Details

sample737.0ms

Algorithm

intervals

Results

346.0ms	83×	body	10240	exit
164.0ms	75×	body	1280	valid
118.0ms	50×	body	640	valid
19.0ms	99×	body	80	valid
14.0ms	23×	body	320	valid
3.0ms	9×	body	160	valid

simplify12.0ms

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

localize33.0ms

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)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`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

3 → 30

Calls

3 calls:

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

series253.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(expm1 (sin (expm1 a)))
82.0ms	(sin (expm1 a))
20.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.6s

Counts

39 → 39

Iterations

Useful iterations: 3 (138.0ms)

Iter	Nodes	Cost
0	61	321
1	100	305
2	190	272
3	403	271
4	936	271
5	2429	271
done	5001	271

prune265.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 31.0b

localize20.0ms

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)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`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×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(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)

series672.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(cbrt (expm1 (sin (expm1 a))))
211.0ms	(cbrt (expm1 (sin (expm1 a))))
232.0ms	(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)

simplify1.8s

Counts

60 → 60

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	52	747
1	89	699
2	160	510
3	293	471
4	682	471
5	2249	471
done	5001	471

prune375.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 30.5b

localize41.0ms

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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 57

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)

series822.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
293.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
256.0ms	(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)

simplify4.3s

Counts

69 → 69

Iterations

Useful iterations: 6 (2.3s)

Iter	Nodes	Cost
0	61	1110
1	100	1074
2	167	841
3	292	802
4	544	693
5	1385	663
6	4602	645
done	5001	645

prune618.0ms

Pruning

29 alts after pruning (26 fresh and 3 done)

Merged error: 30.3b

localize44.0ms

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)

rewrite15.0ms

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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`unpow2` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
7.0ms	(cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2))
4.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0ms	(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)

series824.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
241.0ms	(cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2))
295.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
6.0ms	(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)

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	146	1549
1	278	1435
2	509	1246
3	1186	1237
done	5000	1154

prune635.0ms

Pruning

35 alts after pruning (32 fresh and 3 done)

Merged error: 29.8b

regimes1.0s

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

sample22.6s

Algorithm

intervals

Results

12.2s	2622×	body	10240	exit
6.9s	2374×	body	1280	valid
1.9s	1607×	body	640	valid
469.0ms	2797×	body	80	valid
445.0ms	819×	body	320	valid
183.0ms	398×	body	160	valid
19.0ms	3×	body	5120	valid
6.0ms	2×	body	2560	valid