Details

sample925.0ms

Algorithm

intervals

Results

289.0ms	129×	body	1280	valid
216.0ms	71×	body	2560	valid
188.0ms	28×	body	5120	valid
144.0ms	87×	body	640	valid
23.0ms	31×	body	320	valid
14.0ms	56×	body	80	valid
7.0ms	15×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	19	25
1	44	25
2	146	25
3	798	23
4	4467	21
done	5000	21

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
1.0b	(* (/ (pow t 3.0) (* l l)) (sin k))
14.5b	(/ (pow t 3.0) (* l l))
30.4b	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite778.0ms

Algorithm

rewrite-expression-head

Rules

340×	`times-frac`
272×	`add-exp-log`
153×	`unpow-prod-down`
144×	`add-sqr-sqrt`
137×	`add-cube-cbrt` `*-un-lft-identity`
128×	`div-exp`
103×	`prod-exp`
59×	`add-cbrt-cube`
58×	`associate-*l/`
54×	`associate-/r/`
38×	`tan-quot`
34×	`pow-exp`
32×	`div-inv`
24×	`pow-to-exp`
21×	`cbrt-unprod`
19×	`cbrt-undiv` `frac-times` `associate-*r/`
18×	`associate-/r*`
17×	`associate-/l*`
15×	`sqr-pow`
12×	`associate-l`
11×	`pow1`
6×	`associate-r`
4×	`pow-prod-down` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 354

Calls

4 calls:

101.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
45.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
21.0ms	(/ (pow t 3.0) (* l l))
569.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

444.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
336.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
231.0ms	(/ (pow t 3.0) (* l l))
819.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify961.0ms

Counts

366 → 366

Iterations

Useful iterations: done (942.0ms)

Iter	Nodes	Cost
0	662	10242
1	1504	9739
done	5001	9233

prune2.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.0b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.9b	(* (pow k 2.0) (pow t 1.0))
16.7b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite305.0ms

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×	`add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 600

Calls

4 calls:

36.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
31.0ms	(* (pow k 2.0) (pow t 1.0))
123.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

492.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
141.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
581.0ms	(* (pow k 2.0) (pow t 1.0))
1.0s	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.8s

Counts

612 → 612

Iterations

Useful iterations: 2 (815.0ms)

Iter	Nodes	Cost
0	483	15017
1	1096	13295
2	2840	12595
done	5000	12595

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
0.8b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.0b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.7b	(* (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)))

rewrite770.0ms

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:

8.0ms	(pow (sin k) 2)
100.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
34.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
220.0ms	(* (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)))

series1.7s

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sin k) 2)
529.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
131.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
983.0ms	(* (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)))

simplify2.0s

Counts

1472 → 1472

Iterations

Useful iterations: 2 (880.0ms)

Iter	Nodes	Cost
0	597	50343
1	1262	33112
2	2940	31574
done	5000	31574

prune945.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
3.7b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
5.0b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.3b	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

24975×	`add-exp-log`
19170×	`prod-exp`
16882×	`pow-exp`
11120×	`div-exp`
7942×	`pow-to-exp`
2980×	`rec-exp` `1-exp`
54×	`unpow-prod-down`
41×	`associate-l`
40×	`times-frac`
36×	`add-sqr-sqrt`
32×	`add-cbrt-cube`
31×	`add-cube-cbrt` `*-un-lft-identity`
13×	`cbrt-unprod`
12×	`associate-r`
10×	`sqr-pow`
8×	`associate-/r*`
6×	`cbrt-undiv`
5×	`pow1`
4×	`div-inv` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`associate-l/` `-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 5729

Calls

4 calls:

7.0ms	(pow (sin k) 2)
282.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
32.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
160.0ms	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sin k) 2)
604.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
132.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
567.0ms	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify3.3s

Counts

5741 → 5741

Iterations

Useful iterations: 2 (1.7s)

Iter	Nodes	Cost
0	1426	225300
1	2244	200680
2	4187	189465
done	5000	189465

prune947.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.7b

regimes593.0ms

Accuracy

0% (5.7b remaining)

Error of 18.2b against oracle of 12.4b and baseline of 18.2b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: done (9.0ms)

Iter	Nodes	Cost
0	26	42
1	33	40
done	33	38

end0.0ms

sample32.1s

Algorithm

intervals

Results

8.9s	4128×	body	1280	valid
8.9s	2246×	body	2560	valid
7.3s	918×	body	5120	valid
3.8s	2543×	body	640	valid
1.3s	1024×	body	320	valid
604.0ms	2021×	body	80	valid
258.0ms	440×	body	160	valid