Details

sample832.0ms

Algorithm

intervals

Results

455.0ms	90×	body	10240	exit
184.0ms	62×	body	1280	valid
68.0ms	67×	body	640	valid
16.0ms	86×	body	80	valid
14.0ms	25×	body	320	valid
5.0ms	16×	body	160	valid

simplify27.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize37.0ms

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)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
51.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series134.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(expm1 (sin (expm1 a)))
109.0ms	(sin (expm1 a))
21.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify978.0ms

Counts: 30 → 30

prune235.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 33.4b

localize22.0ms

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)

rewrite51.0ms

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)))
41.0ms	(* (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)

series829.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt (sin (expm1 a)))
266.0ms	(cbrt (sin (expm1 a)))
299.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
7.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify880.0ms

Counts: 81 → 81

prune658.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 32.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.7b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
39.2b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
33×	`cbrt-prod`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
13×	`pow1/3`
12×	`swap-sqr` `associate-r` `associate-l`
8×	`add-exp-log` `unswap-sqr`
4×	`pow-prod-down` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `add-log-exp`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 96

Calls

4 calls:

31.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
17.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
15.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

series836.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
280.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
255.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
9.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

simplify1.1s

Counts: 108 → 108

prune908.0ms

Pruning

41 alts after pruning (40 fresh and 1 done)

Merged error: 32.2b

localize74.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
39.2b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)
39.2b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)
39.2b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

rewrite15.0ms

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`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 30

Calls

4 calls:

14.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

series301.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
16.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)
8.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)
8.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

simplify913.0ms

Counts: 42 → 42

prune322.0ms

Pruning

47 alts after pruning (46 fresh and 1 done)

Merged error: 32.0b

regimes1.5s

Accuracy

0% (2.2b remaining)

Error of 33.5b against oracle of 31.3b and baseline of 33.5b

bsearch0.0ms

simplify2.2s

end0.0ms

sample21.9s

Algorithm

intervals

Results

12.0s	2518×	body	10240	exit
6.0s	2220×	body	1280	valid
2.0s	1694×	body	640	valid
622.0ms	2815×	body	80	valid
587.0ms	846×	body	320	valid
152.0ms	422×	body	160	valid
23.0ms	3×	body	5120	valid