Details

sample967.0ms

Algorithm

intervals

Results

281.0ms	69×	body	2560	valid
262.0ms	36×	body	5120	valid
167.0ms	119×	body	1280	valid
87.0ms	88×	body	640	valid
34.0ms	46×	body	320	valid
13.0ms	64×	body	80	valid
6.0ms	13×	body	160	valid

simplify916.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	856
2	149
1	44
0	19

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
4.7b	(* (pow t 3.0) (/ (sin k) l))
6.1b	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
31.1b	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

569×	`times-frac`
499×	`add-exp-log`
286×	`div-exp`
275×	`add-sqr-sqrt`
230×	`unpow-prod-down`
229×	`*-un-lft-identity` `add-cube-cbrt`
150×	`prod-exp`
147×	`associate-l`
77×	`add-cbrt-cube`
76×	`pow-exp`
57×	`div-inv`
52×	`pow-to-exp`
38×	`associate-*r/`
37×	`associate-/r/`
34×	`cbrt-undiv`
27×	`associate-r`
22×	`sqr-pow`
20×	`cbrt-unprod`
18×	`associate-/r*`
16×	`unswap-sqr`
11×	`associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`frac-times` `pow-prod-down` `associate-*l/` `tan-quot` `associate-/l/`

Counts

4 → 539

Calls

4 calls:

14.0ms	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
33.0ms	(* (pow t 3.0) (/ (sin k) l))
182.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
32.0ms	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

series2.7s

Counts

4 → 12

Calls

4 calls:

439.0ms	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
350.0ms	(* (pow t 3.0) (/ (sin k) l))
1.2s	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
703.0ms	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

simplify1.5s

Counts

551 → 551

Iterations

Iter	Nodes
done	5000
1	2527
0	795

prune4.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ l (tan k))
6.1b	(* (* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k))) (/ l (tan k)))
7.0b	(* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k)))
7.9b	(/ (/ 1 (pow t 1.0)) (pow k 2.0))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

1087×	`add-exp-log`
540×	`prod-exp`
508×	`div-exp`
370×	`times-frac`
319×	`pow-exp`
190×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
150×	`unpow-prod-down`
139×	`pow-to-exp`
64×	`add-cbrt-cube`
63×	`rec-exp` `1-exp`
50×	`sqr-pow`
28×	`cbrt-unprod` `associate-/l*`
27×	`associate-r`
15×	`cbrt-undiv`
12×	`div-inv`
11×	`pow1`
10×	`associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l` `tan-quot` `associate-/r/` `*-commutative`
1×	`frac-times` `associate-*l/` `associate-/l/`

Counts

4 → 558

Calls

4 calls:

9.0ms	(/ l (tan k))
968.0ms	(* (* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k))) (/ l (tan k)))
234.0ms	(* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k)))
28.0ms	(/ (/ 1 (pow t 1.0)) (pow k 2.0))

series2.4s

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ l (tan k))
1.2s	(* (* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k))) (/ l (tan k)))
657.0ms	(* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k)))
464.0ms	(/ (/ 1 (pow t 1.0)) (pow k 2.0))

simplify1.6s

Counts

570 → 570

Iterations

Iter	Nodes
done	5000
1	2190
0	764

prune2.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 9.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ l (tan k))
1.1b	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
6.1b	(* (* (* 2.0 (pow (/ (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (/ l (tan k)))
7.0b	(* (* 2.0 (pow (/ (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

rewrite920.0ms

Algorithm

rewrite-expression-head

Rules

3381×	`add-exp-log`
2061×	`prod-exp`
1425×	`div-exp`
1092×	`pow-exp`
534×	`pow-to-exp`
190×	`rec-exp` `1-exp`
64×	`add-cbrt-cube`
30×	`times-frac`
29×	`cbrt-unprod`
28×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`associate-r`
14×	`cbrt-undiv`
12×	`pow1`
6×	`associate-/l*`
4×	`expm1-log1p-u` `associate-/r` `pow-prod-down` `associate-r/` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l` `tan-quot` `associate-/r/` `*-commutative`
1×	`frac-times` `associate-*l/` `pow-flip` `inv-pow`

Counts

4 → 737

Calls

4 calls:

9.0ms	(/ l (tan k))
16.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
505.0ms	(* (* (* 2.0 (pow (/ (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (/ l (tan k)))
202.0ms	(* (* 2.0 (pow (/ (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

series2.5s

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ l (tan k))
592.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.1s	(* (* (* 2.0 (pow (/ (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (/ l (tan k)))
650.0ms	(* (* 2.0 (pow (/ (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

simplify1.2s

Counts

749 → 749

Iterations

Iter	Nodes
done	5001
1	1989
0	603

prune1.7s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ l (tan k))
0.2b	(/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0))
6.1b	(* (* (* 2.0 (pow (/ (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (/ l (tan k)))
7.0b	(* (* 2.0 (pow (/ (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

rewrite7.3s

Algorithm

rewrite-expression-head

Rules

3400×	`add-exp-log`
1957×	`div-exp`
1548×	`prod-exp`
1111×	`pow-exp`
553×	`pow-to-exp`
370×	`times-frac`
190×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
171×	`rec-exp` `1-exp`
150×	`unpow-prod-down`
64×	`add-cbrt-cube`
50×	`sqr-pow`
28×	`cbrt-unprod` `associate-/l*`
27×	`associate-r`
15×	`cbrt-undiv`
12×	`div-inv`
11×	`pow1`
10×	`associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l` `tan-quot` `associate-/r/` `*-commutative`
1×	`frac-times` `associate-*l/` `associate-/l/`

Counts

4 → 936

Calls

4 calls:

6.0ms	(/ l (tan k))
21.0ms	(/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0))
5.8s	(* (* (* 2.0 (pow (/ (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (/ l (tan k)))
1.4s	(* (* 2.0 (pow (/ (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

series2.5s

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ l (tan k))
568.0ms	(/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0))
1.1s	(* (* (* 2.0 (pow (/ (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (/ l (tan k)))
680.0ms	(* (* 2.0 (pow (/ (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

simplify1.5s

Counts

948 → 948

Iterations

Iter	Nodes
done	5001
1	2787
0	926

prune2.2s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.0b

regimes813.0ms

Accuracy

6.9% (3.8b remaining)

Error of 10.7b against oracle of 7.0b and baseline of 11.0b

bsearch1.0s

Steps

Iters	Range		Point
7	6.996398304437385e+66	3.170816572293664e+68	9.443522340558765e+67
7	3.6089665434874025e-95	7.115096415711233e-94	7.034952289559082e-94

simplify10.0ms

Iterations

Iter	Nodes
done	56
1	56
0	44

end0.0ms

sample33.5s

Algorithm

intervals

Results

9.6s	4129×	body	1280	valid
9.2s	2231×	body	2560	valid
8.8s	1011×	body	5120	valid
3.4s	2447×	body	640	valid
855.0ms	1027×	body	320	valid
527.0ms	2021×	body	80	valid
221.0ms	456×	body	160	valid