Details

sample875.0ms

Algorithm

intervals

Results

351.0ms	76×	body	10240	exit
268.0ms	72×	body	1280	valid
117.0ms	56×	body	640	valid
27.0ms	87×	body	80	valid
24.0ms	25×	body	320	valid
7.0ms	16×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
1	8
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
38.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 43

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(expm1 (sin (expm1 a)))
3.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series278.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
171.0ms	(expm1 (sin (expm1 a)))
94.0ms	(sin (expm1 a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.2s

Counts

55 → 55

Iterations

Iter	Nodes
5	2969
4	1087
3	435
2	205
1	116
0	74

prune908.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 32.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
38.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`sin-diff` `expm1-udef`

Counts

4 → 41

Calls

4 calls:

2.0ms	(sin (expm1 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)

series91.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.5s

Counts

53 → 53

Iterations

Iter	Nodes
6	2636
5	1471
4	630
3	238
2	115
1	71
0	46

prune945.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.0b

localize107.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
38.6b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
38.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite15.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `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 → 73

Calls

4 calls:

13.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (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)

series210.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
2.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.3s

Counts

85 → 85

Iterations

Iter	Nodes
5	6278
4	1755
3	803
2	378
1	171
0	93

prune1.8s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 31.9b

localize160.0ms

Local error

Found 4 expressions with local error:

3.5b	(exp (log (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))))
38.5b	(fmod (atan2 (expm1 (* (exp (log (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)
38.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite39.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `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 → 54

Calls

4 calls:

36.0ms	(exp (log (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))))
0.0ms	(fmod (atan2 (expm1 (* (exp (log (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (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)

series192.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(exp (log (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))))
5.0ms	(fmod (atan2 (expm1 (* (exp (log (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (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)

simplify1.5s

Counts

66 → 66

Iterations

Iter	Nodes
5	2722
4	1073
3	507
2	250
1	136
0	84

prune1.5s

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 31.8b

regimes702.0ms

Accuracy

0% (2.0b remaining)

Error of 33.5b against oracle of 31.4b and baseline of 33.5b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
2	23
1	23
0	21

end0.0ms

sample26.0s

Algorithm

intervals

Results

13.3s	2595×	body	10240	exit
7.3s	2237×	body	1280	valid
3.0s	1702×	body	640	valid
1.2s	2798×	body	80	valid
654.0ms	835×	body	320	valid
216.0ms	424×	body	160	valid
10.0ms	3×	body	2560	valid
9.0ms	1×	body	5120	valid