Details

sample1.4s

Algorithm

intervals

Results

565.0ms	88×	body	10240	exit
419.0ms	86×	body	1280	valid
111.0ms	37×	body	320	valid
98.0ms	54×	body	640	valid
13.0ms	64×	body	80	valid
7.0ms	15×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize99.0ms

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)

rewrite19.0ms

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:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
7.0ms	(sin (expm1 a))
4.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series397.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
128.0ms	(sin (expm1 a))
204.0ms	(expm1 (sin (expm1 a)))
46.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify8.4s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
6	4850
5	2000
4	953
3	412
2	202
1	119
0	74

prune764.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 36.5b

localize110.0ms

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)

rewrite79.0ms

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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `swap-sqr` `pow-sqr`
2×	`pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 82

Calls

4 calls:

19.0ms	(* (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))))
24.0ms	(* (* (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)

series381.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))
31.0ms	(cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
213.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
38.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify6.9s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
4	2214
3	949
2	493
1	172
0	78

prune1.1s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 36.1b

localize449.0ms

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)

rewrite60.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 61

Calls

4 calls:

50.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series262.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
18.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
24.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify6.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
5	2086
4	848
3	545
2	247
1	104
0	54

prune1.2s

Pruning

25 alts after pruning (23 fresh and 2 done)

Merged error: 35.8b

localize687.0ms

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)

rewrite47.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 61

Calls

4 calls:

41.0ms	(* (* (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))) (* (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)

series272.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
49.0ms	(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)
24.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
18.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify12.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5003
5	3897
4	1353
3	724
2	304
1	123
0	67

prune1.0s

Pruning

32 alts after pruning (29 fresh and 3 done)

Merged error: 35.6b

regimes1.8s

Accuracy

0% (2.3b remaining)

Error of 33.5b against oracle of 31.2b and baseline of 33.5b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample21.7s

Algorithm

intervals

Results

11.5s	2682×	body	10240	exit
6.3s	2304×	body	1280	valid
2.3s	1648×	body	640	valid
576.0ms	826×	body	320	valid
450.0ms	2802×	body	80	valid
190.0ms	416×	body	160	valid
9.0ms	1×	body	5120	valid
8.0ms	3×	body	2560	valid