Details

sample142.0ms

Algorithm

intervals

Results

60.0ms	70×	body	1280	valid
29.0ms	55×	body	640	valid
22.0ms	195×	body	80	valid
11.0ms	29×	body	320	valid
4.0ms	15×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	25
1	47	25
2	153	25
3	759	25
4	3754	25
done	5000	25

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize21.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (/ (pow t 3.0) (* l l)) (sin k))
3.4b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
15.5b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.2b	(/ (pow t 3.0) (* l l))

rewrite358.0ms

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×	`tan-quot` `cbrt-undiv` `pow-to-exp` `pow-exp`
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` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r*`

Counts

4 → 144

Calls

4 calls:

15.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
36.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
295.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms	(/ (pow t 3.0) (* l l))

series1.4s

Counts

4 → 12

Calls

4 calls:

248.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
326.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
637.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
177.0ms	(/ (pow t 3.0) (* l l))

simplify1.3s

Counts

156 → 156

Iterations

Useful iterations: 2 (416.0ms)

Iter	Nodes	Cost
0	255	3209
1	786	3070
2	3819	2565
done	5001	2565

prune490.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.4b

localize31.0ms

Local error

Found 4 expressions with local error:

2.6b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
7.7b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.5b	(* (* (* (/ (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))

rewrite568.0ms

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` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 229

Calls

4 calls:

20.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
78.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
452.0ms	(* (* (* (/ (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))

series1.5s

Counts

4 → 12

Calls

4 calls:

242.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
361.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
199.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
730.0ms	(* (* (* (/ (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))

simplify457.0ms

Counts

241 → 241

Iterations

Useful iterations: done (445.0ms)

Iter	Nodes	Cost
0	429	6958
1	1345	6583
done	5000	6450

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.6b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
15.5b	(* (* (* (/ (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))

rewrite1.2s

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:

125.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
20.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
167.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
806.0ms	(* (* (* (/ (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))

series1.6s

Counts

4 → 12

Calls

4 calls:

289.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
241.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
358.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
723.0ms	(* (* (* (/ (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))

simplify745.0ms

Counts

722 → 722

Iterations

Useful iterations: done (714.0ms)

Iter	Nodes	Cost
0	806	20672
1	2723	19457
done	5000	18353

prune3.4s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 10.5b

localize26.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
2.6b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.5b	(/ (* (* (* (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)))
12.7b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite923.0ms

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` `associate-/l/` `unswap-sqr`
4×	`frac-times` `flip3-+` `flip-+` `add-log-exp` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r` `associate-/r/` `associate-/l`

Counts

4 → 264

Calls

4 calls:

73.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
18.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
374.0ms	(/ (* (* (* (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)))
431.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

249.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
240.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
710.0ms	(/ (* (* (* (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)))
528.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify477.0ms

Counts

276 → 276

Iterations

Useful iterations: done (466.0ms)

Iter	Nodes	Cost
0	401	10294
1	1354	9216
done	5000	8481

prune693.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 8.8b

regimes762.0ms

Accuracy

42.8% (4.3b remaining)

Error of 11.3b against oracle of 7.0b and baseline of 14.5b

bsearch280.0ms

Steps

Iters	Range		Point
7	511530637892499.1	13769255811373064.0	516710846836898.25
8	-4.2782436650216614e+117	-5.449563514943669e+113	-5.527279461114905e+113

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	67	177
1	88	177
done	88	177

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.9s	2072×	body	1280	valid
976.0ms	1801×	body	640	valid
682.0ms	5906×	body	80	valid
325.0ms	845×	body	320	valid
105.0ms	391×	body	160	valid