Details

sample309.0ms

Algorithm

intervals

Results

154.0ms	66×	body	2560	valid
65.0ms	75×	body	1280	valid
60.0ms	60×	body	640	valid
11.0ms	34×	body	320	valid
4.0ms	15×	body	160	valid
1.0ms	6×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize19.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.6b	(- 1.0 (cos x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
13.0ms	(- 1.0 (cos x))

series96.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (- 1.0 (cos x)) (sin x))
34.0ms	(- 1.0 (cos x))

simplify3.1s

Counts

58 → 58

Iterations

Useful iterations: 3 (970.0ms)

Iter	Nodes	Cost
0	106	665
1	240	645
2	805	611
3	4711	609
done	5002	609

prune239.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/240 (pow x 5))
0.1b	(* 1/24 (pow x 3))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`associate-r`
12×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp` `add-cbrt-cube`
4×	`cube-prod` `sqr-pow`
2×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`
1×	`cube-mult` `unpow3`

Counts

2 → 56

Calls

2 calls:

25.0ms	(* 1/240 (pow x 5))
14.0ms	(* 1/24 (pow x 3))

series155.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(* 1/240 (pow x 5))
82.0ms	(* 1/24 (pow x 3))

simplify637.0ms

Counts

62 → 62

Iterations

Useful iterations: 2 (177.0ms)

Iter	Nodes	Cost
0	96	484
1	236	416
2	776	396
done	5001	396

prune258.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.6b	(- 1.0 (cos x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

28.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
9.0ms	(exp (log (- 1.0 (cos x))))
9.0ms	(log (- 1.0 (cos x)))
13.0ms	(- 1.0 (cos x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
27.0ms	(exp (log (- 1.0 (cos x))))
96.0ms	(log (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

110 → 110

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	168	1421
1	302	1183
2	837	1107
3	4191	1107
done	5000	1089

prune317.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(log (- 1.0 (cos x)))
0.3b	(pow E (log (- 1.0 (cos x))))
2.6b	(- 1.0 (cos x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `pow-sub`
3×	`associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 124

Calls

4 calls:

21.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
9.0ms	(log (- 1.0 (cos x)))
15.0ms	(pow E (log (- 1.0 (cos x))))
12.0ms	(- 1.0 (cos x))

series750.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
117.0ms	(log (- 1.0 (cos x)))
291.0ms	(pow E (log (- 1.0 (cos x))))
31.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

136 → 136

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	214	2049
1	456	1922
2	1729	1635
done	5000	1631

prune477.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.1b

regimes292.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.4b

bsearch160.0ms

Steps

Iters	Range		Point
11	0.022891638200552334	5.118117448855024e+31	0.02331429387269753
10	-911936.9907706906	-4.3470241882695893e-07	-0.018543641276894153

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	50
1	41	50
done	41	50

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.5s	1654×	body	2560	valid
2.5s	2742×	body	1280	valid
1.6s	1844×	body	640	valid
492.0ms	940×	body	320	valid
105.0ms	489×	body	160	valid
37.0ms	327×	body	80	valid
14.0ms	4×	body	5120	valid