Details

sample839.0ms

Algorithm

intervals

Results

321.0ms	79×	body	10240	exit
229.0ms	76×	body	1280	valid
121.0ms	54×	body	640	valid
16.0ms	90×	body	80	valid
13.0ms	22×	body	320	valid
5.0ms	14×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune8.0ms

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	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite13.0ms

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

series302.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
149.0ms	(expm1 (sin (expm1 a)))
131.0ms	(sin (expm1 a))
17.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.6s

Counts

51 → 51

Iterations

Useful iterations: 3 (159.0ms)

Iter	Nodes	Cost
0	70	438
1	109	422
2	200	375
3	407	374
4	937	374
5	2426	374
done	5000	374

prune322.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 32.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (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

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)

series188.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(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)

simplify4.3s

Counts

52 → 52

Iterations

Useful iterations: 3 (55.0ms)

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

prune475.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 32.5b

localize30.0ms

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)

rewrite3.0ms

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:

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

series23.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify2.3s

Counts

48 → 48

Iterations

Useful iterations: 2 (11.0ms)

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

prune472.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 32.5b

localize30.0ms

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` `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)

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)

simplify2.7s

Counts

48 → 48

Iterations

Useful iterations: 2 (6.0ms)

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

prune361.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 32.5b

regimes292.0ms

Accuracy

0% (1.3b remaining)

Error of 33.4b against oracle of 32.1b and baseline of 33.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	58
1	16	58
done	16	58

end0.0ms

sample22.2s

Algorithm

intervals

Results

11.3s	2610×	body	10240	exit
6.6s	2286×	body	1280	valid
2.5s	1638×	body	640	valid
622.0ms	810×	body	320	valid
615.0ms	2821×	body	80	valid
155.0ms	439×	body	160	valid
13.0ms	5×	body	2560	valid
5.0ms	1×	body	5120	valid