Details

sample672.0ms

Algorithm

intervals

Results

327.0ms	74×	body	10240	exit
204.0ms	84×	body	1280	valid
43.0ms	43×	body	640	valid
14.0ms	85×	body	80	valid
11.0ms	23×	body	320	valid
7.0ms	21×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize24.0ms

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)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 28

Calls

4 calls:

0.0ms	(expm1 (sin (expm1 a)))
0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series107.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(expm1 (sin (expm1 a)))
4.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
78.0ms	(sin (expm1 a))
21.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.1s

Counts

40 → 40

Iterations

Useful iterations: 2 (23.0ms)

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	1209	293
8	4017	293
done	5001	293

prune273.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 32.9b

localize24.0ms

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)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

series118.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sin (expm1 a))
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.6s

Counts

40 → 40

Iterations

Useful iterations: 2 (7.0ms)

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	652	370
8	2140	370
done	5001	370

prune358.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.6b

localize74.0ms

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)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

series12.0ms

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)

simplify1.8s

Counts

40 → 40

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	30	436
5	64	436
6	149	436
7	330	436
8	1065	436
done	5000	436

prune323.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.6b

localize25.0ms

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)

rewrite10.0ms

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` `log-pow` `add-cbrt-cube`
3×	`log-prod`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 40

Calls

4 calls:

2.0ms	(sin (expm1 a))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series149.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sin (expm1 a))
62.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify992.0ms

Counts

52 → 52

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	51	562
1	67	507
2	99	446
3	149	446
4	255	446
5	534	446
6	1471	446
done	5001	446

prune200.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.4b

regimes428.0ms

Accuracy

0% (1.7b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	79
1	16	79
done	16	79

end0.0ms

sample22.7s

Algorithm

intervals

Results

11.5s	2546×	body	10240	exit
6.8s	2319×	body	1280	valid
2.1s	1660×	body	640	valid
976.0ms	819×	body	320	valid
633.0ms	2758×	body	80	valid
169.0ms	440×	body	160	valid
23.0ms	3×	body	5120	valid
2.0ms	1×	body	2560	valid