Details

sample558.0ms

Algorithm

intervals

Results

263.0ms	83×	body	10240	exit
172.0ms	75×	body	1280	valid
43.0ms	50×	body	640	valid
13.0ms	99×	body	80	valid
10.0ms	23×	body	320	valid
2.0ms	9×	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: 31.8b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
36.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite33.0ms

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:

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

series115.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(expm1 (sin (expm1 a)))
99.0ms	(sin (expm1 a))
12.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.7s

Counts

30 → 30

Iterations

Useful iterations: 2 (439.0ms)

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

prune199.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 31.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
36.9b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

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

series506.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt (expm1 (sin (expm1 a))))
170.0ms	(cbrt (expm1 (sin (expm1 a))))
151.0ms	(cbrt (expm1 (sin (expm1 a))))
4.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify1.5s

Counts

52 → 52

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	31	602
1	40	590
2	69	421
3	130	388
4	345	388
5	1411	388
done	5000	388

prune323.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 30.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
36.9b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 49

Calls

4 calls:

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

series537.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
200.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
176.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
5.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify3.0s

Counts

61 → 61

Iterations

Useful iterations: 6 (848.0ms)

Iter	Nodes	Cost
0	40	929
1	54	920
2	78	714
3	120	681
4	195	592
5	482	568
6	1495	550
done	5000	550

prune500.0ms

Pruning

29 alts after pruning (26 fresh and 3 done)

Merged error: 30.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.8b	(cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2))
1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
36.9b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2)) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

50×	`cbrt-prod`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`unpow2` `sqr-pow`

Counts

4 → 60

Calls

4 calls:

3.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
8.0ms	(cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2))
2.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2)) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

series518.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
193.0ms	(cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2))
163.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
9.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2)) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify1.1s

Counts

72 → 72

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	96	1340
1	159	1254
2	258	1077
3	656	1068
done	5000	1001

prune495.0ms

Pruning

35 alts after pruning (32 fresh and 3 done)

Merged error: 29.8b

regimes1.1s

Accuracy

0% (2.0b remaining)

Error of 33.6b against oracle of 31.5b and baseline of 33.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	38
1	16	38
done	16	38

end0.0ms

sample21.8s

Algorithm

intervals

Results

11.5s	2622×	body	10240	exit
6.8s	2374×	body	1280	valid
1.9s	1607×	body	640	valid
584.0ms	2797×	body	80	valid
488.0ms	819×	body	320	valid
141.0ms	398×	body	160	valid
24.0ms	3×	body	5120	valid
6.0ms	2×	body	2560	valid