ \mathbf{else}:\\ \;\;\;\;\left(-zx\right) \cdot yy\\ \end{array} \]
Add Preprocessing

Alternative 9: 52.7% accurate, 1.2× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;yy \leq -3.6 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(yy, xx, yy \cdot \left(-zx\right)\right)\\ \mathbf{elif}\;yy \leq 6.8 \cdot 10^{+37}:\\ \;\;\;\;\left(zy - xy\right) \cdot yx\\ \mathbf{else}:\\ \;\;\;\;\left(xx - zx\right) \cdot yy\\ \end{array} \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (if (<= yy -3.6e-12)
   (fma yy xx (* yy (- zx)))
   (if (<= yy 6.8e+37) (* (- zy xy) yx) (* (- xx zx) yy))))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if (yy <= -3.6e-12) {
		tmp = fma(yy, xx, (yy * -zx));
	} else if (yy <= 6.8e+37) {
		tmp = (zy - xy) * yx;
	} else {
		tmp = (xx - zx) * yy;
	}
	return tmp;
}

function code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0
	if (yy <= -3.6e-12)
		tmp = fma(yy, xx, Float64(yy * Float64(-zx)));
	elseif (yy <= 6.8e+37)
		tmp = Float64(Float64(zy - xy) * yx);
	else
		tmp = Float64(Float64(xx - zx) * yy);
	end
	return tmp
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := If[LessEqual[yy, -3.6e-12], N[(yy * xx + N[(yy * (-zx)), $MachinePrecision]), $MachinePrecision], If[LessEqual[yy, 6.8e+37], N[(N[(zy - xy), $MachinePrecision] * yx), $MachinePrecision], N[(N[(xx - zx), $MachinePrecision] * yy), $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;yy \leq -3.6 \cdot 10^{-12}:\\
\;\;\;\;\mathsf{fma}\left(yy, xx, yy \cdot \left(-zx\right)\right)\\

\mathbf{elif}\;yy \leq 6.8 \cdot 10^{+37}:\\
\;\;\;\;\left(zy - xy\right) \cdot yx\\

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


\end{array}
\end{array}

Derivation

Split input into 3 regimes
if yy < -3.6e-12
1. Initial program 85.1%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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. sub-negN/A
    \[\leadsto \color{blue}{\left(xx + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  3. remove-double-negN/A
    \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right)} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  4. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)\right)\right)} \cdot yy \]
  5. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  6. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right)}\right)\right) \cdot yy \]
  7. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy \]
  8. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right) \cdot yy} \]
  9. mul-1-negN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right)} \cdot yy \]
  10. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  11. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right)\right) \cdot yy \]
  12. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  13. remove-double-negN/A
    \[\leadsto \left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  14. sub-negN/A
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
  15. lower--.f6471.4
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites71.4%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
6. Step-by-step derivation
7. Applied rewrites71.4%
  \[\leadsto \mathsf{fma}\left(yy, \color{blue}{xx}, yy \cdot \left(-zx\right)\right) \]
if -3.6e-12 < yy < 6.80000000000000011e37
1. Initial program 79.0%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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--.f6456.4
    \[\leadsto \color{blue}{\left(zy - xy\right)} \cdot yx \]
5. Applied rewrites56.4%
  \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
if 6.80000000000000011e37 < yy
1. Initial program 88.2%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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. sub-negN/A
    \[\leadsto \color{blue}{\left(xx + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  3. remove-double-negN/A
    \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right)} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  4. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)\right)\right)} \cdot yy \]
  5. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  6. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right)}\right)\right) \cdot yy \]
  7. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy \]
  8. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right) \cdot yy} \]
  9. mul-1-negN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right)} \cdot yy \]
  10. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  11. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right)\right) \cdot yy \]
  12. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  13. remove-double-negN/A
    \[\leadsto \left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  14. sub-negN/A
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
  15. lower--.f6472.2
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites72.2%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
Recombined 3 regimes into one program.
Add Preprocessing

