Details

sample566.0ms

Algorithm

intervals

Results

163.0ms	30×	body	2560	valid
156.0ms	47×	body	1280	valid
105.0ms	40×	body	640	valid
64.0ms	150×	body	80	valid
4.0ms	6×	body	320	valid
3.0ms	5×	body	160	valid

simplify6.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	2576
6	880
5	396
4	166
3	91
2	45
1	21
0	10

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
3.5b	(/ (tan (* PI l)) (* F F))
30.3b	(tan (* PI l))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `tan-quot` `*-commutative` `unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `associate-/l/`

Counts

4 → 78

Calls

4 calls:

11.0ms	(* PI l)
11.0ms	(* PI l)
28.0ms	(/ (tan (* PI l)) (* F F))
19.0ms	(tan (* PI l))

series340.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* PI l)
34.0ms	(* PI l)
153.0ms	(/ (tan (* PI l)) (* F F))
127.0ms	(tan (* PI l))

simplify2.0s

Counts

90 → 90

Iterations

Iter	Nodes
done	5003
3	3184
2	719
1	240
0	108

prune471.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (tan (* PI l)) F)
0.3b	(* PI l)
0.3b	(* PI l)
30.3b	(tan (* PI l))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `prod-exp` `tan-quot` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate-/l/`

Counts

4 → 84

Calls

4 calls:

23.0ms	(/ (tan (* PI l)) F)
11.0ms	(* PI l)
12.0ms	(* PI l)
17.0ms	(tan (* PI l))

series376.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (tan (* PI l)) F)
24.0ms	(* PI l)
42.0ms	(* PI l)
122.0ms	(tan (* PI l))

simplify1.9s

Counts

96 → 96

Iterations

Iter	Nodes
done	5005
3	1667
2	588
1	227
0	114

prune506.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (tan (* PI l)) F)
0.3b	(* PI l)
0.3b	(* PI l)
30.3b	(tan (* PI l))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `prod-exp` `tan-quot` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate-/l/`

Counts

4 → 84

Calls

4 calls:

23.0ms	(/ (tan (* PI l)) F)
11.0ms	(* PI l)
15.0ms	(* PI l)
16.0ms	(tan (* PI l))

series347.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (tan (* PI l)) F)
39.0ms	(* PI l)
38.0ms	(* PI l)
121.0ms	(tan (* PI l))

simplify1.9s

Counts

96 → 96

Iterations

Iter	Nodes
done	5005
3	1667
2	588
1	227
0	114

prune496.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) (* (sqrt PI) l))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
30.3b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate-r` `tan-quot` `*-commutative`

Counts

4 → 67

Calls

4 calls:

32.0ms	(* (sqrt PI) (* (sqrt PI) l))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)
53.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series128.0ms

Counts

4 → 8

Calls

4 calls:

31.0ms	(* (sqrt PI) (* (sqrt PI) l))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
97.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify2.7s

Counts

75 → 75

Iterations

Iter	Nodes
done	5004
4	2879
3	1141
2	451
1	164
0	79

prune354.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.3b

regimes587.0ms

Accuracy

60.6% (2.4b remaining)

Error of 8.9b against oracle of 6.5b and baseline of 12.5b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	36
1	36
0	27

end0.0ms

sample12.3s

Algorithm

intervals

Results

5.1s	854×	body	2560	valid
3.8s	1638×	body	1280	valid
1.4s	938×	body	640	valid
1.1s	4634×	body	80	valid
328.0ms	407×	body	320	valid
185.0ms	6×	body	10240	exit
144.0ms	188×	body	160	valid