Details

sample825.0ms

Algorithm

intervals

Results

433.0ms	76×	body	10240	exit
203.0ms	68×	body	1280	valid
52.0ms	47×	body	640	valid
47.0ms	100×	body	80	valid
15.0ms	32×	body	320	valid
2.0ms	9×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize71.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

1.0ms	(expm1 (sin (expm1 a)))
7.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series241.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(expm1 (sin (expm1 a)))
169.0ms	(sin (expm1 a))
67.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.3s

Counts

30 → 30

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	28	238
1	31	238
2	35	206
3	44	206
4	56	206
5	80	206
6	137	206
7	342	206
8	1219	206
done	5000	206

prune176.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 30.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
35.6b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `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:

3.0ms	(cbrt (sin (expm1 a)))
3.0ms	(cbrt (sin (expm1 a)))
19.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series768.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(cbrt (sin (expm1 a)))
200.0ms	(cbrt (sin (expm1 a)))
290.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
7.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify5.9s

Counts

81 → 81

Iterations

Useful iterations: done (5.9s)

Iter	Nodes	Cost
0	63	945
1	99	864
2	272	648
3	957	601
4	4373	592
done	5000	576

prune507.0ms

Pruning

25 alts after pruning (23 fresh and 2 done)

Merged error: 29.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 28

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)

series94.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(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)

simplify4.3s

Counts

40 → 40

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	21	430
1	23	430
2	26	370
3	33	370
4	42	370
5	59	370
6	98	370
7	246	370
8	833	370
9	3625	370
done	5001	370

prune408.0ms

Pruning

30 alts after pruning (28 fresh and 2 done)

Merged error: 29.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.6b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite38.0ms

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×	`add-cbrt-cube` `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 → 61

Calls

4 calls:

33.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 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 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series273.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
7.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify1.9s

Counts

73 → 73

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	68	1007
1	104	934
2	218	760
3	439	691
4	976	673
done	5000	665

prune421.0ms

Pruning

36 alts after pruning (33 fresh and 3 done)

Merged error: 29.4b

regimes1.0s

Accuracy

0% (1.9b remaining)

Error of 33.4b against oracle of 31.6b and baseline of 33.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	12	21
done	12	21

end0.0ms

sample18.3s

Algorithm

intervals

Results

9.6s	2561×	body	10240	exit
5.5s	2240×	body	1280	valid
1.8s	1705×	body	640	valid
411.0ms	833×	body	320	valid
409.0ms	2811×	body	80	valid
127.0ms	402×	body	160	valid
21.0ms	3×	body	5120	valid
20.0ms	6×	body	2560	valid