Details

sample1.2s

Algorithm

intervals

Results

432.0ms	89×	body	10240	exit
170.0ms	61×	body	1280	valid
131.0ms	59×	body	640	valid
24.0ms	31×	body	320	valid
22.0ms	91×	body	80	valid
6.0ms	14×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
1	8
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 a)
0.0b	(expm1 (sin (expm1 a)))
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

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

series223.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sin (expm1 a))
20.0ms	(expm1 a)
125.0ms	(expm1 (sin (expm1 a)))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

Counts

53 → 53

Iterations

Iter	Nodes
5	3749
4	1419
3	549
2	241
1	125
0	74

prune692.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

12.0ms	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (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)

series202.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.4s

Counts

81 → 81

Iterations

Iter	Nodes
5	5031
4	1092
3	403
2	222
1	104
0	57

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 32.4b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))))
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `exp-prod`
9×	`log-pow`
6×	`pow1/3`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `log-prod` `pow-plus` `exp-sum` `rem-exp-log`

Counts

4 → 50

Calls

4 calls:

13.0ms	(exp (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (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)

series194.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(exp (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))))
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.8s

Counts

62 → 62

Iterations

Iter	Nodes
6	3322
5	997
4	450
3	217
2	127
1	74
0	50

prune998.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.4b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow E (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))))
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1`
12×	`pow-unpow`
9×	`log-pow`
6×	`add-sqr-sqrt` `*-un-lft-identity` `pow1/3` `add-cube-cbrt`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down`
2×	`pow-prod-down` `pow-exp` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-to-exp` `unpow-prod-up` `e-exp-1` `log-prod` `pow-pow` `pow-plus` `sqr-pow`

Counts

4 → 57

Calls

4 calls:

7.0ms	(pow E (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (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)

series556.0ms

Counts

4 → 12

Calls

4 calls:

549.0ms	(pow E (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.6s

Counts

69 → 69

Iterations

Iter	Nodes
4	2457
3	771
2	274
1	134
0	63

prune1.1s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 32.4b

regimes406.0ms

Accuracy

0% (0.8b remaining)

Error of 32.8b against oracle of 32.0b and baseline of 32.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	15
1	15
0	14

end0.0ms

sample25.5s

Algorithm

intervals

Results

13.3s	2652×	body	10240	exit
6.8s	2210×	body	1280	valid
3.4s	1633×	body	640	valid
863.0ms	2912×	body	80	valid
722.0ms	820×	body	320	valid
221.0ms	421×	body	160	valid
15.0ms	2×	body	5120	valid
9.0ms	2×	body	2560	valid