Details

sample418.0ms

Algorithm

intervals

Results

221.0ms	86×	body	10240	exit
115.0ms	65×	body	1280	valid
46.0ms	62×	body	640	valid
9.0ms	87×	body	80	valid
9.0ms	27×	body	320	valid
3.0ms	15×	body	160	valid

simplify1.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

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:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(sin (expm1 a))
1.0ms	(expm1 (sin (expm1 a)))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series163.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
64.0ms	(sin (expm1 a))
93.0ms	(expm1 (sin (expm1 a)))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.3s

Counts

51 → 51

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	70	438
1	110	422
2	202	375
3	414	374
4	944	374
5	2449	374
done	5000	374

prune210.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 32.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.7b	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.1b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `expm1-log1p` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
3.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series126.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(expm1 (sin (expm1 a)))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
33.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify1.7s

Counts

80 → 80

Iterations

Useful iterations: 3 (403.0ms)

Iter	Nodes	Cost
0	87	1076
1	154	878
2	375	777
3	2168	769
done	5001	769

prune241.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 32.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (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)

series124.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (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)

simplify2.5s

Counts

52 → 52

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	30	673
1	39	669
2	67	555
3	128	552
4	445	552
5	2948	552
done	5001	552

prune281.0ms

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 32.5b

localize21.0ms

Local error

Found 4 expressions with local error:

39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.1b	(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)

simplify1.4s

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	30	516
5	40	516
6	61	516
7	125	516
8	427	516
9	1843	516
done	5001	516

prune208.0ms

Pruning

22 alts after pruning (19 fresh and 3 done)

Merged error: 32.5b

regimes312.0ms

Accuracy

0% (1.6b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
done	11	13

end0.0ms

sample12.4s

Algorithm

intervals

Results

6.6s	2614×	body	10240	exit
3.8s	2273×	body	1280	valid
1.1s	1654×	body	640	valid
281.0ms	846×	body	320	valid
267.0ms	2798×	body	80	valid
86.0ms	420×	body	160	valid
31.0ms	7×	body	5120	valid
4.0ms	2×	body	2560	valid