Alternative 10: 28.8% accurate, 1.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;yy \leq -9.2 \cdot 10^{-13} \lor \neg \left(yy \leq 1.86 \cdot 10^{+28}\right):\\ \;\;\;\;\left(-zx\right) \cdot yy\\ \mathbf{else}:\\ \;\;\;\;yx \cdot zy\\ \end{array} \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (if (or (<= yy -9.2e-13) (not (<= yy 1.86e+28))) (* (- zx) yy) (* yx zy)))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((yy <= -9.2e-13) || !(yy <= 1.86e+28)) {
		tmp = -zx * yy;
	} else {
		tmp = yx * zy;
	}
	return tmp;
}

real(8) function code(yx, xx, zy, xy, zx, yy)
    real(8), intent (in) :: yx
    real(8), intent (in) :: xx
    real(8), intent (in) :: zy
    real(8), intent (in) :: xy
    real(8), intent (in) :: zx
    real(8), intent (in) :: yy
    real(8) :: tmp
    if ((yy <= (-9.2d-13)) .or. (.not. (yy <= 1.86d+28))) then
        tmp = -zx * yy
    else
        tmp = yx * zy
    end if
    code = tmp
end function

public static double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((yy <= -9.2e-13) || !(yy <= 1.86e+28)) {
		tmp = -zx * yy;
	} else {
		tmp = yx * zy;
	}
	return tmp;
}

def code(yx, xx, zy, xy, zx, yy):
	tmp = 0
	if (yy <= -9.2e-13) or not (yy <= 1.86e+28):
		tmp = -zx * yy
	else:
		tmp = yx * zy
	return tmp

function code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0
	if ((yy <= -9.2e-13) || !(yy <= 1.86e+28))
		tmp = Float64(Float64(-zx) * yy);
	else
		tmp = Float64(yx * zy);
	end
	return tmp
end

function tmp_2 = code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0;
	if ((yy <= -9.2e-13) || ~((yy <= 1.86e+28)))
		tmp = -zx * yy;
	else
		tmp = yx * zy;
	end
	tmp_2 = tmp;
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := If[Or[LessEqual[yy, -9.2e-13], N[Not[LessEqual[yy, 1.86e+28]], $MachinePrecision]], N[((-zx) * yy), $MachinePrecision], N[(yx * zy), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;yy \leq -9.2 \cdot 10^{-13} \lor \neg \left(yy \leq 1.86 \cdot 10^{+28}\right):\\
\;\;\;\;\left(-zx\right) \cdot yy\\

\mathbf{else}:\\
\;\;\;\;yx \cdot zy\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if yy < -9.19999999999999917e-13 or 1.86000000000000009e28 < yy
1. Initial program 86.6%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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. sub-negN/A
    \[\leadsto \color{blue}{\left(xx + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  3. remove-double-negN/A
    \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right)} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  4. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)\right)\right)} \cdot yy \]
  5. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  6. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right)}\right)\right) \cdot yy \]
  7. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy \]
  8. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right) \cdot yy} \]
  9. mul-1-negN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right)} \cdot yy \]
  10. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  11. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right)\right) \cdot yy \]
  12. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  13. remove-double-negN/A
    \[\leadsto \left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  14. sub-negN/A
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
  15. lower--.f6471.4
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites71.4%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
6. Taylor expanded in xx around 0
  \[\leadsto \left(-1 \cdot zx\right) \cdot yy \]
7. Step-by-step derivation
8. Applied rewrites46.3%
  \[\leadsto \left(-zx\right) \cdot yy \]
if -9.19999999999999917e-13 < yy < 1.86000000000000009e28
1. Initial program 78.6%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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--.f6456.5
    \[\leadsto \color{blue}{\left(zy - xy\right)} \cdot yx \]
5. Applied rewrites56.5%
  \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
6. Taylor expanded in zy around inf
  \[\leadsto yx \cdot \color{blue}{zy} \]
7. Step-by-step derivation
8. Applied rewrites32.5%
  \[\leadsto yx \cdot \color{blue}{zy} \]
Recombined 2 regimes into one program.
Final simplification39.3%
\[\leadsto \begin{array}{l} \mathbf{if}\;yy \leq -9.2 \cdot 10^{-13} \lor \neg \left(yy \leq 1.86 \cdot 10^{+28}\right):\\ \;\;\;\;\left(-zx\right) \cdot yy\\ \mathbf{else}:\\ \;\;\;\;yx \cdot zy\\ \end{array} \]
Add Preprocessing

