Details

sample904.0ms

Algorithm

intervals

Results

402.0ms	89×	body	10240	exit
202.0ms	61×	body	1280	valid
117.0ms	59×	body	640	valid
27.0ms	31×	body	320	valid
24.0ms	91×	body	80	valid
7.0ms	14×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
1	8
0	8

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize48.0ms

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)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

5.0ms	(sin (expm1 a))
0.0ms	(expm1 a)
1.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series537.0ms

Counts

4 → 12

Calls

4 calls:

517.0ms	(sin (expm1 a))
2.0ms	(expm1 a)
3.0ms	(expm1 (sin (expm1 a)))
15.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.2s

Counts

40 → 40

Iterations

Iter	Nodes
9	6083
8	1872
7	702
6	314
5	161
4	84
3	55
2	44
1	39
0	35

prune557.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 32.4b

localize66.0ms

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)

rewrite9.0ms

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×	`add-cbrt-cube` `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 → 61

Calls

4 calls:

7.0ms	(* (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)

series210.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (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)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify6.3s

Counts

73 → 73

Iterations

Iter	Nodes
5	6674
4	1056
3	383
2	200
1	101
0	53

prune966.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 32.4b

localize89.0ms

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)

rewrite14.0ms

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×	`add-cbrt-cube` `add-exp-log` `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 → 42

Calls

4 calls:

12.0ms	(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)

series203.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(exp (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))))
3.0ms	(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)

simplify1.7s

Counts

54 → 54

Iterations

Iter	Nodes
6	3393
5	1052
4	441
3	204
2	122
1	70
0	46

prune974.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.4b

localize68.0ms

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)

rewrite15.0ms

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×	`add-cbrt-cube` `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 → 49

Calls

4 calls:

12.0ms	(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)

series449.0ms

Counts

4 → 12

Calls

4 calls:

439.0ms	(pow E (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (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)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.1s

Counts

61 → 61

Iterations

Iter	Nodes
4	2408
3	708
2	270
1	130
0	59

prune911.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 32.4b

regimes444.0ms

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

sample25.3s

Algorithm

intervals

Results

13.3s	2652×	body	10240	exit
7.1s	2210×	body	1280	valid
2.8s	1633×	body	640	valid
806.0ms	2912×	body	80	valid
670.0ms	820×	body	320	valid
256.0ms	421×	body	160	valid
20.0ms	2×	body	5120	valid
9.0ms	2×	body	2560	valid