Details

sample1.2s

Algorithm

intervals

Results

455.0ms	83×	body	10240	exit
309.0ms	50×	body	640	valid
250.0ms	75×	body	1280	valid
21.0ms	99×	body	80	valid
17.0ms	23×	body	320	valid
4.0ms	9×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune12.0ms

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)

rewrite43.0ms

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)))
5.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series428.0ms

Counts

3 → 9

Calls

3 calls:

337.0ms	(expm1 (sin (expm1 a)))
76.0ms	(sin (expm1 a))
14.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.1s

Counts

39 → 39

Iterations

Useful iterations: 3 (125.0ms)

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

prune225.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 31.0b

localize43.0ms

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)

rewrite7.0ms

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:

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

series861.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(cbrt (expm1 (sin (expm1 a))))
287.0ms	(cbrt (expm1 (sin (expm1 a))))
263.0ms	(cbrt (expm1 (sin (expm1 a))))
7.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify2.0s

Counts

60 → 60

Iterations

Useful iterations: 3 (98.0ms)

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

prune374.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 30.5b

localize49.0ms

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)

rewrite5.0ms

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)

series865.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
338.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
256.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
4.0ms	(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)

simplify4.2s

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

prune588.0ms

Pruning

29 alts after pruning (26 fresh and 3 done)

Merged error: 30.3b

localize73.0ms

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 (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2)) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite11.0ms

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)))))
4.0ms	(cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2))
2.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (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)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

series857.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
300.0ms	(cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2))
281.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
5.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (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)))))) (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	279	1375
2	518	1246
3	1231	1237
done	5000	1154

prune710.0ms

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

sample23.1s

Algorithm

intervals

Results

12.1s	2622×	body	10240	exit
6.8s	2374×	body	1280	valid
2.3s	1607×	body	640	valid
737.0ms	2797×	body	80	valid
489.0ms	819×	body	320	valid
190.0ms	398×	body	160	valid
26.0ms	3×	body	5120	valid
4.0ms	2×	body	2560	valid