Details

sample924.0ms

Algorithm

intervals

Results

387.0ms	76×	body	10240	exit
234.0ms	72×	body	1280	valid
130.0ms	56×	body	640	valid
27.0ms	25×	body	320	valid
23.0ms	87×	body	80	valid
8.0ms	16×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

Iter	Nodes
1	8
0	8

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize28.0ms

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

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	(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)

series130.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
108.0ms	(sin (expm1 a))
15.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.6s

Counts

44 → 44

Iterations

Iter	Nodes
9	6178
8	1865
7	702
6	318
5	165
4	88
3	59
2	48
1	43
0	39

prune667.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 32.3b

localize72.0ms

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)

rewrite7.0ms

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:

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

series120.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(sin (expm1 a))
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.5s

Counts

44 → 44

Iterations

Iter	Nodes
9	2953
8	939
7	361
6	166
5	89
4	50
3	35
2	28
1	25
0	23

prune790.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.1b

localize133.0ms

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)

rewrite26.0ms

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:

24.0ms	(* (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)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series291.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
5.0ms	(fmod (atan2 (expm1 (* (* (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)

simplify2.9s

Counts

77 → 77

Iterations

Iter	Nodes
5	4190
4	995
3	436
2	245
1	122
0	71

prune1.8s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 31.9b

localize94.0ms

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)

rewrite19.0ms

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

series355.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(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)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.3s

Counts

58 → 58

Iterations

Iter	Nodes
6	4098
5	1237
4	494
3	230
2	136
1	88
0	62

prune1.2s

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 31.8b

regimes888.0ms

Accuracy

0% (2.0b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
2	23
1	23
0	21

end0.0ms

sample25.0s

Algorithm

intervals

Results

13.5s	2595×	body	10240	exit
6.8s	2237×	body	1280	valid
2.6s	1702×	body	640	valid
802.0ms	2798×	body	80	valid
665.0ms	835×	body	320	valid
289.0ms	424×	body	160	valid
9.0ms	3×	body	2560	valid
5.0ms	1×	body	5120	valid