Details

sample441.0ms

Algorithm

intervals

Results

93.0ms	30×	body	2560	valid
49.0ms	57×	body	1280	valid
12.0ms	35×	body	640	valid
10.0ms	148×	body	80	valid
2.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify102.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	19	14
2	40	14
3	79	14
4	116	14
5	138	14
6	147	14
7	149	14
done	149	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ 1.0 (* F F))
4.6b	(* (/ 1.0 (* F F)) (tan (* PI l)))
32.4b	(tan (* PI l))

rewrite28.0ms

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:

3.0ms	(* PI l)
3.0ms	(/ 1.0 (* F F))
16.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
3.0ms	(tan (* PI l))

series258.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
24.0ms	(/ 1.0 (* F F))
135.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
78.0ms	(tan (* PI l))

simplify516.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (123.0ms)

Iter	Nodes	Cost
0	143	924
1	330	903
2	1233	771
done	5000	771

prune249.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ (cbrt 1.0) F) (tan (* PI l)))
32.4b	(tan (* PI l))

rewrite28.0ms

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:

3.0ms	(* PI l)
3.0ms	(* PI l)
17.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series270.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
22.0ms	(* PI l)
163.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
65.0ms	(tan (* PI l))

simplify1.2s

Counts

108 → 108

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	139	939
1	305	917
2	873	841
3	2939	841
done	5000	841

prune374.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 15.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(/ (sin (* PI l)) F)
31.8b	(cos (* PI l))
32.1b	(sin (* PI l))

rewrite11.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 67

Calls

4 calls:

3.0ms	(* PI l)
3.0ms	(/ (sin (* PI l)) F)
2.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series118.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
59.0ms	(/ (sin (* PI l)) F)
17.0ms	(cos (* PI l))
23.0ms	(sin (* PI l))

simplify2.0s

Counts

79 → 79

Iterations

Useful iterations: 3 (578.0ms)

Iter	Nodes	Cost
0	130	653
1	255	635
2	791	581
3	4260	579
done	5000	579

prune325.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.5b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt PI)
1.0b	(* (cbrt PI) (cbrt PI))
31.4b	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))
32.1b	(sin (* PI l))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`cbrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
7×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

0.0ms	(cbrt PI)
6.0ms	(* (cbrt PI) (cbrt PI))
7.0ms	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))
2.0ms	(sin (* PI l))

series43.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt PI)
0.0ms	(* (cbrt PI) (cbrt PI))
20.0ms	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))
23.0ms	(sin (* PI l))

simplify1.7s

Counts

81 → 81

Iterations

Useful iterations: 3 (477.0ms)

Iter	Nodes	Cost
0	100	650
1	188	597
2	606	504
3	2985	459
done	5000	459

prune282.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.4b

regimes539.0ms

Accuracy

85.8% (0.6b remaining)

Error of 8.7b against oracle of 8.0b and baseline of 12.5b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	116
1	60	116
done	60	116

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	823×	body	2560	valid
1.2s	1659×	body	1280	valid
339.0ms	959×	body	640	valid
323.0ms	4589×	body	80	valid
93.0ms	4×	body	10240	exit
91.0ms	398×	body	320	valid
34.0ms	213×	body	160	valid