Details

sample729.0ms

Algorithm

intervals

Results

208.0ms	30×	body	2560	valid
71.0ms	56×	body	1280	valid
24.0ms	143×	body	80	valid
22.0ms	31×	body	640	valid
3.0ms	10×	body	160	valid
2.0ms	4×	body	320	valid

simplify228.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	164
7	164
6	162
5	152
4	126
3	82
2	41
1	19
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.4b	(/ 1.0 (* F F))
3.0b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.4b	(tan (* PI l))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube` `add-exp-log`
17×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
8×	`pow1`
7×	`times-frac`
6×	`associate-r` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `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` `clear-num` `associate-/r` `frac-2neg` `associate-l/` `associate-*r/`

Counts

4 → 85

Calls

4 calls:

12.0ms	(* PI l)
8.0ms	(/ 1.0 (* F F))
39.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
8.0ms	(tan (* PI l))

series303.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* PI l)
34.0ms	(/ 1.0 (* F F))
156.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
87.0ms	(tan (* PI l))

simplify1.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1985
1	352
0	143

prune639.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* l PI)
0.3b	(* l PI)
30.1b	(cos (* l PI))
30.4b	(sin (* l PI))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
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:

11.0ms	(* l PI)
11.0ms	(* l PI)
11.0ms	(cos (* l PI))
11.0ms	(sin (* l PI))

series154.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* l PI)
39.0ms	(* l PI)
31.0ms	(cos (* l PI))
50.0ms	(sin (* l PI))

simplify759.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	720
1	174
0	83

prune534.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan (* l PI)) F)
0.3b	(* PI l)
0.3b	(* l PI)
30.4b	(tan (* l PI))

rewrite50.0ms

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` `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 → 80

Calls

4 calls:

23.0ms	(/ (tan (* l PI)) F)
11.0ms	(* PI l)
6.0ms	(* l PI)
6.0ms	(tan (* l PI))

series291.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (tan (* l PI)) F)
24.0ms	(* PI l)
29.0ms	(* l PI)
96.0ms	(tan (* l PI))

simplify1.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	950
1	279
0	133

prune636.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.8b	(/ 1 (/ F (tan (* PI l))))
30.4b	(tan (* PI l))

rewrite63.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 132

Calls

4 calls:

6.0ms	(* PI l)
9.0ms	(* PI l)
30.0ms	(/ 1 (/ F (tan (* PI l))))
13.0ms	(tan (* PI l))

series308.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* PI l)
27.0ms	(* PI l)
169.0ms	(/ 1 (/ F (tan (* PI l))))
87.0ms	(tan (* PI l))

simplify1.5s

Counts

144 → 144

Iterations

Iter	Nodes
done	5001
2	2129
1	481
0	204

prune656.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.0b

regimes808.0ms

Accuracy

75.6% (0.6b remaining)

Error of 10.9b against oracle of 10.3b and baseline of 12.7b

bsearch3.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	48
2	48
1	47
0	39

end0.0ms

sample9.8s

Algorithm

intervals

Results

4.3s	871×	body	2560	valid
2.6s	1652×	body	1280	valid
1.4s	4502×	body	80	valid
797.0ms	976×	body	640	valid
159.0ms	378×	body	320	valid
111.0ms	3×	body	10240	exit
64.0ms	218×	body	160	valid