Details

sample1.1s

Algorithm

intervals

Results

636.0ms	96×	body	10240	exit
233.0ms	75×	body	1280	valid
94.0ms	44×	body	640	valid
54.0ms	102×	body	80	valid
14.0ms	23×	body	320	valid
5.0ms	12×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite57.0ms

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))
1.0ms	(expm1 (sin (expm1 a)))
6.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series130.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(expm1 (sin (expm1 a)))
104.0ms	(sin (expm1 a))
21.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.4s

Counts

40 → 40

Iterations

Useful iterations: 2 (30.0ms)

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	436	293
8	1564	293
done	5001	293

prune275.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 29.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.4b	(cbrt (sin (expm1 a)))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
35.5b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
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 → 69

Calls

4 calls:

3.0ms	(cbrt (sin (expm1 a)))
3.0ms	(cbrt (sin (expm1 a)))
34.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series779.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(cbrt (sin (expm1 a)))
254.0ms	(cbrt (sin (expm1 a)))
273.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
6.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify5.3s

Counts

81 → 81

Iterations

Useful iterations: done (5.3s)

Iter	Nodes	Cost
0	63	945
1	99	864
2	272	648
3	957	601
4	4373	592
done	5000	576

prune423.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 29.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.6b	(* (pow (cbrt (cbrt (sin (expm1 a)))) 2) (cbrt (cbrt (sin (expm1 a)))))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
35.5b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (pow (cbrt (cbrt (sin (expm1 a)))) 2) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
58×	`add-sqr-sqrt`
22×	`unswap-sqr`
20×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
18×	`unpow-prod-down`
15×	`associate-r`
12×	`pow1`
11×	`add-exp-log`
7×	`pow1/3`
6×	`swap-sqr`
5×	`add-cbrt-cube` `unpow2`
4×	`prod-exp` `add-log-exp` `sqr-pow`
3×	`pow-prod-up`
2×	`pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `cbrt-unprod`
1×	`pow2` `pow-to-exp` `pow3` `pow-exp`

Counts

4 → 114

Calls

4 calls:

3.0ms	(cbrt (sin (expm1 a)))
38.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) 2) (cbrt (cbrt (sin (expm1 a)))))
20.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (pow (cbrt (cbrt (sin (expm1 a)))) 2) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

series660.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(cbrt (sin (expm1 a)))
206.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) 2) (cbrt (cbrt (sin (expm1 a)))))
218.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
7.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (pow (cbrt (cbrt (sin (expm1 a)))) 2) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

simplify2.7s

Counts

126 → 126

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	132	2023
1	249	1650
2	574	1266
3	2803	1180
done	5001	1172

prune644.0ms

Pruning

38 alts after pruning (38 fresh and 0 done)

Merged error: 28.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.4b	(pow (cbrt (cbrt (sin (expm1 a)))) 3)
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
35.5b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) 3))) (atan a)) a)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
12.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 3)
16.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) 3))) (atan a)) a)

series817.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (sin (expm1 a)))
457.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 3)
190.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
4.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) 3))) (atan a)) a)

simplify641.0ms

Counts

106 → 106

Iterations

Useful iterations: done (638.0ms)

Iter	Nodes	Cost
0	103	1356
1	206	1029
2	860	806
done	5001	771

prune311.0ms

Pruning

43 alts after pruning (42 fresh and 1 done)

Merged error: 28.8b

regimes334.0ms

Accuracy

0% (2.1b remaining)

Error of 33.1b against oracle of 31.0b and baseline of 33.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	15	24
done	15	24

end0.0ms

sample14.5s

Algorithm

intervals

Results

7.9s	2558×	body	10240	exit
4.1s	2255×	body	1280	valid
1.4s	1613×	body	640	valid
391.0ms	838×	body	320	valid
361.0ms	2867×	body	80	valid
104.0ms	421×	body	160	valid
14.0ms	3×	body	5120	valid
6.0ms	3×	body	2560	valid