Details

sample472.0ms

Algorithm

intervals

Results

149.0ms	72×	body	2560	valid
126.0ms	30×	body	5120	valid
101.0ms	125×	body	1280	valid
42.0ms	80×	body	640	valid
15.0ms	83×	body	80	valid
11.0ms	31×	body	320	valid
6.0ms	25×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 4 (270.0ms)

Iter	Nodes	Cost
0	19	25
1	44	25
2	143	25
3	712	23
4	3894	21
done	5001	21

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin k) (tan k))
0.6b	(* (pow (/ k t) 2.0) (* (sin k) (tan k)))
13.6b	(/ (pow t 3.0) (* l l))
27.8b	(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

405×	`add-exp-log`
213×	`div-exp`
162×	`times-frac`
139×	`prod-exp`
70×	`add-cbrt-cube`
62×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
56×	`pow-exp`
45×	`associate-/l*`
38×	`pow-to-exp`
37×	`unpow-prod-down`
29×	`cbrt-undiv`
20×	`associate-l` `cbrt-unprod`
11×	`div-inv`
9×	`sqr-pow`
6×	`pow1`
5×	`associate-*r/`
4×	`associate-r` `add-log-exp`
3×	`tan-quot` `associate-/r/`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative`
1×	`pow-prod-down` `associate-/l/` `unswap-sqr`

Counts

4 → 262

Calls

4 calls:

7.0ms	(* (sin k) (tan k))
20.0ms	(* (pow (/ k t) 2.0) (* (sin k) (tan k)))
5.0ms	(/ (pow t 3.0) (* l l))
27.0ms	(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))

series1.0s

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin k) (tan k))
239.0ms	(* (pow (/ k t) 2.0) (* (sin k) (tan k)))
182.0ms	(/ (pow t 3.0) (* l l))
575.0ms	(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))

simplify422.0ms

Counts

274 → 274

Iterations

Useful iterations: done (414.0ms)

Iter	Nodes	Cost
0	469	6220
1	1387	5736
done	5000	5701

prune792.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
5.0b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.1b	(* (pow k 2.0) (pow t 1.0))
15.2b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

1597×	`add-exp-log`
1095×	`prod-exp`
882×	`pow-exp`
668×	`div-exp`
492×	`pow-to-exp`
130×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
32×	`unpow-prod-down`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`cbrt-undiv` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 567

Calls

4 calls:

1.0ms	(pow (sin k) 2)
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0ms	(* (pow k 2.0) (pow t 1.0))
34.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin k) 2)
91.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
339.0ms	(* (pow k 2.0) (pow t 1.0))
657.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify2.3s

Counts

579 → 579

Iterations

Useful iterations: 2 (975.0ms)

Iter	Nodes	Cost
0	438	14412
1	1188	12754
2	3607	12085
done	5000	12085

prune620.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.3b	(pow (sin k) 2)
5.0b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.2b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1460

Calls

4 calls:

22.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.0ms	(pow (sin k) 2)
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
64.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

343.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
19.0ms	(pow (sin k) 2)
89.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
646.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify5.5s

Counts

1472 → 1472

Iterations

Useful iterations: 2 (2.6s)

Iter	Nodes	Cost
0	597	50343
1	1752	33118
2	4323	31574
done	5000	31574

prune577.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.8b	(/ (/ (* (cos k) (pow l 2)) (sin k)) (sin k))
3.0b	(/ (* (cos k) (pow l 2)) (sin k))
15.2b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (* (cos k) (pow l 2)) (sin k)) (sin k)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

3151×	`add-exp-log`
2067×	`prod-exp`
1311×	`div-exp`
1250×	`pow-exp`
692×	`pow-to-exp`
217×	`rec-exp` `1-exp`
75×	`times-frac`
54×	`add-sqr-sqrt`
41×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
25×	`associate-r`
15×	`cbrt-undiv`
12×	`div-inv`
11×	`associate-l` `associate-/l*`
10×	`cbrt-unprod`
9×	`unpow-prod-down`
7×	`associate-/r*`
6×	`unswap-sqr`
5×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `sqr-pow`
1×	`pow-flip` `associate-r/` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 819

Calls

4 calls:

25.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
7.0ms	(/ (/ (* (cos k) (pow l 2)) (sin k)) (sin k))
5.0ms	(/ (* (cos k) (pow l 2)) (sin k))
59.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (* (cos k) (pow l 2)) (sin k)) (sin k)))

series1.2s

Counts

4 → 12

Calls

4 calls:

343.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
89.0ms	(/ (/ (* (cos k) (pow l 2)) (sin k)) (sin k))
71.0ms	(/ (* (cos k) (pow l 2)) (sin k))
670.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (* (cos k) (pow l 2)) (sin k)) (sin k)))

simplify5.3s

Counts

831 → 831

Iterations

Useful iterations: 2 (2.2s)

Iter	Nodes	Cost
0	566	28048
1	1708	18127
2	4941	17147
done	5000	17147

prune667.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.1b

regimes436.0ms

Accuracy

18.3% (7.0b remaining)

Error of 18.0b against oracle of 11.0b and baseline of 19.6b

bsearch1.2s

Steps

Iters	Range		Point
9	2.501674882943443e+198	3.068871804357457e+205	1.1239944952301553e+203
9	4.651424770938929e-210	1.8276054982907742e-201	1.782011628913563e-201
9	-2.5350207885127242e-89	-1.6792679832518864e-98	-1.7434504270103252e-90
4	-4.8468419367483295e+113	-2.824627621173921e+113	-2.860188065369137e+113

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	163
1	85	163
done	85	163

end0.0ms

sample14.1s

Algorithm

intervals

Results

4.1s	970×	body	5120	valid
4.1s	2154×	body	2560	valid
3.4s	4083×	body	1280	valid
1.3s	2474×	body	640	valid
380.0ms	1021×	body	320	valid
236.0ms	2010×	body	80	valid
119.0ms	445×	body	160	valid