Details

sample890.0ms

Algorithm

intervals

Results

411.0ms	96×	body	10240	exit
292.0ms	84×	body	1280	valid
60.0ms	47×	body	640	valid
19.0ms	32×	body	320	valid
16.0ms	83×	body	80	valid
4.0ms	10×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.1b	(sin (expm1 a))
40.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`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

4 → 39

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(expm1 (sin (expm1 a)))
4.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series219.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
116.0ms	(expm1 (sin (expm1 a)))
89.0ms	(sin (expm1 a))
10.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.9s

Counts

51 → 51

Iterations

Useful iterations: 3 (317.0ms)

Iter	Nodes	Cost
0	70	438
1	115	422
2	304	375
3	1200	374
done	5000	374

prune374.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(sin (expm1 a))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
40.2b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod`
1×	`rem-log-exp` `sin-diff` `rem-exp-log` `expm1-udef`

Counts

4 → 49

Calls

4 calls:

5.0ms	(sin (expm1 a))
4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
6.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series188.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(sin (expm1 a))
60.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
5.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
7.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify6.5s

Counts

61 → 61

Iterations

Useful iterations: 3 (172.0ms)

Iter	Nodes	Cost
0	77	658
1	116	590
2	236	529
3	772	528
4	4921	528
done	5000	528

prune360.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 33.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.4b	(cbrt (sin (expm1 a)))
0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
40.2b	(fmod (log (exp (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)))) a)

rewrite54.0ms

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:

3.0ms	(cbrt (sin (expm1 a)))
3.0ms	(cbrt (sin (expm1 a)))
43.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(fmod (log (exp (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)))) a)

series623.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt (sin (expm1 a)))
208.0ms	(cbrt (sin (expm1 a)))
209.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
7.0ms	(fmod (log (exp (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)))) a)

simplify914.0ms

Counts

89 → 89

Iterations

Useful iterations: done (910.0ms)

Iter	Nodes	Cost
0	99	1103
1	205	979
2	750	738
done	5001	690

prune694.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 32.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a)))))
0.6b	(* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1)))
0.6b	(pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))
40.1b	(fmod (log (exp (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)))) a)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-prod`
45×	`add-sqr-sqrt`
27×	`unpow-prod-down`
23×	`associate-r`
20×	`add-exp-log` `*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`unswap-sqr`
11×	`pow1`
10×	`associate-l` `prod-exp`
7×	`add-cbrt-cube`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `pow-prod-up` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp`
2×	`unpow-prod-up` `pow-pow` `*-commutative`
1×	`pow-plus` `pow1/3` `pow-prod-down` `distribute-lft-out`

Counts

4 → 119

Calls

4 calls:

75.0ms	(* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a)))))
36.0ms	(* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1)))
10.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))
0.0ms	(fmod (log (exp (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)))) a)

series796.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a)))))
277.0ms	(* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1)))
253.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))
9.0ms	(fmod (log (exp (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)))) a)

simplify2.4s

Counts

131 → 131

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	201	2841
1	522	2388
2	2441	1798
done	5002	1566

prune926.0ms

Pruning

38 alts after pruning (37 fresh and 1 done)

Merged error: 32.5b

regimes1.2s

Accuracy

0% (2.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	23
1	18	23
done	18	23

end0.0ms

sample21.9s

Algorithm

intervals

Results

11.7s	2718×	body	10240	exit
6.6s	2262×	body	1280	valid
1.9s	1656×	body	640	valid
626.0ms	2809×	body	80	valid
528.0ms	862×	body	320	valid
150.0ms	410×	body	160	valid
5.0ms	1×	body	5120	valid