Details

sample442.0ms

Algorithm

intervals

Results

242.0ms	98×	body	10240	exit
121.0ms	69×	body	1280	valid
46.0ms	63×	body	640	valid
8.0ms	86×	body	80	valid
8.0ms	24×	body	320	valid
3.0ms	14×	body	160	valid

simplify3.0ms

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: 34.3b

localize18.0ms

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))
39.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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

series65.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(expm1 (sin (expm1 a)))
57.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify118.0ms

Counts

40 → 40

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	248
1	44	212
2	54	212
3	68	212
4	114	212
5	228	212
6	919	212
7	3184	212
8	5001	212
done	5001	212

prune159.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sin (expm1 a))
0.2b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
39.3b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite7.0ms

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:

2.0ms	(sin (expm1 a))
2.0ms	(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)

series93.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sin (expm1 a))
3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
29.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify97.0ms

Counts

52 → 52

Iterations

Useful iterations: 7 (94.0ms)

Iter	Nodes	Cost
0	63	401
1	92	342
2	121	342
3	180	342
4	339	342
5	863	342
6	3913	342
7	5001	338
done	5001	338

prune209.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
39.3b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.3b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.3b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify74.0ms

Counts

44 → 44

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	430
1	60	361
2	78	361
3	118	361
4	218	361
5	534	361
6	2589	361
7	5001	361
done	5001	361

prune276.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 32.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
39.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.3b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.3b	(fmod (log (exp (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` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`exp-prod`
1×	`rem-exp-log`

Counts

4 → 32

Calls

4 calls:

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

series41.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify74.0ms

Counts

44 → 44

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	47	370
1	63	319
2	81	319
3	121	319
4	221	319
5	537	319
6	2592	319
7	5001	319
done	5001	319

prune207.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 32.6b

regimes288.0ms

Accuracy

0% (1.8b remaining)

Error of 33.0b against oracle of 31.2b and baseline of 33.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	37
1	23	37
done	23	37

end0.0ms

sample12.2s

Algorithm

intervals

Results

6.5s	2604×	body	10240	exit
3.7s	2276×	body	1280	valid
1.1s	1624×	body	640	valid
281.0ms	2890×	body	80	valid
260.0ms	814×	body	320	valid
82.0ms	389×	body	160	valid
23.0ms	5×	body	5120	valid
4.0ms	2×	body	2560	valid