Alternative 11: 30.1% accurate, 1.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;xy \leq -3.2 \cdot 10^{+36}:\\ \;\;\;\;\left(-yx\right) \cdot xy\\ \mathbf{elif}\;xy \leq 4.6 \cdot 10^{+85}:\\ \;\;\;\;\left(-zx\right) \cdot yy\\ \mathbf{else}:\\ \;\;\;\;zx \cdot xy\\ \end{array} \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (if (<= xy -3.2e+36)
   (* (- yx) xy)
   (if (<= xy 4.6e+85) (* (- zx) yy) (* zx xy))))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if (xy <= -3.2e+36) {
		tmp = -yx * xy;
	} else if (xy <= 4.6e+85) {
		tmp = -zx * yy;
	} else {
		tmp = zx * xy;
	}
	return tmp;
}

real(8) function code(yx, xx, zy, xy, zx, yy)
    real(8), intent (in) :: yx
    real(8), intent (in) :: xx
    real(8), intent (in) :: zy
    real(8), intent (in) :: xy
    real(8), intent (in) :: zx
    real(8), intent (in) :: yy
    real(8) :: tmp
    if (xy <= (-3.2d+36)) then
        tmp = -yx * xy
    else if (xy <= 4.6d+85) then
        tmp = -zx * yy
    else
        tmp = zx * xy
    end if
    code = tmp
end function

public static double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if (xy <= -3.2e+36) {
		tmp = -yx * xy;
	} else if (xy <= 4.6e+85) {
		tmp = -zx * yy;
	} else {
		tmp = zx * xy;
	}
	return tmp;
}

def code(yx, xx, zy, xy, zx, yy):
	tmp = 0
	if xy <= -3.2e+36:
		tmp = -yx * xy
	elif xy <= 4.6e+85:
		tmp = -zx * yy
	else:
		tmp = zx * xy
	return tmp

function code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0
	if (xy <= -3.2e+36)
		tmp = Float64(Float64(-yx) * xy);
	elseif (xy <= 4.6e+85)
		tmp = Float64(Float64(-zx) * yy);
	else
		tmp = Float64(zx * xy);
	end
	return tmp
end

function tmp_2 = code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0;
	if (xy <= -3.2e+36)
		tmp = -yx * xy;
	elseif (xy <= 4.6e+85)
		tmp = -zx * yy;
	else
		tmp = zx * xy;
	end
	tmp_2 = tmp;
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := If[LessEqual[xy, -3.2e+36], N[((-yx) * xy), $MachinePrecision], If[LessEqual[xy, 4.6e+85], N[((-zx) * yy), $MachinePrecision], N[(zx * xy), $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;xy \leq -3.2 \cdot 10^{+36}:\\
\;\;\;\;\left(-yx\right) \cdot xy\\

