Details

sample942.0ms

Algorithm

intervals

Results

390.0ms	80×	body	10240	exit
211.0ms	68×	body	1280	valid
50.0ms	48×	body	640	valid
19.0ms	95×	body	80	valid
17.0ms	30×	body	320	valid
5.0ms	15×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize24.0ms

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))
36.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

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:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series128.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
89.0ms	(sin (expm1 a))
32.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.2s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
8	4003
7	1217
6	519
5	217
4	84
3	55
2	44
1	39
0	35

prune351.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 31.1b

localize52.0ms

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))))
36.7b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`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 → 69

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
1.0ms	(cbrt (sin (expm1 a)))
19.0ms	(* (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)

series744.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt (sin (expm1 a)))
262.0ms	(cbrt (sin (expm1 a)))
264.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
4.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify1.9s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	499
1	120
0	63

prune762.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 30.6b

localize162.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
36.7b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
36.7b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
36.7b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite15.0ms

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:

12.0ms	(* (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)
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series247.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify5.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
3	3143
2	456
1	116
0	61

prune1.0s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 30.2b

localize155.0ms

Local error

Found 4 expressions with local error:

3.4b	(exp (log (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))))
36.7b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
36.7b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
36.7b	(fmod (atan2 (expm1 (* (exp (log (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite23.0ms

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:

20.0ms	(exp (log (* (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)
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (* (exp (log (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series330.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(exp (log (* (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)
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (* (exp (log (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify7.0s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
4	2242
3	563
2	208
1	100
0	63

prune467.0ms

Pruning

44 alts after pruning (44 fresh and 0 done)

Merged error: 30.0b

regimes1.1s

Accuracy

0% (2.2b remaining)

Error of 33.3b against oracle of 31.2b and baseline of 33.3b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample20.9s

Algorithm

intervals

Results

11.3s	2619×	body	10240	exit
6.0s	2315×	body	1280	valid
1.8s	1623×	body	640	valid
748.0ms	2825×	body	80	valid
429.0ms	810×	body	320	valid
144.0ms	423×	body	160	valid
18.0ms	3×	body	5120	valid
2.0ms	1×	body	2560	valid