Details

sample389.0ms

Algorithm

intervals

Results

217.0ms	88×	body	10240	exit
103.0ms	67×	body	1280	valid
31.0ms	48×	body	640	valid
14.0ms	102×	body	80	valid
9.0ms	27×	body	320	valid
3.0ms	12×	body	160	valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
35.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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

series67.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
61.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.3s

Counts

40 → 40

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	35	339
1	39	339
2	44	293
3	55	293
4	70	293
5	101	293
6	176	293
7	397	293
8	1211	293
9	4879	293
done	5000	293

prune316.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
0.7b	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
35.6b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 58

Calls

4 calls:

1.0ms	(sin (expm1 a))
1.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series99.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sin (expm1 a))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
39.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify1.6s

Counts

70 → 70

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	67	966
1	113	791
2	289	693
3	1675	693
done	5000	693

prune215.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 29.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0b	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
35.5b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
26×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
7×	`add-exp-log` `pow1/3`
6×	`unpow-prod-down` `cube-prod` `swap-sqr` `associate-r` `associate-l`
5×	`add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `pow-prod-down` `pow-sqr` `pow-prod-up` `sqr-pow`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
7.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series219.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
180.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
33.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify1.6s

Counts

103 → 103

Iterations

Useful iterations: 3 (373.0ms)

Iter	Nodes	Cost
0	104	2302
1	182	2021
2	469	1245
3	2147	1014
done	5001	1014

prune379.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 29.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (cbrt (cbrt (sin (expm1 a)))) 4)
0.7b	(cbrt (pow (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) 3)
35.5b	(fmod (cbrt (pow (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
15×	`unpow-prod-down`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `pow-unpow` `cube-prod`
5×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-pow` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `pow1/3` `unpow3` `pow-exp`
1×	`rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 75

Calls

4 calls:

3.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 4)
2.0ms	(cbrt (pow (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) 3))
1.0ms	(pow (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) 3)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series235.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 4)
3.0ms	(cbrt (pow (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) 3))
36.0ms	(pow (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) 3)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify1.7s

Counts

87 → 87

Iterations

Useful iterations: 3 (357.0ms)

Iter	Nodes	Cost
0	116	2890
1	217	2316
2	497	1973
3	2378	1599
done	5000	1599

prune332.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 29.2b

regimes436.0ms

Accuracy

0% (2.0b remaining)

Error of 33.5b against oracle of 31.4b and baseline of 33.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	53
1	24	53
done	24	53

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.5s	2556×	body	10240	exit
3.8s	2256×	body	1280	valid
1.1s	1639×	body	640	valid
283.0ms	839×	body	320	valid
273.0ms	2820×	body	80	valid
92.0ms	440×	body	160	valid
13.0ms	3×	body	5120	valid
6.0ms	3×	body	2560	valid