Details

sample501.0ms

Algorithm

intervals

Results

103.0ms	27×	body	2560	valid
42.0ms	59×	body	1280	valid
11.0ms	142×	body	80	valid
9.0ms	28×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	5×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	41	7
2	82	7
3	122	7
4	147	7
5	157	7
6	159	7
7	159	7
done	159	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.6b	(/ 1.0 (* F F))
2.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.5b	(tan (* PI l))

rewrite75.0ms

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:

6.0ms	(* PI l)
7.0ms	(/ 1.0 (* F F))
48.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series264.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
26.0ms	(/ 1.0 (* F F))
136.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
79.0ms	(tan (* PI l))

simplify42.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	334	468
1	1442	399
2	5001	398
done	5001	398

prune238.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ 1.0 F) (tan (* PI l)))
29.5b	(tan (* PI l))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`associate-l`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `times-frac`
9×	`associate-r`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`tan-quot` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `div-inv`

Counts

4 → 86

Calls

4 calls:

7.0ms	(* PI l)
6.0ms	(* PI l)
32.0ms	(* (/ 1.0 F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series241.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
26.0ms	(* PI l)
129.0ms	(* (/ 1.0 F) (tan (* PI l)))
66.0ms	(tan (* PI l))

simplify88.0ms

Counts

98 → 98

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	286	403
1	1032	363
2	3928	361
3	5001	360
done	5001	360

prune275.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ (sin (* PI l)) (* (cos (* PI l)) F))
29.2b	(cos (* PI l))
29.3b	(sin (* PI l))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

9.0ms	(* PI l)
19.0ms	(/ (sin (* PI l)) (* (cos (* PI l)) F))
7.0ms	(cos (* PI l))
7.0ms	(sin (* PI l))

series174.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
112.0ms	(/ (sin (* PI l)) (* (cos (* PI l)) F))
17.0ms	(cos (* PI l))
24.0ms	(sin (* PI l))

simplify38.0ms

Counts

73 → 73

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	278	386
1	1052	331
2	5002	329
done	5002	329

prune243.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.6b	(/ 1 (/ (* (cos (* PI l)) F) (sin (* PI l))))
29.2b	(cos (* PI l))
29.3b	(sin (* PI l))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
27×	`add-exp-log`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-cbrt-cube`
12×	`div-exp`
7×	`pow1` `associate-/r*`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-unprod`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

9.0ms	(* PI l)
17.0ms	(/ 1 (/ (* (cos (* PI l)) F) (sin (* PI l))))
7.0ms	(cos (* PI l))
7.0ms	(sin (* PI l))

series175.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
113.0ms	(/ 1 (/ (* (cos (* PI l)) F) (sin (* PI l))))
18.0ms	(cos (* PI l))
23.0ms	(sin (* PI l))

simplify55.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	435	813
1	2001	720
2	5002	681
done	5002	681

prune239.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.5b

regimes380.0ms

Accuracy

69.9% (1.4b remaining)

Error of 9.2b against oracle of 7.8b and baseline of 12.3b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	48
1	65	48
done	65	48

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.5s	834×	body	2560	valid
1.2s	1643×	body	1280	valid
326.0ms	976×	body	640	valid
293.0ms	4550×	body	80	valid
82.0ms	377×	body	320	valid
47.0ms	2×	body	10240	exit
27.0ms	181×	body	160	valid