Details

sample1.0s

Algorithm

intervals

Results

301.0ms	78×	body	2560	valid
277.0ms	42×	body	5120	valid
234.0ms	131×	body	1280	valid
89.0ms	78×	body	640	valid
24.0ms	31×	body	320	valid
16.0ms	77×	body	80	valid
12.0ms	22×	body	160	valid

simplify834.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.3b	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
15.4b	(/ (pow t 3.0) (/ l (/ (sin k) l)))
29.1b	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

12306×	`times-frac`
4664×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
1468×	`unpow-prod-down`
954×	`associate-/l*`
486×	`sqr-pow`
358×	`associate-/r*`
345×	`add-exp-log`
328×	`div-inv`
253×	`div-exp`
93×	`associate-/r/`
72×	`add-cbrt-cube`
46×	`cbrt-undiv`
45×	`pow-exp`
44×	`prod-exp`
33×	`pow-to-exp`
5×	`pow1` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg`
1×	`pow-pow` `tan-quot` `associate-*r/` `associate-/l/`

Counts

4 → 3656

Calls

4 calls:

10.0ms	(pow (/ k t) 2.0)
96.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
44.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
347.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

series1.7s

Counts

4 → 12

Calls

4 calls:

97.0ms	(pow (/ k t) 2.0)
460.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
385.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
709.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

simplify1.9s

Counts

3668 → 3668

Iterations

Iter	Nodes
done	5341
0	5341

prune43.8s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
6.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.8b	(* (pow t 1.0) (pow k 2.0))
16.8b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite221.0ms

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:

16.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
13.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0ms	(* (pow t 1.0) (pow k 2.0))
111.0ms	(* (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:

598.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
143.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
472.0ms	(* (pow t 1.0) (pow k 2.0))
1.0s	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify775.0ms

Counts

612 → 612

Iterations

Iter	Nodes
done	5000
1	1217
0	437

prune1.5s

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 12.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
0.6b	(/ 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))
16.8b	(* (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)))

rewrite577.0ms

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)
60.0ms	(/ 1 (* (* (pow k (/ 2.0 2)) (pow t 1.0)) (pow k (/ 2.0 2))))
13.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
200.0ms	(* (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:

36.0ms	(pow (sin k) 2)
553.0ms	(/ 1 (* (* (pow k (/ 2.0 2)) (pow t 1.0)) (pow k (/ 2.0 2))))
144.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
934.0ms	(* (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)))

simplify964.0ms

Counts

1472 → 1472

Iterations

Iter	Nodes
done	5000
1	1742
0	574

prune1.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.7b

localize92.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
6.0b	(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l)) (pow (sin k) 2))
8.4b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l))
9.3b	(* (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)))

rewrite1.4s

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:

15.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
74.0ms	(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l)) (pow (sin k) 2))
79.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l))
265.0ms	(* (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)))

series2.8s

Counts

4 → 12

Calls

4 calls:

519.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
469.0ms	(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l)) (pow (sin k) 2))
444.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (cos k) l) l))
1.4s	(* (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)))

simplify2.2s

Counts

4018 → 4018

Iterations

Iter	Nodes
done	5000
1	4575
0	1318

prune1.7s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 5.8b

regimes1.7s

Accuracy

18% (6.7b remaining)

Error of 11.5b against oracle of 4.9b and baseline of 13.0b

bsearch3.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	65
2	65
1	64
0	49

end0.0ms

sample32.5s

Algorithm

intervals

Results

8.9s	2227×	body	2560	valid
8.5s	3980×	body	1280	valid
7.8s	981×	body	5120	valid
4.4s	2551×	body	640	valid
981.0ms	1044×	body	320	valid
639.0ms	2011×	body	80	valid
284.0ms	504×	body	160	valid