Details

sample371.0ms

Algorithm

intervals

Results

113.0ms	23×	body	2560	valid
112.0ms	54×	body	1280	valid
25.0ms	32×	body	640	valid
19.0ms	138×	body	80	valid
7.0ms	16×	body	320	valid
3.0ms	9×	body	160	valid

simplify241.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
1.1b	(/ 1.0 (* F F))
5.6b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.3b	(tan (* PI l))

rewrite139.0ms

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:

14.0ms	(* PI l)
16.0ms	(/ 1.0 (* F F))
91.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
10.0ms	(tan (* PI l))

series395.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* PI l)
33.0ms	(/ 1.0 (* F F))
212.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
120.0ms	(tan (* PI l))

simplify3.0s

Counts

97 → 97

Iterations

Useful iterations: 2 (217.0ms)

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

prune392.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ (sqrt 1.0) F) (tan (* PI l)))
30.3b	(tan (* PI l))

rewrite133.0ms

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` `add-cbrt-cube`
10×	`pow1` `sqrt-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:

15.0ms	(* PI l)
21.0ms	(* PI l)
80.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
11.0ms	(tan (* PI l))

series430.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* PI l)
41.0ms	(* PI l)
262.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
101.0ms	(tan (* PI l))

simplify2.6s

Counts

108 → 108

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	140	946
1	305	921
2	839	840
3	2766	840
done	5001	835

prune544.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 12.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ (sqrt 1.0) F))
0.6b	(cbrt (/ (sqrt 1.0) F))
0.6b	(cbrt (/ (sqrt 1.0) F))
30.3b	(tan (* PI l))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

66×	`cbrt-prod`
54×	`times-frac`
43×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`sqrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`tan-quot`

Counts

4 → 109

Calls

4 calls:

7.0ms	(cbrt (/ (sqrt 1.0) F))
7.0ms	(cbrt (/ (sqrt 1.0) F))
7.0ms	(cbrt (/ (sqrt 1.0) F))
18.0ms	(tan (* PI l))

series1.3s

Counts

4 → 12

Calls

4 calls:

371.0ms	(cbrt (/ (sqrt 1.0) F))
430.0ms	(cbrt (/ (sqrt 1.0) F))
432.0ms	(cbrt (/ (sqrt 1.0) F))
104.0ms	(tan (* PI l))

simplify2.8s

Counts

121 → 121

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	129	1366
1	208	1277
2	391	1239
3	929	1221
4	2896	1191
done	5000	1147

prune726.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt F)
0.6b	(cbrt (/ (sqrt 1.0) F))
0.6b	(cbrt (/ (sqrt 1.0) F))
30.3b	(tan (* PI l))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

47×	`cbrt-prod`
36×	`times-frac`
31×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`sqrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-div` `div-inv`
1×	`tan-quot`

Counts

4 → 89

Calls

4 calls:

1.0ms	(cbrt F)
4.0ms	(cbrt (/ (sqrt 1.0) F))
9.0ms	(cbrt (/ (sqrt 1.0) F))
17.0ms	(tan (* PI l))

series1.2s

Counts

4 → 12

Calls

4 calls:

318.0ms	(cbrt F)
360.0ms	(cbrt (/ (sqrt 1.0) F))
440.0ms	(cbrt (/ (sqrt 1.0) F))
76.0ms	(tan (* PI l))

simplify3.1s

Counts

101 → 101

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	145	1018
1	239	954
2	483	896
3	1200	881
4	3933	859
done	5000	857

prune572.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 12.0b

regimes760.0ms

Accuracy

0% (0.4b remaining)

Error of 12.7b against oracle of 12.3b and baseline of 12.7b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	32
1	21	32
done	21	32

end0.0ms

sample9.4s

Algorithm

intervals

Results

4.6s	828×	body	2560	valid
2.1s	1679×	body	1280	valid
1.1s	4497×	body	80	valid
790.0ms	936×	body	640	valid
196.0ms	380×	body	320	valid
62.0ms	219×	body	160	valid
26.0ms	1×	body	10240	exit