Details

sample835.0ms

Algorithm

intervals

Results

411.0ms	95×	body	10240	exit
232.0ms	81×	body	1280	valid
93.0ms	44×	body	640	valid
16.0ms	94×	body	80	valid
12.0ms	25×	body	320	valid
5.0ms	12×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	556
done	8	556

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 29

Calls

3 calls:

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

series148.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
136.0ms	(expm1 (sin (expm1 a)))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.8s

Counts

38 → 38

Iterations

Useful iterations: 6 (2.4s)

Iter	Nodes	Cost
0	49	16642
1	77	15978
2	134	15953
3	258	15953
4	508	15953
5	1214	15953
6	2956	15928
done	5001	15928

prune325.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 31.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

series161.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
6.0ms	(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)

simplify6.5s

Counts

52 → 52

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	30	32102
1	42	31629
2	72	31590
3	143	31430
4	599	31430
5	2736	31430
done	5001	31430

prune472.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 31.0b

localize154.0ms

Local error

Found 4 expressions with local error:

37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `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)

series14.0ms

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

simplify10.1s

Counts

48 → 48

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	27408
1	17	27408
2	19	27408
3	24	27408
4	32	27408
5	44	27408
6	78	27408
7	371	27408
8	656	27408
9	1142	27408
10	3506	27408
done	5008	27408

prune514.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 31.0b

localize203.0ms

Local error

Found 4 expressions with local error:

37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `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)

simplify7.5s

Counts

48 → 48

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	27408
1	17	27408
2	19	27408
3	24	27408
4	32	27408
5	44	27408
6	78	27408
7	371	27408
8	656	27408
9	1142	27408
10	3506	27408
done	5008	27408

prune291.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 31.0b

regimes263.0ms

Accuracy

0% (1.3b remaining)

Error of 33.5b against oracle of 32.2b and baseline of 33.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	17	1076
1	21	1076
done	21	1076

end0.0ms

sample15.0s

Algorithm

intervals

Results

7.9s	2672×	body	10240	exit
4.1s	2264×	body	1280	valid
1.4s	1686×	body	640	valid
664.0ms	831×	body	320	valid
624.0ms	2800×	body	80	valid
98.0ms	416×	body	160	valid
14.0ms	3×	body	5120	valid