Details

sample214.0ms

Algorithm

intervals

Results

102.0ms	49×	body	2560	valid
54.0ms	85×	body	1280	valid
26.0ms	60×	body	640	valid
7.0ms	27×	body	320	valid
5.0ms	1×	body	5120	valid
4.0ms	21×	body	160	valid
1.0ms	13×	body	80	valid

simplify14.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.3b	(- 1.0 (cos x))

rewrite36.0ms

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:

25.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
27.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	106	665
1	235	645
2	531	609
3	1194	609
4	3136	608
done	5000	608

prune250.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

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)))
2.3b	(- 1.0 (cos x))

rewrite92.0ms

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:

46.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
14.0ms	(exp (log (- 1.0 (cos x))))
11.0ms	(log (- 1.0 (cos x)))
14.0ms	(- 1.0 (cos x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
21.0ms	(exp (log (- 1.0 (cos x))))
96.0ms	(log (- 1.0 (cos x)))
33.0ms	(- 1.0 (cos x))

simplify3.0s

Counts

110 → 110

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	168	1421
1	285	1183
2	624	1107
3	1442	1107
4	3676	1088
done	5000	1088

prune299.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.3b	(- 1.0 (cos x))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
44.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
29.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms	(- 1.0 (cos x))

series178.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
66.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
44.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
26.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

124 → 124

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	163	1406
1	304	1293
2	639	1220
3	1394	1218
4	3567	1217
done	5000	1217

prune481.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.3b	(- 1.0 (cos x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`log-prod`
16×	`add-cube-cbrt`
13×	`times-frac` `associate-r` `exp-sum`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1` `log-div` `associate-l`
6×	`exp-diff` `add-log-exp` `unswap-sqr`
5×	`flip3--` `flip--`
4×	`exp-prod` `prod-exp` `distribute-lft-out--` `difference-of-squares`
2×	`frac-times` `div-exp` `associate-*l/` `log-pow` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `rem-exp-log`

Counts

4 → 97

Calls

4 calls:

53.0ms	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
7.0ms	(exp (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
10.0ms	(- 1.0 (cos x))

series236.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
33.0ms	(exp (log (- 1.0 (cos x))))
107.0ms	(log (- 1.0 (cos x)))
33.0ms	(- 1.0 (cos x))

simplify2.5s

Counts

109 → 109

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	178	1355
1	361	1073
2	891	961
3	2591	961
done	5000	955

prune317.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.2b

regimes253.0ms

Accuracy

98.5% (0.5b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.4b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	58
1	39	58
done	39	58

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.0s	1584×	body	2560	valid
1.9s	2834×	body	1280	valid
654.0ms	1868×	body	640	valid
210.0ms	893×	body	320	valid
88.0ms	468×	body	160	valid
54.0ms	7×	body	5120	valid
33.0ms	346×	body	80	valid