Details

sample843.0ms

Algorithm

intervals

Results

458.0ms	94×	body	10240	exit
197.0ms	74×	body	1280	valid
65.0ms	51×	body	640	valid
18.0ms	96×	body	80	valid
16.0ms	27×	body	320	valid
3.0ms	8×	body	160	valid

simplify10.0ms

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

localize79.0ms

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)

rewrite18.0ms

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:

1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
9.0ms	(sin (expm1 a))
3.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series280.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
95.0ms	(sin (expm1 a))
166.0ms	(expm1 (sin (expm1 a)))
16.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.7s

Counts

51 → 51

Iterations

Useful iterations: 3 (163.0ms)

Iter	Nodes	Cost
0	70	438
1	110	422
2	202	375
3	414	374
4	944	374
5	2449	374
done	5000	374

prune341.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 30.9b

localize24.0ms

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)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

series547.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
186.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
172.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms	(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)

simplify1.6s

Counts

60 → 60

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	34	945
1	43	933
2	72	645
3	124	606
4	339	606
5	1425	606
done	5000	606

prune332.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 30.8b

localize23.0ms

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)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

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

series213.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(expm1 (sin (expm1 a)))
3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
59.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
6.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify4.7s

Counts

62 → 62

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	73	666
1	106	592
2	179	528
3	332	528
4	625	528
5	1367	528
6	3992	528
done	5000	528

prune312.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 30.7b

localize38.0ms

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)

rewrite50.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
2×	`rem-exp-log`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
35.0ms	(* (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)

series183.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
72.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
43.0ms	(* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
6.0ms	(fmod (log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify2.8s

Counts

107 → 107

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	91	1983
1	143	1272
2	292	1101
3	590	1062
4	1367	1011
done	5000	1002

prune418.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 30.7b

regimes313.0ms

Accuracy

0% (1.6b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample22.3s

Algorithm

intervals

Results

11.2s	2607×	body	10240	exit
6.2s	2279×	body	1280	valid
2.1s	1640×	body	640	valid
1.4s	2844×	body	80	valid
781.0ms	828×	body	320	valid
149.0ms	402×	body	160	valid
20.0ms	4×	body	5120	valid
10.0ms	3×	body	2560	valid