trig

identities

Algebraic trigonometric identities over the reals or complexes, and where they fail (sqrt of a square).

inverse

asin(sin x) = x and friends: true exactly on the principal range of the inverse.

periodicity

Shifts by multiples of pi: periods, half-periods, and where a shifted value coincides.

Case set 1e4dbd2f7d86 — latest run per system

One column per CAS: the best of its routines (wrong if any is wrong, else solved if any solved it, else declined correctly if any did); +N shows the routines, older older versions. Click a category to see its cases.

always-none, sympy-ask, sympy-refine, sympy-simplify, wolfram-fullsimplify, wolfram-refine, wolfram-simplify: old report format (graded with a combined score): its nulls are shown as no verdict, because an old report cannot tell a correct decline on a contingent case from no verdict

Each cell shows what the system said, coloured by outcome: true ✓ solved, true ✗ wrong, no verdict: the system ran but did not commit to true or false (null); no verdict ✓ (grey ✓, on a contingent case) declined correctly: Correct: neither true nor false holds here. Not counted as solved, since a system that never answers would get this too.

Case set 45d6b9056f06 — latest run per system

One column per CAS: the best of its routines (wrong if any is wrong, else solved if any solved it, else declined correctly if any did); +N shows the routines, older older versions. Click a category to see its cases.

always-none, sympy-ask, sympy-refine, sympy-simplify, wolfram-fullsimplify, wolfram-refine, wolfram-simplify: old report format (graded with a combined score): its nulls are shown as no verdict, because an old report cannot tell a correct decline on a contingent case from no verdict

Each cell shows what the system said, coloured by outcome: true ✓ solved, true ✗ wrong, no verdict: the system ran but did not commit to true or false (null); no verdict ✓ (grey ✓, on a contingent case) declined correctly: Correct: neither true nor false holds here. Not counted as solved, since a system that never answers would get this too.