Details

sample486.0ms

Algorithm

intervals

Results

82.0ms	25×	body	2560	valid
35.0ms	161×	body	80	valid
35.0ms	49×	body	1280	valid
10.0ms	27×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	5×	body	160	valid

simplify145.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 14.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.5b	(/ 1.0 (* F F))
4.1b	(* (/ 1.0 (* F F)) (tan (* PI l)))
27.7b	(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:

7.0ms	(* PI l)
7.0ms	(/ 1.0 (* F F))
46.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series260.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
28.0ms	(/ 1.0 (* F F))
133.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
78.0ms	(tan (* PI l))

simplify2.0s

Counts

97 → 97

Iterations

Useful iterations: 2 (167.0ms)

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

prune244.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.5b

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)))
27.7b	(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:

7.0ms	(* PI l)
7.0ms	(* PI l)
37.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series274.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
23.0ms	(* PI l)
165.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
65.0ms	(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

prune351.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) (* (sqrt PI) l))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
27.5b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

26.0ms	(* (sqrt PI) (* (sqrt PI) l))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
23.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series90.0ms

Counts

4 → 8

Calls

4 calls:

25.0ms	(* (sqrt PI) (* (sqrt PI) l))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
64.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify3.2s

Counts

71 → 71

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	76	524
1	159	349
2	439	315
3	1198	315
4	4278	315
done	5000	315

prune255.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.5b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
27.6b	(tan (* (sqrt PI) (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) l)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`tan-quot`

Counts

4 → 55

Calls

4 calls:

1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
63.0ms	(tan (* (sqrt PI) (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) l)))

series69.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
69.0ms	(tan (* (sqrt PI) (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) l)))

simplify1.7s

Counts

61 → 61

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	53	427
1	96	269
2	220	261
3	642	261
4	2489	261
done	5001	259

prune225.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.5b

regimes386.0ms

Accuracy

0% (0.3b remaining)

Error of 12.8b against oracle of 12.5b and baseline of 12.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	35
1	23	35
done	23	35

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.6s	835×	body	2560	valid
1.2s	1657×	body	1280	valid
331.0ms	934×	body	640	valid
329.0ms	4545×	body	80	valid
105.0ms	422×	body	320	valid
34.0ms	209×	body	160	valid
24.0ms	1×	body	10240	exit