Details

sample230.0ms

Algorithm

intervals

Results

96.0ms	63×	body	1280	valid
43.0ms	53×	body	640	valid
36.0ms	203×	body	80	valid
17.0ms	30×	body	320	valid
6.0ms	16×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	873
2	158
1	48
0	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize43.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.3b	(* (/ (pow t 3.0) (* l l)) (sin k))
14.9b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.8b	(/ (pow t 3.0) (* l l))

rewrite691.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
58×	`prod-exp`
52×	`add-cbrt-cube`
26×	`cbrt-unprod`
24×	`div-exp`
21×	`add-sqr-sqrt`
20×	`pow1`
19×	`*-un-lft-identity`
17×	`times-frac`
16×	`associate-*l/`
14×	`add-cube-cbrt`
13×	`associate-l`
11×	`associate-r`
10×	`frac-times` `unpow-prod-down` `pow-prod-down`
8×	`pow-to-exp` `cbrt-undiv` `pow-exp` `tan-quot`
7×	`associate-/l*`
6×	`associate-*r/`
4×	`flip3-+` `flip-+` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in`

Counts

4 → 144

Calls

4 calls:

67.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
32.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
576.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
9.0ms	(/ (pow t 3.0) (* l l))

series2.1s

Counts

4 → 12

Calls

4 calls:

507.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
396.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
918.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
243.0ms	(/ (pow t 3.0) (* l l))

simplify1.6s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
1	822
0	254

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.6b

localize90.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.3b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.6b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.9b	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

304×	`add-exp-log`
184×	`prod-exp`
78×	`add-cbrt-cube`
77×	`div-exp`
50×	`add-sqr-sqrt`
49×	`times-frac`
44×	`associate-*l/` `cbrt-unprod`
42×	`*-un-lft-identity`
37×	`add-cube-cbrt`
36×	`associate-l`
34×	`frac-times`
33×	`pow-exp`
29×	`pow1`
24×	`unpow-prod-down`
22×	`pow-to-exp`
17×	`pow-prod-down`
16×	`tan-quot`
14×	`associate-*r/`
12×	`cbrt-undiv`
11×	`associate-r`
10×	`cbrt-prod`
8×	`flip3-+` `flip-+` `sqr-pow`
5×	`associate-/l*` `unswap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in`

Counts

4 → 229

Calls

4 calls:

188.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
45.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
908.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.3s

Counts

4 → 12

Calls

4 calls:

504.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
344.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
275.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.2s	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify1.8s

Counts

241 → 241

Iterations

Iter	Nodes
done	5000
1	1368
0	432

prune2.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.0b

localize75.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.7b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.3b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.9b	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

1050×	`add-exp-log`
674×	`times-frac`
554×	`prod-exp`
435×	`div-exp`
404×	`unpow-prod-down`
381×	`associate-l`
343×	`add-sqr-sqrt`
335×	`*-un-lft-identity`
330×	`add-cube-cbrt`
202×	`cbrt-prod`
151×	`add-cbrt-cube`
145×	`pow-to-exp` `pow-exp`
78×	`cbrt-unprod`
68×	`sqr-pow`
47×	`associate-*l/`
37×	`cbrt-undiv`
35×	`frac-times`
34×	`pow1`
20×	`pow-prod-down`
16×	`tan-quot`
15×	`associate-*r/`
12×	`associate-r` `div-inv`
8×	`flip3-+` `flip-+`
5×	`unswap-sqr`
4×	`*-commutative` `add-log-exp`
3×	`distribute-lft-out`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`

Counts

4 → 710

Calls

4 calls:

235.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
282.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
40.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.6s	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.6s

Counts

4 → 12

Calls

4 calls:

488.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
550.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
340.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.2s	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify2.9s

Counts

722 → 722

Iterations

Iter	Nodes
done	5001
1	2742
0	809

prune7.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.0b

localize100.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
4.3b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.9b	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
11.7b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

745×	`add-exp-log`
479×	`prod-exp`
210×	`div-exp`
142×	`add-cbrt-cube`
79×	`cbrt-unprod`
75×	`pow-to-exp` `pow-exp`
40×	`add-sqr-sqrt`
36×	`associate-l`
35×	`times-frac`
32×	`*-un-lft-identity`
30×	`cbrt-undiv`
27×	`add-cube-cbrt`
20×	`unpow-prod-down`
18×	`associate-*l/`
13×	`pow1`
11×	`associate-r` `associate-*r/`
10×	`cbrt-prod`
5×	`pow-prod-down` `unswap-sqr` `associate-/l/`
4×	`frac-times` `flip3-+` `flip-+` `add-log-exp` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `associate-/r/` `associate-/l`

Counts

4 → 264

Calls

4 calls:

182.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
44.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
822.0ms	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
832.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.9s

Counts

4 → 12

Calls

4 calls:

378.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
349.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.4s	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
770.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify2.4s

Counts

276 → 276

Iterations

Iter	Nodes
done	5001
1	1393
0	402

prune1.9s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 2.4b

regimes1.3s

Accuracy

58.1% (5.4b remaining)

Error of 7.5b against oracle of 2.1b and baseline of 15.0b

bsearch412.0ms

Steps

Iters	Range		Point
6	2.1407404787068644e-105	1.0323538399107104e-104	1.020078012341946e-104
6	-4.498239330844293e+71	-8.246628317525982e+70	-8.573355553736767e+70

simplify48.0ms

Iterations

Iter	Nodes
done	74
1	74
0	56

end0.0ms

sample11.3s

Algorithm

intervals

Results

4.4s	2044×	body	1280	valid
2.5s	5812×	body	80	valid
2.5s	1826×	body	640	valid
984.0ms	819×	body	320	valid
284.0ms	439×	body	160	valid