\mathbf{elif}\;xy \leq 4.6 \cdot 10^{+85}:\\
\;\;\;\;\left(-zx\right) \cdot yy\\

\mathbf{else}:\\
\;\;\;\;zx \cdot xy\\


\end{array}
\end{array}

Derivation

Split input into 3 regimes
if xy < -3.1999999999999999e36
1. Initial program 68.4%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
3. Taylor expanded in xy around inf
  \[\leadsto \color{blue}{xy \cdot \left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  3. cancel-sign-sub-invN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(zx - xx\right)\right)} \cdot xy \]
  4. metadata-evalN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{1} \cdot \left(zx - xx\right)\right) \cdot xy \]
  5. *-lft-identityN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{\left(zx - xx\right)}\right) \cdot xy \]
  6. associate-+r-N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  7. lower--.f64N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  8. lower-+.f64N/A
    \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(yx - xx\right) + zx\right)} - xx\right) \cdot xy \]
  9. mul-1-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\mathsf{neg}\left(\left(yx - xx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  10. sub-negN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(yx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  11. +-commutativeN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + yx\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  12. distribute-neg-inN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  13. unsub-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) - yx\right)} + zx\right) - xx\right) \cdot xy \]
  14. remove-double-negN/A
    \[\leadsto \left(\left(\left(\color{blue}{xx} - yx\right) + zx\right) - xx\right) \cdot xy \]
  15. lower--.f6460.3
    \[\leadsto \left(\left(\color{blue}{\left(xx - yx\right)} + zx\right) - xx\right) \cdot xy \]
5. Applied rewrites60.3%
  \[\leadsto \color{blue}{\left(\left(\left(xx - yx\right) + zx\right) - xx\right) \cdot xy} \]
6. Taylor expanded in yx around inf
  \[\leadsto \left(-1 \cdot yx\right) \cdot xy \]
7. Step-by-step derivation
8. Applied rewrites56.8%
  \[\leadsto \left(-yx\right) \cdot xy \]
if -3.1999999999999999e36 < xy < 4.5999999999999998e85
1. Initial program 93.9%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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. sub-negN/A
    \[\leadsto \color{blue}{\left(xx + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  3. remove-double-negN/A
    \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right)} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  4. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)\right)\right)} \cdot yy \]
  5. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  6. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right)}\right)\right) \cdot yy \]
  7. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy \]
  8. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right) \cdot yy} \]
  9. mul-1-negN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right)} \cdot yy \]
  10. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  11. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right)\right) \cdot yy \]
  12. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  13. remove-double-negN/A
    \[\leadsto \left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  14. sub-negN/A
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
  15. lower--.f6454.5
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites54.5%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
6. Taylor expanded in xx around 0
  \[\leadsto \left(-1 \cdot zx\right) \cdot yy \]
7. Step-by-step derivation
8. Applied rewrites34.7%
  \[\leadsto \left(-zx\right) \cdot yy \]
if 4.5999999999999998e85 < xy
1. Initial program 65.2%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
2. Add Preprocessing
3. Taylor expanded in xy around inf
  \[\leadsto \color{blue}{xy \cdot \left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  2. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) - -1 \cdot \left(zx - xx\right)\right) \cdot xy} \]
  3. cancel-sign-sub-invN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(yx - xx\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(zx - xx\right)\right)} \cdot xy \]
  4. metadata-evalN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{1} \cdot \left(zx - xx\right)\right) \cdot xy \]
  5. *-lft-identityN/A
    \[\leadsto \left(-1 \cdot \left(yx - xx\right) + \color{blue}{\left(zx - xx\right)}\right) \cdot xy \]
  6. associate-+r-N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  7. lower--.f64N/A
    \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(yx - xx\right) + zx\right) - xx\right)} \cdot xy \]
  8. lower-+.f64N/A
    \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(yx - xx\right) + zx\right)} - xx\right) \cdot xy \]
  9. mul-1-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\mathsf{neg}\left(\left(yx - xx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  10. sub-negN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(yx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  11. +-commutativeN/A
    \[\leadsto \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + yx\right)}\right)\right) + zx\right) - xx\right) \cdot xy \]
  12. distribute-neg-inN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(yx\right)\right)\right)} + zx\right) - xx\right) \cdot xy \]
  13. unsub-negN/A
    \[\leadsto \left(\left(\color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) - yx\right)} + zx\right) - xx\right) \cdot xy \]
  14. remove-double-negN/A
    \[\leadsto \left(\left(\left(\color{blue}{xx} - yx\right) + zx\right) - xx\right) \cdot xy \]
  15. lower--.f6452.8
    \[\leadsto \left(\left(\color{blue}{\left(xx - yx\right)} + zx\right) - xx\right) \cdot xy \]
5. Applied rewrites52.8%
  \[\leadsto \color{blue}{\left(\left(\left(xx - yx\right) + zx\right) - xx\right) \cdot xy} \]
6. Taylor expanded in yx around 0
  \[\leadsto xy \cdot \color{blue}{zx} \]
7. Step-by-step derivation
8. Applied rewrites47.7%
  \[\leadsto zx \cdot \color{blue}{xy} \]
Recombined 3 regimes into one program.
Add Preprocessing

Alternative 12: 30.6% accurate, 1.4× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;xx \leq -1.75 \cdot 10^{+94} \lor \neg \left(xx \leq 1.18 \cdot 10^{-11}\right):\\ \;\;\;\;yy \cdot xx\\ \mathbf{else}:\\ \;\;\;\;yx \cdot zy\\ \end{array} \end{array} \]

