Details

sample727.0ms

Algorithm

intervals

Results

329.0ms	92×	body	10240	exit
240.0ms	77×	body	1280	valid
55.0ms	58×	body	640	valid
14.0ms	79×	body	80	valid
13.0ms	27×	body	320	valid
11.0ms	15×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 a)
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
40.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite6.0ms

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

series28.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(expm1 a)
5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
18.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.8s

Counts

40 → 40

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	35	326
1	39	326
2	44	282
3	55	282
4	84	282
5	217	282
6	519	282
7	1209	282
8	4017	282
done	5001	282

prune321.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
40.6b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite15.0ms

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)))
4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
8.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series60.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(expm1 (sin (expm1 a)))
46.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
5.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
6.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.1s

Counts

52 → 52

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	51	575
1	67	520
2	99	457
3	149	457
4	255	457
5	534	457
6	1471	457
done	5001	457

prune344.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 33.5b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))))
0.7b	(* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
40.6b	(fmod (log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

52×	`sqrt-pow1`
39×	`exp-prod`
37×	`add-sqr-sqrt`
35×	`pow1`
25×	`add-cube-cbrt` `*-un-lft-identity`
23×	`log-pow`
18×	`sqrt-prod`
16×	`pow1/2` `pow-prod-up`
12×	`pow-prod-down` `pow-sqr`
9×	`add-exp-log`
8×	`swap-sqr`
6×	`associate-r` `associate-l` `add-cbrt-cube`
5×	`add-log-exp`
4×	`unswap-sqr`
2×	`pow2` `pow-plus` `rem-log-exp` `prod-exp`
1×	`log-prod` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `rem-exp-log`

Counts

4 → 109

Calls

4 calls:

4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
46.0ms	(log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))))
26.0ms	(* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
0.0ms	(fmod (log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series130.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
6.0ms	(log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))))
64.0ms	(* (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)

simplify1.2s

Counts

121 → 121

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	99	2267
1	187	1423
2	721	1206
done	5000	1185

prune686.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 33.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
40.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
1.0ms	(fmod (atan2 (expm1 (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)

series173.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.1s

Counts

44 → 44

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	26	591
1	38	587
2	85	473
3	228	470
4	1222	470
done	5000	470

prune259.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 33.4b

regimes606.0ms

Accuracy

0% (1.5b remaining)

Error of 33.7b against oracle of 32.1b and baseline of 33.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	23
done	12	23

end0.0ms

sample22.4s

Algorithm

intervals

Results

12.1s	2598×	body	10240	exit
6.3s	2318×	body	1280	valid
2.1s	1655×	body	640	valid
567.0ms	834×	body	320	valid
547.0ms	2773×	body	80	valid
194.0ms	414×	body	160	valid
20.0ms	2×	body	5120	valid
11.0ms	4×	body	2560	valid