Details

sample440.0ms

Algorithm

intervals

Results

189.0ms	42×	body	1280	valid
97.0ms	24×	body	2560	valid
48.0ms	29×	body	640	valid
17.0ms	157×	body	80	valid
6.0ms	11×	body	320	valid
5.0ms	6×	body	160	valid

simplify228.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	14
1	18	14
2	39	14
3	76	14
4	118	14
5	141	14
6	148	14
done	148	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.5b	(/ 1.0 (* F F))
3.7b	(* (/ 1.0 (* F F)) (tan (* PI l)))
26.4b	(tan (* PI l))

rewrite156.0ms

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` `div-exp` `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 → 77

Calls

4 calls:

14.0ms	(* PI l)
22.0ms	(/ 1.0 (* F F))
92.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
22.0ms	(tan (* PI l))

series408.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* PI l)
50.0ms	(/ 1.0 (* F F))
213.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
105.0ms	(tan (* PI l))

simplify1.4s

Counts

89 → 89

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	135	872
1	339	854
2	1966	740
done	5001	726

prune309.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(/ (tan (* PI l)) F)
26.4b	(tan (* PI l))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

7.0ms	(* PI l)
7.0ms	(* PI l)
24.0ms	(/ (tan (* PI l)) F)
8.0ms	(tan (* PI l))

series284.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
27.0ms	(* PI l)
139.0ms	(/ (tan (* PI l)) F)
94.0ms	(tan (* PI l))

simplify2.0s

Counts

84 → 84

Iterations

Useful iterations: 3 (750.0ms)

Iter	Nodes	Cost
0	106	669
1	216	646
2	672	604
3	3213	594
done	5001	594

prune346.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (tan (* PI l)) (/ 1 F))
26.4b	(tan (* PI l))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`associate-r`
17×	`add-exp-log` `*-un-lft-identity`
16×	`add-cube-cbrt`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`pow1`
9×	`associate-l`
6×	`prod-exp`
5×	`unswap-sqr`
4×	`cbrt-unprod` `add-log-exp`
3×	`tan-quot` `pow-prod-down` `*-commutative`
2×	`div-exp`
1×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-r/` `associate-l/` `un-div-inv` `div-inv`

Counts

4 → 82

Calls

4 calls:

13.0ms	(* PI l)
7.0ms	(* PI l)
46.0ms	(* (tan (* PI l)) (/ 1 F))
16.0ms	(tan (* PI l))

series257.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* PI l)
22.0ms	(* PI l)
126.0ms	(* (tan (* PI l)) (/ 1 F))
78.0ms	(tan (* PI l))

simplify1.4s

Counts

94 → 94

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	131	797
1	322	733
2	1442	616
done	5000	608

prune403.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(/ (sin (* PI l)) F)
25.3b	(sin (* PI l))
25.8b	(cos (* PI l))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

14.0ms	(* PI l)
25.0ms	(/ (sin (* PI l)) F)
16.0ms	(sin (* PI l))
15.0ms	(cos (* PI l))

series197.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* PI l)
85.0ms	(/ (sin (* PI l)) F)
51.0ms	(sin (* PI l))
36.0ms	(cos (* PI l))

simplify887.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (298.0ms)

Iter	Nodes	Cost
0	122	611
1	259	595
2	1028	551
done	5000	551

prune413.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.1b

regimes631.0ms

Accuracy

84.2% (0.8b remaining)

Error of 8.5b against oracle of 7.8b and baseline of 12.7b

bsearch4.0ms

simplify21.0ms

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	41	90
1	56	70
done	56	70

end0.0ms

sample10.1s

Algorithm

intervals

Results

4.7s	819×	body	2560	valid
3.0s	1724×	body	1280	valid
812.0ms	956×	body	640	valid
750.0ms	4513×	body	80	valid
170.0ms	368×	body	320	valid
133.0ms	4×	body	10240	exit
70.0ms	206×	body	160	valid