Details

sample794.0ms

Algorithm

intervals

Results

325.0ms	74×	body	10240	exit
294.0ms	84×	body	1280	valid
50.0ms	43×	body	640	valid
15.0ms	85×	body	80	valid
13.0ms	23×	body	320	valid
7.0ms	21×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.3b	(sin (expm1 a))
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
50.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series238.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(expm1 (sin (expm1 a)))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
91.0ms	(sin (expm1 a))
20.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.7s

Counts

51 → 51

Iterations

Useful iterations: 3 (313.0ms)

Iter	Nodes	Cost
0	70	438
1	115	422
2	302	375
3	1200	374
done	5000	374

prune311.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 32.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`sin-diff` `expm1-udef`

Counts

4 → 37

Calls

4 calls:

3.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series106.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify6.5s

Counts

49 → 49

Iterations

Useful iterations: 3 (148.0ms)

Iter	Nodes	Cost
0	44	524
1	71	519
2	163	459
3	659	458
4	4828	458
done	5000	458

prune472.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.6b

localize69.0ms

Local error

Found 4 expressions with local error:

38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 36

Calls

4 calls:

0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series11.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.2s

Counts

48 → 48

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	16	588
1	17	588
2	19	516
3	24	516
4	32	516
5	66	516
6	147	516
7	321	516
8	917	516
done	5000	516

prune445.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
38.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod`
1×	`rem-log-exp` `sin-diff` `rem-exp-log` `expm1-udef`

Counts

4 → 49

Calls

4 calls:

2.0ms	(sin (expm1 a))
3.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
6.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series151.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sin (expm1 a))
35.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify6.6s

Counts

61 → 61

Iterations

Useful iterations: 3 (186.0ms)

Iter	Nodes	Cost
0	77	658
1	116	590
2	236	529
3	772	528
4	4921	528
done	5000	528

prune374.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.4b

regimes339.0ms

Accuracy

0% (1.7b remaining)

Error of 33.8b against oracle of 32.1b and baseline of 33.8b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	79
1	17	79
done	17	79

end0.0ms

sample22.2s

Algorithm

intervals

Results

10.2s	2546×	body	10240	exit
8.0s	2319×	body	1280	valid
2.1s	1660×	body	640	valid
612.0ms	819×	body	320	valid
512.0ms	2758×	body	80	valid
159.0ms	440×	body	160	valid
26.0ms	3×	body	5120	valid
2.0ms	1×	body	2560	valid