Details

sample518.0ms

Algorithm

intervals

Results

118.0ms	37×	body	2560	valid
35.0ms	49×	body	1280	valid
33.0ms	150×	body	80	valid
8.0ms	23×	body	640	valid
3.0ms	12×	body	320	valid
2.0ms	11×	body	160	valid

simplify144.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	19	14
2	41	14
3	82	14
4	122	14
5	147	14
6	156	14
7	158	14
done	158	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(/ 1.0 (* F F))
2.8b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.6b	(tan (* PI l))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
8×	`pow1`
7×	`times-frac`
6×	`associate-r` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `associate-/l*` `unswap-sqr`
2×	`pow-prod-down` `*-commutative` `div-inv`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r*`

Counts

4 → 85

Calls

4 calls:

7.0ms	(* PI l)
8.0ms	(/ 1.0 (* F F))
47.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series257.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
30.0ms	(/ 1.0 (* F F))
131.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
76.0ms	(tan (* PI l))

simplify2.0s

Counts

97 → 97

Iterations

Useful iterations: 2 (237.0ms)

Iter	Nodes	Cost
0	143	924
1	316	903
2	1013	771
3	4042	771
done	5000	771

prune250.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.3b	(* (/ (cbrt 1.0) F) (tan (* PI l)))
30.6b	(tan (* PI l))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
28×	`associate-l`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
13×	`add-exp-log`
12×	`add-cbrt-cube`
10×	`pow1` `cbrt-prod`
9×	`associate-r`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `div-inv`

Counts

4 → 96

Calls

4 calls:

7.0ms	(* PI l)
7.0ms	(* PI l)
38.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series275.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
25.0ms	(* PI l)
164.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
66.0ms	(tan (* PI l))

simplify1.6s

Counts

108 → 108

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	139	939
1	303	917
2	803	841
3	2603	841
done	5001	832

prune360.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cbrt 1.0) (tan (* PI l))) F)
0.3b	(* PI l)
0.3b	(* PI l)
30.6b	(tan (* PI l))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log`
12×	`add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`tan-quot` `cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `clear-num` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 74

Calls

4 calls:

20.0ms	(/ (* (cbrt 1.0) (tan (* PI l))) F)
7.0ms	(* PI l)
7.0ms	(* PI l)
8.0ms	(tan (* PI l))

series276.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (* (cbrt 1.0) (tan (* PI l))) F)
26.0ms	(* PI l)
20.0ms	(* PI l)
65.0ms	(tan (* PI l))

simplify1.7s

Counts

86 → 86

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	117	694
1	264	669
2	824	595
3	3549	595
done	5000	591

prune270.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) l)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
30.8b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `unswap-sqr`
1×	`tan-quot` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 64

Calls

4 calls:

10.0ms	(* (sqrt PI) l)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
27.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series116.0ms

Counts

4 → 8

Calls

4 calls:

48.0ms	(* (sqrt PI) l)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
68.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify2.1s

Counts

72 → 72

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	76	454
1	138	363
2	343	349
3	884	349
4	3001	349
done	5000	347

prune216.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.8b

regimes459.0ms

Accuracy

0% (0.3b remaining)

Error of 12.2b against oracle of 11.9b and baseline of 12.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	30
1	23	30
done	23	30

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	815×	body	2560	valid
1.2s	1665×	body	1280	valid
311.0ms	908×	body	640	valid
295.0ms	4622×	body	80	valid
140.0ms	6×	body	10240	exit
83.0ms	380×	body	320	valid
36.0ms	239×	body	160	valid