Details

sample75.0ms

Algorithm

intervals

Results

20.0ms	63×	body	1280	valid
17.0ms	278×	body	80	valid
17.0ms	74×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	21×	body	160	valid

simplify98.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	12	19
1	26	13
2	52	12
3	75	12
4	102	12
5	122	12
6	139	12
7	143	12
8	145	12
done	145	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 176

Calls

4 calls:

16.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
16.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms	(/ (cos th) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series356.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
114.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
64.0ms	(/ (cos th) (sqrt 2.0))
60.0ms	(/ (cos th) (sqrt 2.0))

simplify729.0ms

Counts

188 → 188

Iterations

Useful iterations: done (723.0ms)

Iter	Nodes	Cost
0	187	2182
1	498	2076
2	1609	1894
done	5000	1874

prune516.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
345×	`add-sqr-sqrt`
340×	`add-cube-cbrt` `*-un-lft-identity`
37×	`associate-/l*`
25×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
22×	`associate-l`
14×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 477

Calls

4 calls:

19.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
19.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
4.0ms	(/ (cos th) (sqrt 2.0))

series345.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
99.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
66.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
66.0ms	(/ (cos th) (sqrt 2.0))

simplify1.1s

Counts

489 → 489

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	485	9926
1	1116	8596
2	2622	7985
done	5000	7983

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) a2)
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
349×	`add-sqr-sqrt`
341×	`add-cube-cbrt` `*-un-lft-identity`
37×	`associate-/l*`
24×	`associate-/r*`
22×	`associate-l`
18×	`add-exp-log` `add-cbrt-cube`
14×	`div-inv`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `unswap-sqr`
2×	`prod-exp` `cbrt-unprod`
1×	`pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 474

Calls

4 calls:

15.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
19.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
4.0ms	(/ (cos th) (sqrt 2.0))

series318.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
94.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
61.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify1.1s

Counts

486 → 486

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	479	9763
1	1062	8440
2	2398	7873
done	5001	7871

prune868.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

1188×	`sqrt-prod`
1152×	`times-frac`
620×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
68×	`associate-/l*`
36×	`associate-/r*`
24×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 778

Calls

4 calls:

5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
22.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
19.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
96.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
64.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
60.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify2.4s

Counts

790 → 790

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	397	17670
1	873	15116
2	1750	14096
3	4411	13744
done	5000	13744

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes300.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	31	37
done	31	37

end0.0ms

sample2.3s

Algorithm

intervals

Results

813.0ms	2478×	body	1280	valid
488.0ms	2138×	body	640	valid
399.0ms	7988×	body	80	valid
161.0ms	1016×	body	320	valid
57.0ms	545×	body	160	valid