Details

sample220.0ms

Algorithm

intervals

Results

108.0ms	51×	body	2560	valid
61.0ms	94×	body	1280	valid
19.0ms	54×	body	640	valid
9.0ms	33×	body	320	valid
7.0ms	12×	body	80	valid
2.0ms	12×	body	160	valid

simplify12.0ms

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: 31.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.7b	(- 1.0 (cos x))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

58.0ms	(/ (- 1.0 (cos x)) (sin x))
8.0ms	(- 1.0 (cos x))

series88.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (- 1.0 (cos x)) (sin x))
35.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

74 → 74

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	134	964
1	295	831
2	743	731
3	2333	692
done	5000	683

prune289.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.3b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
1.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

series302.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
218.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify1.2s

Counts

26 → 26

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	36	358
1	62	349
2	177	307
3	967	307
done	5001	307

prune149.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

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)))
1.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.7b	(- 1.0 (cos x))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `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 → 132

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
28.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
35.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
8.0ms	(- 1.0 (cos x))

series206.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (- 1.0 (cos x)) (sin x))
74.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
48.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
34.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

144 → 144

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	195	1743
1	370	1509
2	856	1372
3	2563	1333
done	5000	1322

prune587.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

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)))
1.7b	(- 1.0 (cos x))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`log-prod`
25×	`exp-sum`
24×	`times-frac`
9×	`prod-diff`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `flip--` `log1p-expm1-u`
3×	`fma-neg` `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 → 118

Calls

4 calls:

32.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
14.0ms	(exp (log (- 1.0 (cos x))))
11.0ms	(log (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series235.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
23.0ms	(exp (log (- 1.0 (cos x))))
122.0ms	(log (- 1.0 (cos x)))
38.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

130 → 130

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	200	1750
1	351	1386
2	804	1245
3	2433	1206
done	5001	1178

prune330.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes276.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 31.6b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	24	51
1	31	41
done	31	41

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.6s	1634×	body	2560	valid
2.8s	2721×	body	1280	valid
995.0ms	1865×	body	640	valid
795.0ms	947×	body	320	valid
136.0ms	477×	body	160	valid
41.0ms	351×	body	80	valid
17.0ms	5×	body	5120	valid