Details

sample1.1s

Algorithm

intervals

Results

442.0ms	84×	body	10240	exit
232.0ms	76×	body	1280	valid
96.0ms	60×	body	640	valid
58.0ms	81×	body	80	valid
31.0ms	28×	body	320	valid
7.0ms	11×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

3 → 24

Calls

3 calls:

6.0ms	(sin (expm1 a))
0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series144.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(sin (expm1 a))
3.0ms	(expm1 (sin (expm1 a)))
16.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.4s

Counts

33 → 33

Iterations

Iter	Nodes
done	2114
9	2114
8	1246
7	493
6	231
5	124
4	69
3	47
2	38
1	34
0	31

prune298.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 34.2b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

15.0ms	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (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)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series258.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	2001
5	2001
4	1270
3	501
2	238
1	106
0	55

prune620.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 34.2b

localize69.0ms

Local error

Found 4 expressions with local error:

40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 32

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:

2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.7s

Counts

44 → 44

Iterations

Iter	Nodes
done	2000
10	2000
9	1400
8	417
7	168
6	84
5	50
4	31
3	23
2	18
1	16
0	15

prune413.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 34.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))))
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `exp-prod`
9×	`log-pow`
6×	`pow1/3`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `log-prod` `pow-plus` `exp-sum` `rem-exp-log`

Counts

4 → 46

Calls

4 calls:

18.0ms	(exp (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (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)

series197.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(exp (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))))
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.5s

Counts

58 → 58

Iterations

Iter	Nodes
done	2000
6	2000
5	1261
4	504
3	238
2	135
1	75
0	48

prune420.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 34.2b

regimes413.0ms

Accuracy

0% (1.1b remaining)

Error of 33.3b against oracle of 32.2b and baseline of 33.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	19
2	19
1	17
0	14

end0.0ms

sample28.4s

Algorithm

intervals

Results

15.0s	2572×	body	10240	exit
7.7s	2298×	body	1280	valid
3.0s	1566×	body	640	valid
1.3s	2837×	body	80	valid
794.0ms	851×	body	320	valid
293.0ms	440×	body	160	valid
64.0ms	7×	body	5120	valid
4.0ms	1×	body	2560	valid