Details

sample884.0ms

Algorithm

intervals

Results

247.0ms	125×	body	1280	valid
237.0ms	32×	body	5120	valid
199.0ms	71×	body	2560	valid
71.0ms	79×	body	640	valid
60.0ms	18×	body	160	valid
23.0ms	38×	body	320	valid
15.0ms	72×	body	80	valid

simplify662.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	832
2	147
1	44
0	19

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
0.8b	(* (pow (/ k t) 2.0) (tan k))
16.0b	(/ (pow t 3.0) (/ l (/ (sin k) l)))
30.2b	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

rewrite998.0ms

Algorithm

rewrite-expression-head

Rules

12307×	`times-frac`
4673×	`add-sqr-sqrt`
4665×	`*-un-lft-identity` `add-cube-cbrt`
1470×	`unpow-prod-down`
954×	`associate-/l*`
487×	`sqr-pow`
358×	`associate-/r*`
350×	`add-exp-log`
328×	`div-inv`
253×	`div-exp`
93×	`associate-/r/`
74×	`add-cbrt-cube`
48×	`prod-exp`
46×	`cbrt-undiv`
45×	`pow-exp`
33×	`pow-to-exp`
17×	`associate-l`
6×	`cbrt-unprod`
4×	`pow1` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `associate-r`
2×	`tan-quot` `associate-*r/`
1×	`*-commutative` `associate-/l/`

Counts

4 → 3666

Calls

4 calls:

83.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
38.0ms	(* (pow (/ k t) 2.0) (tan k))
25.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
297.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

series2.0s

Counts

4 → 12

Calls

4 calls:

372.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
261.0ms	(* (pow (/ k t) 2.0) (tan k))
269.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
1.1s	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

simplify1.6s

Counts

3678 → 3678

Iterations

Iter	Nodes
done	5342
0	5342

prune42.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
6.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.4b	(* (pow t 1.0) (pow k 2.0))
15.0b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 600

Calls

4 calls:

14.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
14.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
27.0ms	(* (pow t 1.0) (pow k 2.0))
104.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

530.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
128.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
466.0ms	(* (pow t 1.0) (pow k 2.0))
1.1s	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify833.0ms

Counts

612 → 612

Iterations

Iter	Nodes
done	5000
1	1217
0	437

prune1.6s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.7b

localize97.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.4b	(/ 1 (* (* (pow k (/ 2.0 2)) (pow t 1.0)) (pow k (/ 2.0 2))))
6.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.0b	(* (pow (/ 1 (* (* (pow k (/ 2.0 2)) (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite586.0ms

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×	`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 → 1460

Calls

4 calls:

5.0ms	(pow (sin k) 2)
81.0ms	(/ 1 (* (* (pow k (/ 2.0 2)) (pow t 1.0)) (pow k (/ 2.0 2))))
27.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
159.0ms	(* (pow (/ 1 (* (* (pow k (/ 2.0 2)) (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sin k) 2)
529.0ms	(/ 1 (* (* (pow k (/ 2.0 2)) (pow t 1.0)) (pow k (/ 2.0 2))))
147.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
988.0ms	(* (pow (/ 1 (* (* (pow k (/ 2.0 2)) (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.0s

Counts

1472 → 1472

Iterations

Iter	Nodes
done	5000
1	1742
0	574

prune1.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.8b

localize71.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
6.2b	(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l)) (pow (sin k) 2))
6.5b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l))
6.7b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l)) (pow (sin k) 2)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

19231×	`add-exp-log`
14163×	`prod-exp`
10781×	`pow-exp`
7888×	`div-exp`
4640×	`pow-to-exp`
2057×	`rec-exp` `1-exp`
52×	`add-cbrt-cube`
51×	`unpow-prod-down`
43×	`times-frac`
40×	`associate-l`
36×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `add-cube-cbrt`
24×	`cbrt-unprod`
13×	`associate-r`
10×	`cbrt-undiv`
9×	`associate-/r*` `sqr-pow`
5×	`pow1` `div-inv`
4×	`associate-/l*` `add-log-exp`
3×	`unpow2` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 4006

Calls

4 calls:

29.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
67.0ms	(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l)) (pow (sin k) 2))
100.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l))
309.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l)) (pow (sin k) 2)))

series2.6s

Counts

4 → 12

Calls

4 calls:

541.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
536.0ms	(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l)) (pow (sin k) 2))
484.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l))
1.0s	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l)) (pow (sin k) 2)))

simplify2.5s

Counts

4018 → 4018

Iterations

Iter	Nodes
done	5000
1	4575
0	1318

prune2.2s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 5.5b

regimes1.3s

Accuracy

22% (5.7b remaining)

Error of 11.2b against oracle of 5.5b and baseline of 12.8b

bsearch1.1s

Steps

Iters	Range		Point
8	1.6675236871481135e-12	7.42116589675916e-09	1.0995633895537175e-10
8	-5.220427904009889e+88	-1.1825419614466222e+86	-7.529474516601856e+87

simplify6.0ms

Iterations

Iter	Nodes
done	58
1	58
0	44

end0.0ms

sample30.1s

Algorithm

intervals

Results

8.8s	4025×	body	1280	valid
8.6s	2196×	body	2560	valid
6.6s	952×	body	5120	valid
3.3s	2527×	body	640	valid
915.0ms	947×	body	320	valid
645.0ms	437×	body	160	valid
517.0ms	2009×	body	80	valid