(FPCore (yx xx zy xy zx yy)
 :precision binary64
 (if (or (<= xx -1.75e+94) (not (<= xx 1.18e-11))) (* yy xx) (* yx zy)))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((xx <= -1.75e+94) || !(xx <= 1.18e-11)) {
		tmp = yy * xx;
	} else {
		tmp = yx * zy;
	}
	return tmp;
}

real(8) function code(yx, xx, zy, xy, zx, yy)
    real(8), intent (in) :: yx
    real(8), intent (in) :: xx
    real(8), intent (in) :: zy
    real(8), intent (in) :: xy
    real(8), intent (in) :: zx
    real(8), intent (in) :: yy
    real(8) :: tmp
    if ((xx <= (-1.75d+94)) .or. (.not. (xx <= 1.18d-11))) then
        tmp = yy * xx
    else
        tmp = yx * zy
    end if
    code = tmp
end function

public static double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	double tmp;
	if ((xx <= -1.75e+94) || !(xx <= 1.18e-11)) {
		tmp = yy * xx;
	} else {
		tmp = yx * zy;
	}
	return tmp;
}

def code(yx, xx, zy, xy, zx, yy):
	tmp = 0
	if (xx <= -1.75e+94) or not (xx <= 1.18e-11):
		tmp = yy * xx
	else:
		tmp = yx * zy
	return tmp

function code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0
	if ((xx <= -1.75e+94) || !(xx <= 1.18e-11))
		tmp = Float64(yy * xx);
	else
		tmp = Float64(yx * zy);
	end
	return tmp
end

function tmp_2 = code(yx, xx, zy, xy, zx, yy)
	tmp = 0.0;
	if ((xx <= -1.75e+94) || ~((xx <= 1.18e-11)))
		tmp = yy * xx;
	else
		tmp = yx * zy;
	end
	tmp_2 = tmp;
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := If[Or[LessEqual[xx, -1.75e+94], N[Not[LessEqual[xx, 1.18e-11]], $MachinePrecision]], N[(yy * xx), $MachinePrecision], N[(yx * zy), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;xx \leq -1.75 \cdot 10^{+94} \lor \neg \left(xx \leq 1.18 \cdot 10^{-11}\right):\\
\;\;\;\;yy \cdot xx\\

\mathbf{else}:\\
\;\;\;\;yx \cdot zy\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if xx < -1.7499999999999999e94 or 1.18e-11 < xx
1. Initial program 66.8%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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. sub-negN/A
    \[\leadsto \color{blue}{\left(xx + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  3. remove-double-negN/A
    \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right)} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  4. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)\right)\right)} \cdot yy \]
  5. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  6. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right)}\right)\right) \cdot yy \]
  7. mul-1-negN/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy \]
  8. lower-*.f64N/A
    \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right) \cdot yy} \]
  9. mul-1-negN/A
    \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right)} \cdot yy \]
  10. sub-negN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
  11. +-commutativeN/A
    \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right)\right) \cdot yy \]
  12. distribute-neg-inN/A
    \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
  13. remove-double-negN/A
    \[\leadsto \left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
  14. sub-negN/A
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
  15. lower--.f6453.7
    \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
5. Applied rewrites53.7%
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
6. Taylor expanded in xx around inf
  \[\leadsto xx \cdot \color{blue}{yy} \]
7. Step-by-step derivation
8. Applied rewrites45.0%
  \[\leadsto yy \cdot \color{blue}{xx} \]
if -1.7499999999999999e94 < xx < 1.18e-11
1. Initial program 94.6%
  \[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
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--.f6449.6
    \[\leadsto \color{blue}{\left(zy - xy\right)} \cdot yx \]
5. Applied rewrites49.6%
  \[\leadsto \color{blue}{\left(zy - xy\right) \cdot yx} \]
6. Taylor expanded in zy around inf
  \[\leadsto yx \cdot \color{blue}{zy} \]
7. Step-by-step derivation
8. Applied rewrites31.3%
  \[\leadsto yx \cdot \color{blue}{zy} \]
Recombined 2 regimes into one program.
Final simplification37.3%
\[\leadsto \begin{array}{l} \mathbf{if}\;xx \leq -1.75 \cdot 10^{+94} \lor \neg \left(xx \leq 1.18 \cdot 10^{-11}\right):\\ \;\;\;\;yy \cdot xx\\ \mathbf{else}:\\ \;\;\;\;yx \cdot zy\\ \end{array} \]
Add Preprocessing

