Details

sample872.0ms

Algorithm

intervals

Results

399.0ms	88×	body	10240	exit
247.0ms	86×	body	1280	valid
59.0ms	54×	body	640	valid
20.0ms	37×	body	320	valid
11.0ms	64×	body	80	valid
6.0ms	15×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
44.1b	(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))
3.0ms	(sin (expm1 a))
0.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series103.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
91.0ms	(sin (expm1 a))
2.0ms	(expm1 (sin (expm1 a)))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.2s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
8	1654
7	641
6	292
5	157
4	88
3	59
2	48
1	43
0	39

prune291.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 36.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
1.0b	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-plus` `pow-prod-up`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow2` `swap-sqr` `pow-sqr`
2×	`pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 74

Calls

4 calls:

14.0ms	(* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))
27.0ms	(cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
48.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series94.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
53.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
5.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify3.0s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
4	2204
3	952
2	449
1	164
0	70

prune564.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 36.1b

localize104.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `pow-sqr`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

28.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series55.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
5.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
5.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
5.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify3.6s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
5	2266
4	991
3	518
2	228
1	98
0	50

prune543.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 35.8b

localize155.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
44.1b	(fmod (cbrt (* (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) a)
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `pow-sqr`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

39.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (cbrt (* (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) a)
1.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
1.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series68.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms	(fmod (cbrt (* (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) a)
10.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
5.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify3.9s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
5	2612
4	1075
3	669
2	299
1	116
0	61

prune624.0ms

Pruning

29 alts after pruning (26 fresh and 3 done)

Merged error: 35.7b

regimes659.0ms

Accuracy

0% (2.2b remaining)

Error of 33.5b against oracle of 31.3b and baseline of 33.5b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample22.6s

Algorithm

intervals

Results

11.8s	2682×	body	10240	exit
6.3s	2304×	body	1280	valid
2.4s	1648×	body	640	valid
1.1s	826×	body	320	valid
625.0ms	2802×	body	80	valid
207.0ms	416×	body	160	valid
8.0ms	3×	body	2560	valid
5.0ms	1×	body	5120	valid