Details

sample381.0ms

Algorithm

intervals

Results

193.0ms	76×	body	10240	exit
121.0ms	68×	body	1280	valid
33.0ms	47×	body	640	valid
10.0ms	100×	body	80	valid
10.0ms	32×	body	320	valid
2.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7
done	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

3 → 30

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series156.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(expm1 (sin (expm1 a)))
65.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify118.0ms

Counts

39 → 39

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	215
1	231	188
2	706	188
3	2915	188
4	5001	188
done	5001	188

prune159.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 30.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
35.6b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `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 → 77

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
2.0ms	(cbrt (sin (expm1 a)))
15.0ms	(* (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)

series430.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (sin (expm1 a)))
141.0ms	(cbrt (sin (expm1 a)))
151.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify117.0ms

Counts

89 → 89

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	182	758
1	639	657
2	3589	621
3	5001	605
done	5001	605

prune392.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 29.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
35.5b	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (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)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`

Counts

4 → 42

Calls

4 calls:

10.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
7.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
8.0ms	(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 (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series469.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
159.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
151.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
4.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (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)

simplify75.0ms

Counts

54 → 54

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	91	843
1	182	714
2	466	708
3	1540	708
4	5001	708
done	5001	708

prune385.0ms

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 29.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a)))))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
35.5b	(fmod (atan2 (expm1 (* (* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-prod`
23×	`add-sqr-sqrt`
16×	`pow1`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
11×	`add-exp-log`
10×	`pow1/3`
7×	`associate-l` `pow-prod-down`
6×	`swap-sqr`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 89

Calls

4 calls:

51.0ms	(* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a)))))
15.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
11.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series460.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a)))))
152.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
149.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
4.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify44.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	291	1391
1	1214	1210
2	5001	1127
done	5001	1127

prune387.0ms

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 29.2b

regimes656.0ms

Accuracy

0% (2.0b remaining)

Error of 33.5b against oracle of 31.5b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	28
1	20	28
done	20	28

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.4s	2561×	body	10240	exit
3.7s	2240×	body	1280	valid
1.2s	1705×	body	640	valid
273.0ms	2811×	body	80	valid
265.0ms	833×	body	320	valid
83.0ms	402×	body	160	valid
19.0ms	3×	body	5120	valid
12.0ms	6×	body	2560	valid