Alternative 13: 20.8% accurate, 4.3× speedup?

\[\begin{array}{l} \\ yy \cdot xx \end{array} \]

(FPCore (yx xx zy xy zx yy) :precision binary64 (* yy xx))

double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	return yy * xx;
}

real(8) function code(yx, xx, zy, xy, zx, yy)
    real(8), intent (in) :: yx
    real(8), intent (in) :: xx
    real(8), intent (in) :: zy
    real(8), intent (in) :: xy
    real(8), intent (in) :: zx
    real(8), intent (in) :: yy
    code = yy * xx
end function

public static double code(double yx, double xx, double zy, double xy, double zx, double yy) {
	return yy * xx;
}

def code(yx, xx, zy, xy, zx, yy):
	return yy * xx

function code(yx, xx, zy, xy, zx, yy)
	return Float64(yy * xx)
end

function tmp = code(yx, xx, zy, xy, zx, yy)
	tmp = yy * xx;
end

code[yx_, xx_, zy_, xy_, zx_, yy_] := N[(yy * xx), $MachinePrecision]

\begin{array}{l}

\\
yy \cdot xx
\end{array}

Derivation

Initial program 82.6%
\[\left(yx - xx\right) \cdot \left(zy - xy\right) - \left(zx - xx\right) \cdot \left(yy - xy\right) \]
Add Preprocessing
Taylor expanded in yy around inf
\[\leadsto \color{blue}{yy \cdot \left(xx - zx\right)} \]
Step-by-step derivation
1. *-commutativeN/A
  \[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
2. sub-negN/A
  \[\leadsto \color{blue}{\left(xx + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
3. remove-double-negN/A
  \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right)} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
4. distribute-neg-inN/A
  \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)\right)\right)} \cdot yy \]
5. +-commutativeN/A
  \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
6. sub-negN/A
  \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx - xx\right)}\right)\right) \cdot yy \]
7. mul-1-negN/A
  \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right)} \cdot yy \]
8. lower-*.f64N/A
  \[\leadsto \color{blue}{\left(-1 \cdot \left(zx - xx\right)\right) \cdot yy} \]
9. mul-1-negN/A
  \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(zx - xx\right)\right)\right)} \cdot yy \]
10. sub-negN/A
  \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(zx + \left(\mathsf{neg}\left(xx\right)\right)\right)}\right)\right) \cdot yy \]
11. +-commutativeN/A
  \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(xx\right)\right) + zx\right)}\right)\right) \cdot yy \]
12. distribute-neg-inN/A
  \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(xx\right)\right)\right)\right) + \left(\mathsf{neg}\left(zx\right)\right)\right)} \cdot yy \]
13. remove-double-negN/A
  \[\leadsto \left(\color{blue}{xx} + \left(\mathsf{neg}\left(zx\right)\right)\right) \cdot yy \]
14. sub-negN/A
  \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
15. lower--.f6441.9
  \[\leadsto \color{blue}{\left(xx - zx\right)} \cdot yy \]
Applied rewrites41.9%
\[\leadsto \color{blue}{\left(xx - zx\right) \cdot yy} \]
Taylor expanded in xx around inf
\[\leadsto xx \cdot \color{blue}{yy} \]
Step-by-step derivation
Applied rewrites22.3%
\[\leadsto yy \cdot \color{blue}{xx} \]
Add Preprocessing

47.1% 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: 82.6% accurate, 1.0× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Alternative 1: 96.2% accurate, 0.9× speedupMathFPCoreCJuliaWolframTeX?

Alternative 2: 89.2% accurate, 0.5× speedupMathFPCoreCJavaPythonJuliaMATLABWolframTeX?

