Details

sample1.1s

Algorithm

intervals

Results

642.0ms	84×	body	10240	exit
218.0ms	70×	body	1280	valid
84.0ms	58×	body	640	valid
20.0ms	29×	body	320	valid
16.0ms	79×	body	80	valid
9.0ms	20×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 29

Calls

3 calls:

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

series210.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
161.0ms	(expm1 (sin (expm1 a)))
45.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
4	2832
3	619
2	191
1	77
0	49

prune378.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 34.3b

localize51.0ms

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))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
40.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
4.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series209.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(expm1 (sin (expm1 a)))
5.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
41.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
5.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify3.0s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
4	3028
3	706
2	250
1	112
0	73

prune507.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 34.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
40.7b	(fmod (log (pow (pow (exp (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)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

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

series546.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
173.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
166.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
15.0ms	(fmod (log (pow (pow (exp (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)

simplify4.4s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
4	3807
3	582
2	192
1	75
0	41

prune561.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 33.8b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

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

series171.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
7.0ms	(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)

simplify1.3s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
4	1143
3	237
2	91
1	42
0	30

prune314.0ms

Pruning

20 alts after pruning (17 fresh and 3 done)

Merged error: 33.8b

regimes593.0ms

Accuracy

0% (1.7b remaining)

Error of 33.7b against oracle of 32.0b and baseline of 33.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
0	10

end0.0ms

sample21.9s

Algorithm

intervals

Results

11.4s	2619×	body	10240	exit
6.6s	2307×	body	1280	valid
2.1s	1666×	body	640	valid
614.0ms	2774×	body	80	valid
482.0ms	823×	body	320	valid
220.0ms	426×	body	160	valid
16.0ms	2×	body	5120	valid
7.0ms	2×	body	2560	valid