Details

sample324.0ms

Algorithm

intervals

Results

131.0ms	50×	body	2560	valid
119.0ms	80×	body	1280	valid
37.0ms	68×	body	640	valid
13.0ms	36×	body	320	valid
3.0ms	13×	body	160	valid
1.0ms	9×	body	80	valid

simplify15.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.1b	(- 1.0 (cos x))

rewrite55.0ms

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:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
13.0ms	(- 1.0 (cos x))

series114.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(/ (- 1.0 (cos x)) (sin x))
38.0ms	(- 1.0 (cos x))

simplify3.9s

Counts

58 → 58

Iterations

Useful iterations: 3 (1.2s)

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

prune384.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.1b	(- 1.0 (cos x))

rewrite81.0ms

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:

37.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
13.0ms	(exp (log (- 1.0 (cos x))))
14.0ms	(log (- 1.0 (cos x)))
11.0ms	(- 1.0 (cos x))

series257.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
31.0ms	(exp (log (- 1.0 (cos x))))
129.0ms	(log (- 1.0 (cos x)))
33.0ms	(- 1.0 (cos x))

simplify3.1s

Counts

110 → 110

Iterations

Useful iterations: done (3.1s)

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

prune581.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 1 (exp (log (- 1.0 (cos x))))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.1b	(- 1.0 (cos x))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

45.0ms	(/ (* 1 (exp (log (- 1.0 (cos x))))) (sin x))
13.0ms	(exp (log (- 1.0 (cos x))))
9.0ms	(log (- 1.0 (cos x)))
11.0ms	(- 1.0 (cos x))

series262.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (* 1 (exp (log (- 1.0 (cos x))))) (sin x))
30.0ms	(exp (log (- 1.0 (cos x))))
138.0ms	(log (- 1.0 (cos x)))
31.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

85 → 85

Iterations

Useful iterations: 2 (261.0ms)

Iter	Nodes	Cost
0	148	963
1	310	786
2	1347	706
done	5000	706

prune511.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin x) (- 1.0 (cos x)))
0.2b	(/ (exp (log 1)) (/ (sin x) (- 1.0 (cos x))))
1.1b	(- 1.0 (cos x))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

246×	`times-frac`
172×	`add-sqr-sqrt` `*-un-lft-identity`
120×	`add-cube-cbrt`
66×	`log-prod` `exp-sum`
26×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
17×	`associate-/r/`
10×	`add-cbrt-cube`
9×	`flip3--` `flip--` `div-inv` `associate-/l*`
8×	`add-exp-log`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `diff-log`

Counts

3 → 219

Calls

3 calls:

32.0ms	(/ (sin x) (- 1.0 (cos x)))
47.0ms	(/ (exp (log 1)) (/ (sin x) (- 1.0 (cos x))))
11.0ms	(- 1.0 (cos x))

series164.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ (sin x) (- 1.0 (cos x)))
68.0ms	(/ (exp (log 1)) (/ (sin x) (- 1.0 (cos x))))
31.0ms	(- 1.0 (cos x))

simplify2.5s

Counts

228 → 228

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	333	4785
1	843	3616
2	4171	3509
done	5000	3505

prune668.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.2b

regimes367.0ms

Accuracy

98.5% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.0b

bsearch2.0ms

simplify15.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	41	73
1	54	69
2	56	69
done	56	69

end0.0ms

sample11.0s

Algorithm

intervals

Results

4.2s	1561×	body	2560	valid
3.9s	2783×	body	1280	valid
1.8s	1938×	body	640	valid
434.0ms	933×	body	320	valid
116.0ms	449×	body	160	valid
49.0ms	335×	body	80	valid
5.0ms	1×	body	5120	valid