[Rafael-SOWNet]

Evaluation takes a negative real to a rational power with an odd denominator below ten as the real root to the numerator: Number.Pow's search for a good root finds it, so (-8)^(1/3) is -2 and (-8)^(2/3) is 4. Both compilers took the principal power instead, and Compile<double, double> took Math.Pow, which is NaN there. Whether the exponent is such a rational is known only where the power is written, so each compiler now makes that choice as it compiles a power: RealProducts.RealRootPower takes the real root to the numerator for a negative real base, and the power as before for any other.

at x = -8	evaluated	compiled, 2.6.0 and master	now
x^(1/3)	-2	<1; 1.73>; NaN over double	-2
x^(2/3)	4	<-2; 3.46>	4
x^(-1/3)	-1/2	<0.25; -0.43>	-1/2

• Newton's method, which Solve falls back to, runs on the compiled function, so roots that need the real root weren't found. Each of these is now:
  • (3 - 4x)^(1/3) + sqrt(4 + 4x) = 3 was missing 8.379;
  • (1 + x)^(1/3) + sqrt(-1 - 2x) = 4 + 2x was missing -1.672;
  • (-4x)^(1/3) + sqrt(2 + 2x) = 3 was missing 30.81.
• Unchanged, as in evaluation: a base off the real line, a positive base, an even denominator (sqrt(-4) is still 2i), and a denominator of ten or more ((-1)^(1/11) is principal).
• Found by a cross-check of equations in roots. I first put the 8.379 miss down to Newton's search grid. Compiling the equation showed the real cause.
• Seven of the new cases fail on master, and the four principal-power controls pass on both. The suite, the trio, F#, AOT and the eight harnesses pass. BREAKING-CHANGES.md has an entry.

No issue was filed.

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[codecov]

Codecov Report

❌ Patch coverage is 96.15385% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 86.78%. Comparing base (b20a516) to head (44cb586).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
.../AngouriMath/Functions/Compilation/RealProducts.cs	87.50%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #2318   +/-   ##
=======================================
  Coverage   86.77%   86.78%           
=======================================
  Files         311      311           
  Lines       68216    68241   +25     
  Branches    19827    19833    +6     
=======================================
+ Hits        59197    59220   +23     
  Misses       4878     4878           
- Partials     4141     4143    +2     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.32% <96.15%> (+<0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...gouriMath/Functions/Compilation/IntoFE/Compiler.cs	85.71% <100.00%> (+0.37%)	⬆️
...ath/Functions/Compilation/IntoFE/FastExpression.cs	96.80% <100.00%> (+0.03%)	⬆️
...ctions/Compilation/IntoLinq/CompilationProtocol.cs	93.70% <100.00%> (+0.18%)	⬆️
.../AngouriMath/Functions/Compilation/RealProducts.cs	90.90% <87.50%> (-0.76%)	⬇️

... and 5 files with indirect coverage changes

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