Details

sample986.0ms

Algorithm

intervals

Results

314.0ms	36×	body	5120	valid
262.0ms	69×	body	2560	valid
207.0ms	119×	body	1280	valid
95.0ms	88×	body	640	valid
36.0ms	46×	body	320	valid
15.0ms	64×	body	80	valid
7.0ms	13×	body	160	valid

simplify803.0ms

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
0.4b	(* (pow (/ k t) 2.0) (tan k))
14.9b	(/ (pow t 3.0) (/ l (/ (sin k) l)))
31.3b	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

rewrite1.2s

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:

106.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
32.0ms	(* (pow (/ k t) 2.0) (tan k))
30.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
363.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

series2.4s

Counts

4 → 12

Calls

4 calls:

419.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
365.0ms	(* (pow (/ k t) 2.0) (tan k))
365.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
1.2s	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

simplify2.0s

Counts

3678 → 3678

Iterations

Iter	Nodes
done	5342
0	5342

prune44.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 17.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
6.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.7b	(* (pow t 1.0) (pow k 2.0))
18.1b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite210.0ms

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:

24.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
14.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.0ms	(* (pow t 1.0) (pow k 2.0))
76.0ms	(* (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:

586.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
121.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
476.0ms	(* (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)))

simplify750.0ms

Counts

612 → 612

Iterations

Iter	Nodes
done	5000
1	1217
0	437

prune1.4s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.5b

localize72.0ms

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))))
6.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.1b	(* (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)))

rewrite532.0ms

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)
55.0ms	(/ 1 (* (* (pow k (/ 2.0 2)) (pow t 1.0)) (pow k (/ 2.0 2))))
15.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
161.0ms	(* (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:

40.0ms	(pow (sin k) 2)
570.0ms	(/ 1 (* (* (pow k (/ 2.0 2)) (pow t 1.0)) (pow k (/ 2.0 2))))
132.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
965.0ms	(* (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)))

simplify914.0ms

Counts

1472 → 1472

Iterations

Iter	Nodes
done	5000
1	1742
0	574

prune1.2s

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 9.8b

localize48.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
6.4b	(/ (pow (sin k) 2) (pow l 2))
7.8b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (/ (pow (sin k) 2) (pow l 2))))
10.0b	(* (pow (/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (/ (pow (sin k) 2) (pow l 2)))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

9103×	`add-exp-log`
5465×	`div-exp`
5283×	`pow-exp`
4783×	`prod-exp`
2567×	`pow-to-exp`
898×	`times-frac`
708×	`add-sqr-sqrt`
476×	`unpow-prod-down`
462×	`rec-exp` `1-exp`
285×	`*-un-lft-identity`
231×	`add-cube-cbrt`
210×	`associate-r`
197×	`sqr-pow`
162×	`unswap-sqr`
138×	`unpow2`
43×	`associate-l`
34×	`add-cbrt-cube`
14×	`associate-/l*`
11×	`cbrt-unprod`
9×	`cbrt-undiv` `associate-/r*` `sqrt-prod`
8×	`div-inv`
4×	`pow1` `add-log-exp`
3×	`associate-*r/`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-/r/`

Counts

4 → 2436

Calls

4 calls:

11.0ms	(/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
12.0ms	(/ (pow (sin k) 2) (pow l 2))
210.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (/ (pow (sin k) 2) (pow l 2))))
233.0ms	(* (pow (/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (/ (pow (sin k) 2) (pow l 2)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

550.0ms	(/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
79.0ms	(/ (pow (sin k) 2) (pow l 2))
543.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (/ (pow (sin k) 2) (pow l 2))))
943.0ms	(* (pow (/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (/ (pow (sin k) 2) (pow l 2)))))

simplify2.2s

Counts

2448 → 2448

Iterations

Iter	Nodes
done	5001
1	4573
0	1430

prune5.1s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 4.2b

regimes1.4s

Accuracy

-10.9% (4.7b remaining)

Error of 9.7b against oracle of 5.0b and baseline of 9.3b

bsearch690.0ms

Steps

Iters	Range		Point
7	3.242665664247682e+116	4.480502010750583e+118	4.306881873618755e+117
7	5.913977118434343e-49	3.175481108824353e-47	1.0934188082756232e-47

simplify26.0ms

Iterations

Iter	Nodes
done	72
3	72
2	69
1	64
0	50

end0.0ms

sample32.4s

Algorithm

intervals

Results

9.8s	4129×	body	1280	valid
8.0s	2231×	body	2560	valid
7.6s	1011×	body	5120	valid
3.8s	2447×	body	640	valid
1.1s	2021×	body	80	valid
881.0ms	1027×	body	320	valid
270.0ms	456×	body	160	valid