Details

sample408.0ms

Algorithm

intervals

Results

128.0ms	28×	body	2560	valid
79.0ms	52×	body	1280	valid
74.0ms	153×	body	80	valid
37.0ms	35×	body	640	valid
5.0ms	10×	body	320	valid
3.0ms	8×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
7	2002
6	817
5	388
4	156
3	86
2	43
1	20
0	10

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
4.2b	(/ (tan (* PI l)) (* F F))
30.2b	(tan (* PI l))

rewrite35.0ms

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×	`insert-posit16` `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 → 70

Calls

4 calls:

5.0ms	(* PI l)
5.0ms	(* PI l)
14.0ms	(/ (tan (* PI l)) (* F F))
9.0ms	(tan (* PI l))

series332.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* PI l)
23.0ms	(* PI l)
166.0ms	(/ (tan (* PI l)) (* F F))
110.0ms	(tan (* PI l))

simplify919.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	2000
3	2000
2	709
1	230
0	102

prune489.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan (* PI l)) F)
0.2b	(* PI l)
0.2b	(* PI l)
30.2b	(tan (* PI l))

rewrite66.0ms

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×	`insert-posit16` `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 → 76

Calls

4 calls:

22.0ms	(/ (tan (* PI l)) F)
11.0ms	(* PI l)
11.0ms	(* PI l)
20.0ms	(tan (* PI l))

series320.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (tan (* PI l)) F)
25.0ms	(* PI l)
33.0ms	(* PI l)
98.0ms	(tan (* PI l))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	2029
4	2029
3	1729
2	583
1	221
0	108

prune441.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.5b	(/ 1 (/ F (tan (* PI l))))
30.2b	(tan (* PI l))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
55×	`add-sqr-sqrt`
51×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-exp-log`
14×	`associate-/r*`
13×	`add-cbrt-cube`
9×	`pow1`
7×	`div-exp`
6×	`associate-r` `associate-l`
5×	`tan-quot` `associate-/r/` `div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-flip` `inv-pow`

Counts

4 → 128

Calls

4 calls:

5.0ms	(* PI l)
5.0ms	(* PI l)
24.0ms	(/ 1 (/ F (tan (* PI l))))
8.0ms	(tan (* PI l))

series338.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* PI l)
30.0ms	(* PI l)
185.0ms	(/ 1 (/ F (tan (* PI l))))
97.0ms	(tan (* PI l))

simplify1.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	2006
3	2006
2	1085
1	464
0	201

prune498.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 F) (/ (tan (* PI l)) F))
0.2b	(* PI l)
0.2b	(* PI l)
30.2b	(tan (* PI l))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
30×	`add-exp-log`
25×	`times-frac`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube`
19×	`associate-r` `associate-l`
10×	`pow1` `prod-exp`
8×	`div-exp` `unswap-sqr`
6×	`cbrt-unprod`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `associate-l/` `tan-quot` `associate-r/`

Counts

4 → 104

Calls

4 calls:

16.0ms	(* (/ 1 F) (/ (tan (* PI l)) F))
11.0ms	(* PI l)
10.0ms	(* PI l)
8.0ms	(tan (* PI l))

series310.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (/ 1 F) (/ (tan (* PI l)) F))
39.0ms	(* PI l)
40.0ms	(* PI l)
91.0ms	(tan (* PI l))

simplify1.3s

Counts

116 → 116

Iterations

Iter	Nodes
done	2016
3	2016
2	1411
1	470
0	165

prune568.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

regimes617.0ms

Accuracy

62.5% (2.2b remaining)

Error of 8.6b against oracle of 6.4b and baseline of 12.2b

bsearch3.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample11.5s

Algorithm

intervals

Results

4.5s	821×	body	2560	valid
3.4s	1636×	body	1280	valid
1.5s	968×	body	640	valid
1.3s	4615×	body	80	valid
292.0ms	360×	body	320	valid
242.0ms	6×	body	10240	exit
128.0ms	206×	body	160	valid