Details

sample474.0ms

Algorithm

intervals

Results

82.0ms	26×	body	2560	valid
38.0ms	54×	body	1280	valid
34.0ms	146×	body	80	valid
11.0ms	31×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	4×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	41	7
2	82	7
3	122	7
4	147	7
5	157	7
6	159	7
7	159	7
done	159	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.6b	(/ 1.0 (* F F))
4.5b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.8b	(tan (* PI l))

rewrite73.0ms

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:

6.0ms	(* PI l)
8.0ms	(/ 1.0 (* F F))
47.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series261.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
25.0ms	(/ 1.0 (* F F))
134.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
78.0ms	(tan (* PI l))

simplify42.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	334	468
1	1442	399
2	5001	398
done	5001	398

prune249.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.3b

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)))
29.8b	(tan (* PI l))

rewrite61.0ms

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:

6.0ms	(* PI l)
6.0ms	(* PI l)
34.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
10.0ms	(tan (* PI l))

series275.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
20.0ms	(* PI l)
168.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
66.0ms	(tan (* PI l))

simplify93.0ms

Counts

108 → 108

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	303	519
1	1044	478
2	4000	476
3	5001	475
done	5001	475

prune406.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
28.9b	(cos (* PI l))
29.5b	(sin (* PI l))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

7.0ms	(* PI l)
7.0ms	(* PI l)
7.0ms	(cos (* PI l))
7.0ms	(sin (* PI l))

series86.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
21.0ms	(* PI l)
18.0ms	(cos (* PI l))
27.0ms	(sin (* PI l))

simplify109.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	162	201
1	606	181
2	3058	180
3	5002	180
done	5002	180

prune276.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt l)
0.6b	(cbrt l)
29.4b	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
29.5b	(sin (* PI l))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt l)
1.0ms	(cbrt l)
41.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
7.0ms	(sin (* PI l))

series409.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt l)
181.0ms	(cbrt l)
28.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
23.0ms	(sin (* PI l))

simplify82.0ms

Counts

56 → 56

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	156	247
1	513	219
2	2269	215
3	5001	210
done	5001	210

prune240.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.3b

regimes435.0ms

Accuracy

78% (1.0b remaining)

Error of 8.9b against oracle of 7.8b and baseline of 12.6b

bsearch3.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	67
1	70	67
done	70	67

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	810×	body	2560	valid
1.2s	1666×	body	1280	valid
334.0ms	952×	body	640	valid
313.0ms	4610×	body	80	valid
94.0ms	4×	body	10240	exit
85.0ms	359×	body	320	valid
31.0ms	199×	body	160	valid