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

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

Alternative 3: 81.1% accurate, 0.9× speedupMathFPCoreCJuliaWolframTeX?

if xy < -1.90000000000000008e24 or 5.99999999999999967e69 < xy

if -1.90000000000000008e24 < xy < 5.99999999999999967e69

Alternative 4: 77.7% accurate, 0.9× speedupMathFPCoreCJuliaWolframTeX?

if xy < -1.0000000000000001e97 or 5.1999999999999995e86 < xy

if -1.0000000000000001e97 < xy < 5.1999999999999995e86

Alternative 5: 64.9% accurate, 1.0× speedupMathFPCoreCJuliaWolframTeX?

if zx < -9.20000000000000067e69 or 3.69999999999999996e80 < zx

if -9.20000000000000067e69 < zx < 3.69999999999999996e80

Alternative 6: 53.1% accurate, 1.2× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if yy < -3.6e-12 or 6.80000000000000011e37 < yy

if -3.6e-12 < yy < 6.80000000000000011e37

Alternative 7: 53.9% accurate, 1.2× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if xy < -4.6999999999999998e33 or 6.50000000000000027e84 < xy

if -4.6999999999999998e33 < xy < 6.50000000000000027e84

Alternative 8: 42.2% accurate, 1.2× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if xy < -4.09999999999999981e32 or 9.19999999999999953e82 < xy

if -4.09999999999999981e32 < xy < 9.19999999999999953e82

Alternative 9: 52.7% accurate, 1.2× speedupMathFPCoreCJuliaWolframTeX?

if yy < -3.6e-12

if -3.6e-12 < yy < 6.80000000000000011e37

if 6.80000000000000011e37 < yy

Alternative 10: 28.8% accurate, 1.3× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if yy < -9.19999999999999917e-13 or 1.86000000000000009e28 < yy

if -9.19999999999999917e-13 < yy < 1.86000000000000009e28

Alternative 11: 30.1% accurate, 1.3× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if xy < -3.1999999999999999e36

if -3.1999999999999999e36 < xy < 4.5999999999999998e85

if 4.5999999999999998e85 < xy

Alternative 12: 30.6% accurate, 1.4× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if xx < -1.7499999999999999e94 or 1.18e-11 < xx

if -1.7499999999999999e94 < xx < 1.18e-11

Alternative 13: 20.8% accurate, 4.3× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Reproduce

Initial Program: 82.6% accurate, 1.0× speedup?

Alternative 1: 96.2% accurate, 0.9× speedup?

Alternative 2: 89.2% accurate, 0.5× speedup?

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

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

Alternative 3: 81.1% accurate, 0.9× speedup?

`if xy < -1.90000000000000008e24 or 5.99999999999999967e69 < xy`

`if -1.90000000000000008e24 < xy < 5.99999999999999967e69`

Alternative 4: 77.7% accurate, 0.9× speedup?

`if xy < -1.0000000000000001e97 or 5.1999999999999995e86 < xy`

`if -1.0000000000000001e97 < xy < 5.1999999999999995e86`

Alternative 5: 64.9% accurate, 1.0× speedup?

`if zx < -9.20000000000000067e69 or 3.69999999999999996e80 < zx`

`if -9.20000000000000067e69 < zx < 3.69999999999999996e80`

Alternative 6: 53.1% accurate, 1.2× speedup?

`if yy < -3.6e-12 or 6.80000000000000011e37 < yy`

`if -3.6e-12 < yy < 6.80000000000000011e37`

Alternative 7: 53.9% accurate, 1.2× speedup?

`if xy < -4.6999999999999998e33 or 6.50000000000000027e84 < xy`

`if -4.6999999999999998e33 < xy < 6.50000000000000027e84`

Alternative 8: 42.2% accurate, 1.2× speedup?

`if xy < -4.09999999999999981e32 or 9.19999999999999953e82 < xy`

`if -4.09999999999999981e32 < xy < 9.19999999999999953e82`

Alternative 9: 52.7% accurate, 1.2× speedup?

`if yy < -3.6e-12`

`if -3.6e-12 < yy < 6.80000000000000011e37`

`if 6.80000000000000011e37 < yy`

Alternative 10: 28.8% accurate, 1.3× speedup?

`if yy < -9.19999999999999917e-13 or 1.86000000000000009e28 < yy`

`if -9.19999999999999917e-13 < yy < 1.86000000000000009e28`

Alternative 11: 30.1% accurate, 1.3× speedup?

`if xy < -3.1999999999999999e36`

`if -3.1999999999999999e36 < xy < 4.5999999999999998e85`

`if 4.5999999999999998e85 < xy`

Alternative 12: 30.6% accurate, 1.4× speedup?

`if xx < -1.7499999999999999e94 or 1.18e-11 < xx`

`if -1.7499999999999999e94 < xx < 1.18e-11`

Alternative 13: 20.8% accurate, 4.3× speedup?