Details

sample808.0ms

Algorithm

intervals

Results

435.0ms	94×	body	10240	exit
194.0ms	74×	body	1280	valid
58.0ms	51×	body	640	valid
18.0ms	96×	body	80	valid
15.0ms	27×	body	320	valid
2.0ms	8×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize74.0ms

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
9.0ms	(sin (expm1 a))
0.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series120.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
95.0ms	(sin (expm1 a))
4.0ms	(expm1 (sin (expm1 a)))
19.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.6s

Counts

40 → 40

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	35	339
1	39	339
2	44	293
3	55	293
4	70	293
5	101	293
6	176	293
7	436	293
8	1564	293
done	5001	293

prune281.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 30.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.4b	(fmod (* (* (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)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (* (* (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)

series571.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
185.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
203.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(fmod (* (* (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)

simplify1.9s

Counts

52 → 52

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	30	833
1	39	821
2	68	565
3	129	532
4	343	532
5	1385	532
done	5000	532

prune317.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 30.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.4b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite6.0ms

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` `log-pow` `add-cbrt-cube`
3×	`log-prod`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 40

Calls

4 calls:

0.0ms	(expm1 (sin (expm1 a)))
3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series69.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(expm1 (sin (expm1 a)))
5.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
57.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.9s

Counts

52 → 52

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	51	575
1	63	520
2	80	457
3	104	457
4	151	457
5	277	457
6	600	457
7	1813	457
done	5000	455

prune228.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 30.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
37.4b	(fmod (log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`sqrt-pow1`
24×	`exp-prod`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1`
18×	`sqrt-prod`
8×	`pow1/2` `swap-sqr` `pow-prod-up`
6×	`add-exp-log` `associate-r` `associate-l` `pow-prod-down` `pow-sqr` `add-cbrt-cube` `add-log-exp`
4×	`unswap-sqr`
2×	`rem-exp-log`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
60.0ms	(* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
1.0ms	(fmod (log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series205.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
71.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
63.0ms	(* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
7.0ms	(fmod (log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify2.1s

Counts

99 → 99

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	85	1861
1	136	1198
2	279	1027
3	565	988
4	1299	937
done	5001	928

prune342.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 30.7b

regimes301.0ms

Accuracy

0% (1.6b remaining)

Error of 33.3b against oracle of 31.7b and baseline of 33.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	12	29
done	12	29

end0.0ms

sample22.8s

Algorithm

intervals

Results

11.2s	2607×	body	10240	exit
7.2s	2279×	body	1280	valid
2.3s	1640×	body	640	valid
837.0ms	828×	body	320	valid
603.0ms	2844×	body	80	valid
146.0ms	402×	body	160	valid
26.0ms	4×	body	5120	valid
9.0ms	3×	body	2560	valid