Details

sample908.0ms

Algorithm

intervals

Results

415.0ms	83×	body	10240	exit
269.0ms	85×	body	1280	valid
73.0ms	47×	body	640	valid
29.0ms	33×	body	320	valid
19.0ms	72×	body	80	valid
10.0ms	19×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 a)
0.0b	(expm1 (sin (expm1 a)))
42.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`log1p-expm1-u`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`expm1-udef`
2×	`expm1-log1p`
1×	`sin-diff`

Counts

4 → 45

Calls

4 calls:

5.0ms	(sin (expm1 a))
1.0ms	(expm1 a)
2.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series257.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(sin (expm1 a))
15.0ms	(expm1 a)
112.0ms	(expm1 (sin (expm1 a)))
12.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.2s

Counts

57 → 57

Iterations

Iter	Nodes
done	2026
5	2026
4	1387
3	627
2	286
1	137
0	78

prune364.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 35.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 (sin (expm1 a))))
0.5b	(cbrt (expm1 (sin (expm1 a))))
0.5b	(cbrt (expm1 (sin (expm1 a))))
42.6b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 52

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)

series780.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(cbrt (expm1 (sin (expm1 a))))
263.0ms	(cbrt (expm1 (sin (expm1 a))))
296.0ms	(cbrt (expm1 (sin (expm1 a))))
5.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	2022
5	2022
4	1097
3	404
2	181
1	94
0	54

prune435.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 35.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 (sin (expm1 a))))
42.6b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
42.6b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
42.6b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

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

series221.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(cbrt (expm1 (sin (expm1 a))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify1.0s

Counts

56 → 56

Iterations

Iter	Nodes
done	2022
5	2022
4	1097
3	404
2	181
1	94
0	54

prune705.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 35.1b

localize108.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
42.6b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
42.6b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
42.6b	(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)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

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

series286.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
13.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
5.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
6.0ms	(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)

simplify998.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	2009
5	2009
4	917
3	434
2	202
1	118
0	76

prune584.0ms

Pruning

39 alts after pruning (38 fresh and 1 done)

Merged error: 35.0b

regimes1.3s

Accuracy

0% (1.9b remaining)

Error of 34.0b against oracle of 32.1b and baseline of 34.0b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample25.4s

Algorithm

intervals

Results

13.3s	2570×	body	10240	exit
7.5s	2342×	body	1280	valid
2.5s	1685×	body	640	valid
751.0ms	800×	body	320	valid
719.0ms	2721×	body	80	valid
264.0ms	444×	body	160	valid
28.0ms	4×	body	5120	valid
17.0ms	4×	body	2560	valid