Details

sample946.0ms

Algorithm

intervals

Results

321.0ms	80×	body	2560	valid
262.0ms	42×	body	5120	valid
178.0ms	125×	body	1280	valid
77.0ms	83×	body	640	valid
53.0ms	34×	body	320	valid
13.0ms	60×	body	80	valid
6.0ms	14×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5174
4	3622
3	689
2	142
1	44
0	19

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (pow (/ k t) 2.0) (tan k))
0.4b	(/ 2.0 (pow t 3.0))
19.8b	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
31.9b	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

410×	`add-exp-log`
181×	`div-exp`
173×	`prod-exp`
144×	`times-frac`
89×	`add-cbrt-cube`
80×	`add-sqr-sqrt`
72×	`*-un-lft-identity` `add-cube-cbrt`
55×	`pow-exp`
54×	`unpow-prod-down`
47×	`associate-l`
38×	`pow-to-exp`
34×	`cbrt-unprod`
30×	`cbrt-undiv`
28×	`associate-/l*`
15×	`sqr-pow`
9×	`pow1`
8×	`associate-/r*`
7×	`div-inv`
4×	`associate-r` `associate-*r/` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-*l/` `tan-quot`
2×	`clear-num` `frac-2neg` `associate-/r/` `*-commutative`
1×	`frac-times` `associate-/l/`

Counts

4 → 292

Calls

4 calls:

38.0ms	(* (pow (/ k t) 2.0) (tan k))
6.0ms	(/ 2.0 (pow t 3.0))
93.0ms	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
25.0ms	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

series2.4s

Counts

4 → 12

Calls

4 calls:

296.0ms	(* (pow (/ k t) 2.0) (tan k))
569.0ms	(/ 2.0 (pow t 3.0))
1.1s	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
503.0ms	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

simplify3.3s

Counts

304 → 304

Iterations

Iter	Nodes
done	5001
2	4954
1	1212
0	433

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
0.7b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
7.7b	(* (pow t 1.0) (pow k 2.0))
16.5b	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

rewrite567.0ms

Algorithm

rewrite-expression-head

Rules

1239×	`add-exp-log`
740×	`prod-exp`
455×	`div-exp`
318×	`pow-exp`
138×	`pow-to-exp`
85×	`add-cbrt-cube`
70×	`rec-exp` `1-exp`
32×	`cbrt-unprod`
29×	`cbrt-undiv`
26×	`add-sqr-sqrt`
17×	`associate-l`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`unpow-prod-down`
9×	`times-frac` `unswap-sqr`
8×	`associate-r` `sqr-pow`
7×	`pow1`
6×	`associate-/r/` `associate-/l*`
4×	`add-log-exp`
3×	`associate-*l/` `div-inv`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-r/` `*-commutative`
1×	`pow-prod-down` `pow-flip` `inv-pow`

Counts

4 → 359

Calls

4 calls:

400.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
21.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
14.0ms	(* (pow t 1.0) (pow k 2.0))
105.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
425.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
514.0ms	(* (pow t 1.0) (pow k 2.0))
616.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

simplify8.0s

Counts

371 → 371

Iterations

Iter	Nodes
done	5002
2	3679
1	1252
0	432

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.2b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin k) l) (/ (sin k) l))
0.6b	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
0.7b	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
16.5b	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

3948×	`add-exp-log`
2751×	`prod-exp`
1320×	`div-exp`
1152×	`pow-exp`
594×	`pow-to-exp`
217×	`rec-exp` `1-exp`
99×	`add-cbrt-cube`
50×	`add-sqr-sqrt`
49×	`times-frac`
38×	`*-un-lft-identity` `add-cube-cbrt`
37×	`cbrt-unprod`
34×	`cbrt-undiv`
23×	`associate-l`
14×	`pow1` `associate-r`
13×	`swap-sqr`
7×	`div-inv`
6×	`associate-/r/` `associate-/l*`
4×	`associate-*l/` `add-log-exp` `unswap-sqr`
3×	`frac-times` `associate-*r/`
2×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative`
1×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up` `pow-flip` `inv-pow`

Counts

4 → 827

Calls

4 calls:

23.0ms	(* (/ (sin k) l) (/ (sin k) l))
28.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
67.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
136.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (/ (sin k) l) (/ (sin k) l))
119.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
519.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
635.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0))

simplify8.3s

Counts

839 → 839

Iterations

Iter	Nodes
done	5001
1	1862
0	639

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin k) l) (/ (sin k) l))
0.6b	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
0.6b	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
16.5b	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) (pow k (/ 2.0 2))) 1.0) 2.0))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

3792×	`add-exp-log`
2067×	`prod-exp`
1824×	`div-exp`
1092×	`pow-exp`
534×	`pow-to-exp`
190×	`rec-exp` `1-exp`
95×	`add-cbrt-cube`
50×	`add-sqr-sqrt`
49×	`times-frac`
38×	`*-un-lft-identity` `add-cube-cbrt`
35×	`cbrt-unprod`
33×	`cbrt-undiv`
23×	`associate-l`
14×	`pow1` `associate-r`
13×	`swap-sqr`
7×	`div-inv`
6×	`associate-/r/` `associate-/l*`
4×	`associate-*l/` `add-log-exp` `unswap-sqr`
3×	`frac-times` `associate-*r/`
2×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative`
1×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up` `pow-flip` `inv-pow`

Counts

4 → 763

Calls

4 calls:

22.0ms	(* (/ (sin k) l) (/ (sin k) l))
30.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
24.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
167.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) (pow k (/ 2.0 2))) 1.0) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (/ (sin k) l) (/ (sin k) l))
117.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
523.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
628.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) (pow k (/ 2.0 2))) 1.0) 2.0))

simplify8.5s

Counts

775 → 775

Iterations

Iter	Nodes
done	5000
1	1752
0	634

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.1b

regimes853.0ms

Accuracy

16.5% (5.2b remaining)

Error of 15.5b against oracle of 10.3b and baseline of 16.5b

bsearch408.0ms

Steps

Iters	Range		Point
8	-8.950291804104186e-77	-8.995463716080387e-80	-9.12674325213613e-80

simplify8.0ms

Iterations

Iter	Nodes
done	44
1	44
0	34

end0.0ms

sample30.0s

Algorithm

intervals

Results

8.7s	2317×	body	2560	valid
8.0s	3989×	body	1280	valid
7.4s	932×	body	5120	valid
3.4s	2554×	body	640	valid
796.0ms	977×	body	320	valid
760.0ms	1985×	body	80	valid
217.0ms	421×	body	160	valid