Details

sample884.0ms

Algorithm

intervals

Results

329.0ms	66×	body	10240	exit
244.0ms	70×	body	1280	valid
78.0ms	48×	body	640	valid
61.0ms	22×	body	160	valid
27.0ms	26×	body	320	valid
25.0ms	90×	body	80	valid

simplify59.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

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)))
0.4b	(sin (expm1 a))
37.4b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

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)

series132.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
117.0ms	(sin (expm1 a))
8.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.0s

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

prune450.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 31.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(sin (expm1 a))
37.4b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.4b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.4b	(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)

series107.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sin (expm1 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)

simplify2.7s

Counts

44 → 44

Iterations

Iter	Nodes
done	5013
9	2582
8	841
7	342
6	174
5	81
4	50
3	35
2	28
1	25
0	23

prune513.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.6b

localize97.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
37.3b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
37.4b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.4b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite35.0ms

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:

32.0ms	(* (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)

series331.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
4.0ms	(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)

simplify2.3s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
4	1464
3	542
2	263
1	125
0	71

prune884.0ms

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 31.4b

localize555.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
37.3b	(fmod (atan2 (expm1 (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)
37.4b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.4b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite13.0ms

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`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 34

Calls

4 calls:

12.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (* (cbrt (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)

series300.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
6.0ms	(fmod (atan2 (expm1 (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (* (cbrt (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)

simplify3.5s

Counts

46 → 46

Iterations

Iter	Nodes
done	5026
7	3484
6	1014
5	443
4	245
3	151
2	100
1	64
0	45

prune469.0ms

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 31.3b

regimes968.0ms

Accuracy

0% (2.0b remaining)

Error of 33.4b against oracle of 31.3b and baseline of 33.4b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample25.7s

Algorithm

intervals

Results

13.3s	2530×	body	10240	exit
7.1s	2264×	body	1280	valid
2.4s	1619×	body	640	valid
1.2s	2827×	body	80	valid
1.1s	858×	body	320	valid
253.0ms	427×	body	160	valid
29.0ms	3×	body	5120	valid
7.0ms	2×	body	2560	valid