Details

sample860.0ms

Algorithm

intervals

Results

286.0ms	128×	body	1280	valid
212.0ms	35×	body	5120	valid
208.0ms	74×	body	2560	valid
65.0ms	68×	body	640	valid
26.0ms	40×	body	320	valid
16.0ms	71×	body	80	valid
10.0ms	20×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3734
3	704
2	144
1	44
0	19

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2.0 (pow (/ k t) 2.0))
6.8b	(/ (* l l) (* (sin k) (tan k)))
15.3b	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
28.0b	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

9211×	`times-frac`
3212×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
2953×	`unpow-prod-down`
656×	`div-inv`
491×	`sqr-pow`
467×	`add-exp-log`
459×	`associate-/r/`
401×	`tan-quot` `associate-*r/`
331×	`div-exp`
92×	`add-cbrt-cube`
76×	`prod-exp`
71×	`associate-/r*`
66×	`associate-/l*`
64×	`pow-exp`
50×	`cbrt-undiv`
47×	`pow-to-exp`
16×	`cbrt-unprod`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

4 → 2993

Calls

4 calls:

23.0ms	(/ 2.0 (pow (/ k t) 2.0))
31.0ms	(/ (* l l) (* (sin k) (tan k)))
38.0ms	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
139.0ms	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

251.0ms	(/ 2.0 (pow (/ k t) 2.0))
195.0ms	(/ (* l l) (* (sin k) (tan k)))
454.0ms	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
913.0ms	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

simplify6.2s

Counts

3005 → 3005

Iterations

Iter	Nodes
done	5069
0	5069

prune37.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.2b

localize71.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
6.2b	(* (pow t 1.0) (pow k 2.0))
6.7b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.0b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite222.0ms

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×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`clear-num` `pow-pow` `frac-2neg` `associate-r/` `associate-/l`

Counts

4 → 575

Calls

4 calls:

5.0ms	(pow (sin k) 2)
24.0ms	(* (pow t 1.0) (pow k 2.0))
23.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
111.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.6s

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (sin k) 2)
487.0ms	(* (pow t 1.0) (pow k 2.0))
112.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
948.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify5.2s

Counts

587 → 587

Iterations

Iter	Nodes
done	5038
2	3015
1	1115
0	424

prune1.6s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 6.1b

localize84.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
0.4b	(pow (sin k) 2)
6.7b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.0b	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite569.0ms

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×	`*-un-lft-identity` `add-cube-cbrt`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-r/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 1468

Calls

4 calls:

81.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
4.0ms	(pow (sin k) 2)
14.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
182.0ms	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

508.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
21.0ms	(pow (sin k) 2)
110.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.1s	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify5.5s

Counts

1480 → 1480

Iterations

Iter	Nodes
done	5001
2	3692
1	1607
0	582

prune1.5s

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 4.8b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
5.6b	(/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (/ (* (sin k) (sin k)) (cos k)) (* l l)))
6.7b	(/ (/ (* (sin k) (sin k)) (cos k)) (* l l))
7.2b	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (/ (* (sin k) (sin k)) (cos k)) (* l l))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

16036×	`add-exp-log`
10094×	`div-exp`
7277×	`pow-exp`
7172×	`prod-exp`
2585×	`pow-to-exp`
1946×	`times-frac`
1574×	`rec-exp` `1-exp`
898×	`unpow-prod-down`
757×	`add-sqr-sqrt`
563×	`*-un-lft-identity`
536×	`add-cube-cbrt`
324×	`associate-r`
148×	`div-inv` `sqr-pow`
97×	`add-cbrt-cube`
84×	`unswap-sqr`
46×	`cbrt-undiv`
39×	`associate-/l*`
24×	`cbrt-unprod`
13×	`associate-/r*`
11×	`associate-l`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`div-sub` `associate-/r/`
1×	`associate-r/` `-commutative` `sqr-sin` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 3800

Calls

4 calls:

18.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
64.0ms	(/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (/ (* (sin k) (sin k)) (cos k)) (* l l)))
22.0ms	(/ (/ (* (sin k) (sin k)) (cos k)) (* l l))
283.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (/ (* (sin k) (sin k)) (cos k)) (* l l))))

series2.3s

Counts

4 → 12

Calls

4 calls:

512.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
527.0ms	(/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (/ (* (sin k) (sin k)) (cos k)) (* l l)))
90.0ms	(/ (/ (* (sin k) (sin k)) (cos k)) (* l l))
1.1s	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (/ (* (sin k) (sin k)) (cos k)) (* l l))))

simplify11.2s

Counts

3812 → 3812

Iterations

Iter	Nodes
done	5001
0	2399

prune10.3s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 1.5b

regimes1.0s

Accuracy

0% (2.0b remaining)

Error of 4.1b against oracle of 2.1b and baseline of 4.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample30.1s

Algorithm

intervals

Results

9.3s	2294×	body	2560	valid
7.3s	4085×	body	1280	valid
7.1s	963×	body	5120	valid
3.9s	2405×	body	640	valid
948.0ms	2002×	body	80	valid
828.0ms	1026×	body	320	valid
198.0ms	450×	body	160	valid