Details

sample1.1s

Algorithm

intervals

Results

468.0ms	97×	body	10240	exit
283.0ms	64×	body	1280	valid
144.0ms	64×	body	640	valid
81.0ms	1×	body	5120	valid
52.0ms	32×	body	320	valid
16.0ms	84×	body	80	valid
4.0ms	11×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize71.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 28

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(expm1 (sin (expm1 a)))
4.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series126.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(expm1 (sin (expm1 a)))
105.0ms	(sin (expm1 a))
17.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.8s

Counts

40 → 40

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	35	339
1	39	339
2	44	293
3	55	293
4	84	293
5	217	293
6	519	293
7	1217	293
8	4003	293
done	5000	293

prune244.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 33.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.3b	(sin (expm1 a))
40.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(sin (expm1 a))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series130.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
39.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
83.0ms	(sin (expm1 a))
5.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify880.0ms

Counts

52 → 52

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	51	562
1	67	507
2	99	446
3	148	446
4	250	446
5	524	446
6	1433	446
done	5002	446

prune385.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 33.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 28

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)

series97.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sin (expm1 a))
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.3s

Counts

40 → 40

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	21	430
1	23	430
2	26	370
3	33	370
4	48	370
5	115	370
6	275	370
7	643	370
8	2114	370
done	5001	370

prune443.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 33.4b

localize45.0ms

Local error

Found 4 expressions with local error:

40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 28

Calls

4 calls:

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

series22.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.3s

Counts

40 → 40

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	30	436
5	64	436
6	142	436
7	319	436
8	1013	436
done	5001	436

prune229.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 33.4b

regimes616.0ms

Accuracy

0% (1.6b remaining)

Error of 33.6b against oracle of 31.9b and baseline of 33.6b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	44
1	20	44
done	20	44

end0.0ms

sample21.9s

Algorithm

intervals

Results

10.5s	2578×	body	10240	exit
7.1s	2340×	body	1280	valid
2.3s	1624×	body	640	valid
560.0ms	420×	body	160	valid
552.0ms	2786×	body	80	valid
485.0ms	824×	body	320	valid
20.0ms	3×	body	5120	valid
9.0ms	3×	body	2560	valid