Details

sample944.0ms

Algorithm

intervals

Results

387.0ms	92×	body	10240	exit
270.0ms	72×	body	1280	valid
61.0ms	51×	body	640	valid
18.0ms	30×	body	320	valid
17.0ms	89×	body	80	valid
5.0ms	13×	body	160	valid
2.0ms	1×	body	2560	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 a)
0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

6×	`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`
3×	`expm1-udef`
2×	`expm1-log1p`
1×	`sin-diff`

Counts

4 → 41

Calls

4 calls:

5.0ms	(expm1 a)
1.0ms	(expm1 (sin (expm1 a)))
7.0ms	(sin (expm1 a))
37.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series296.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(expm1 a)
151.0ms	(expm1 (sin (expm1 a)))
113.0ms	(sin (expm1 a))
17.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.9s

Counts

53 → 53

Iterations

Useful iterations: 3 (441.0ms)

Iter	Nodes	Cost
0	73	380
1	131	356
2	380	319
3	1664	318
done	5001	318

prune359.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(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:

2.0ms	(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)

series124.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(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)

simplify6.3s

Counts

49 → 49

Iterations

Useful iterations: 3 (107.0ms)

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

prune393.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
38.4b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

42.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series220.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (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)

simplify6.1s

Counts

81 → 81

Iterations

Useful iterations: done (6.1s)

Iter	Nodes	Cost
0	90	1125
1	173	1047
2	526	856
3	3316	776
done	5000	758

prune814.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 32.4b

localize74.0ms

Local error

Found 4 expressions with local error:

38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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)
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)

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)

simplify1.3s

Counts

48 → 48

Iterations

Useful iterations: 2 (10.0ms)

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

prune473.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 32.4b

regimes725.0ms

Accuracy

0% (1.3b remaining)

Error of 33.7b against oracle of 32.4b and baseline of 33.7b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	90
1	24	90
done	24	90

end0.0ms

sample20.9s

Algorithm

intervals

Results

10.4s	2608×	body	10240	exit
6.5s	2319×	body	1280	valid
1.8s	1671×	body	640	valid
955.0ms	807×	body	320	valid
507.0ms	2766×	body	80	valid
182.0ms	430×	body	160	valid
22.0ms	3×	body	5120	valid
11.0ms	4×	body	2560	valid