Details

sample836.0ms

Algorithm

intervals

Results

442.0ms	90×	body	10240	exit
183.0ms	62×	body	1280	valid
83.0ms	67×	body	640	valid
23.0ms	86×	body	80	valid
15.0ms	25×	body	320	valid
6.0ms	16×	body	160	valid

simplify11.0ms

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: 34.2b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
39.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`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

3 → 30

Calls

3 calls:

1.0ms	(expm1 (sin (expm1 a)))
8.0ms	(sin (expm1 a))
49.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series237.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(expm1 (sin (expm1 a)))
90.0ms	(sin (expm1 a))
17.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.4s

Counts

39 → 39

Iterations

Useful iterations: 3 (151.0ms)

Iter	Nodes	Cost
0	61	321
1	100	305
2	190	272
3	403	271
4	936	271
5	2429	271
done	5001	271

prune214.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 33.4b

localize29.0ms

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))))
39.2b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite23.0ms

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×	`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 → 77

Calls

4 calls:

2.0ms	(cbrt (sin (expm1 a)))
2.0ms	(cbrt (sin (expm1 a)))
16.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series643.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(cbrt (sin (expm1 a)))
236.0ms	(cbrt (sin (expm1 a)))
195.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
16.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify2.8s

Counts

89 → 89

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	97	1079
1	181	979
2	450	738
3	1338	682
done	5001	676

prune583.0ms

Pruning

29 alts after pruning (27 fresh and 2 done)

Merged error: 32.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.6b	(* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a)))))
0.7b	(pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1))
39.3b	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
43×	`add-sqr-sqrt`
27×	`unpow-prod-down`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`unswap-sqr`
14×	`associate-l`
10×	`add-exp-log`
9×	`associate-r`
6×	`pow1`
5×	`add-cbrt-cube` `sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp`
2×	`unpow-prod-up` `pow-to-exp` `pow-pow` `pow1/3` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 104

Calls

4 calls:

3.0ms	(cbrt (sin (expm1 a)))
76.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a)))))
9.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1))
0.0ms	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series734.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(cbrt (sin (expm1 a)))
270.0ms	(* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a)))))
234.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1))
9.0ms	(fmod (atan2 (expm1 (* (* (pow (cbrt (cbrt (sin (expm1 a)))) (+ 4 1)) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify2.7s

Counts

116 → 116

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	172	2130
1	388	1541
2	968	1456
3	2961	1299
done	5001	1289

prune1.1s

Pruning

40 alts after pruning (39 fresh and 1 done)

Merged error: 32.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
0.8b	(cbrt (cbrt (cbrt (sin (expm1 a)))))
0.8b	(cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2))
39.3b	(fmod (atan2 (expm1 (* (* (* (cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2)) (pow (cbrt (cbrt (sin (expm1 a)))) 5)) (cbrt (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

50×	`cbrt-prod`
18×	`unpow-prod-down`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`pow-pow` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `unpow2`

Counts

4 → 78

Calls

4 calls:

11.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
5.0ms	(cbrt (cbrt (cbrt (sin (expm1 a)))))
9.0ms	(cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2))
1.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2)) (pow (cbrt (cbrt (sin (expm1 a)))) 5)) (cbrt (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series751.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(pow (cbrt (cbrt (sin (expm1 a)))) 5)
231.0ms	(cbrt (cbrt (cbrt (sin (expm1 a)))))
231.0ms	(cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2))
7.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (pow (cbrt (cbrt (sin (expm1 a)))) 2)) (pow (cbrt (cbrt (sin (expm1 a)))) 5)) (cbrt (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify1.4s

Counts

90 → 90

Iterations

Useful iterations: 3 (579.0ms)

Iter	Nodes	Cost
0	177	1438
1	346	1323
2	664	1221
3	1514	1212
done	5001	1212

prune608.0ms

Pruning

48 alts after pruning (48 fresh and 0 done)

Merged error: 31.7b

regimes983.0ms

Accuracy

0% (2.4b remaining)

Error of 33.5b against oracle of 31.1b and baseline of 33.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	108
1	26	108
done	26	108

end0.0ms

sample22.0s

Algorithm

intervals

Results

10.8s	2518×	body	10240	exit
7.4s	2220×	body	1280	valid
2.1s	1694×	body	640	valid
532.0ms	2815×	body	80	valid
513.0ms	846×	body	320	valid
152.0ms	422×	body	160	valid
21.0ms	3×	body	5120	valid