Details

sample1.0s

Algorithm

intervals

Results

515.0ms	96×	body	10240	exit
235.0ms	74×	body	1280	valid
128.0ms	47×	body	640	valid
29.0ms	97×	body	80	valid
25.0ms	22×	body	320	valid
10.0ms	1×	body	5120	valid
9.0ms	15×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize33.0ms

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))
36.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(expm1 (sin (expm1 a)))
3.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series118.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(expm1 (sin (expm1 a)))
95.0ms	(sin (expm1 a))
17.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.2s

Counts

44 → 44

Iterations

Iter	Nodes
done	2008
9	2008
8	1654
7	641
6	292
5	157
4	88
3	59
2	48
1	43
0	39

prune316.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 30.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.6b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16`
3×	`log-prod`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 44

Calls

4 calls:

2.0ms	(sin (expm1 a))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series130.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sin (expm1 a))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
32.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.4s

Counts

56 → 56

Iterations

Iter	Nodes
done	2002
8	2002
7	1211
6	530
5	268
4	155
3	111
2	89
1	71
0	55

prune401.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 30.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
36.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

5.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
7.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series108.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sin (expm1 a))
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.3s

Counts

44 → 44

Iterations

Iter	Nodes
done	2003
9	2003
8	841
7	342
6	174
5	81
4	50
3	35
2	28
1	25
0	23

prune505.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.1b

localize131.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
36.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.6b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite27.0ms

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` `insert-posit16` `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 → 65

Calls

4 calls:

24.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series306.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify1.6s

Counts

77 → 77

Iterations

Iter	Nodes
done	2002
5	2002
4	1482
3	538
2	263
1	125
0	71

prune670.0ms

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 30.0b

regimes633.0ms

Accuracy

0% (2.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	20

end0.0ms

sample26.1s

Algorithm

intervals

Results

13.0s	2581×	body	10240	exit
7.2s	2336×	body	1280	valid
2.6s	1596×	body	640	valid
1.5s	801×	body	320	valid
1.2s	2848×	body	80	valid
220.0ms	412×	body	160	valid
34.0ms	4×	body	5120	valid
12.0ms	3×	body	2560	valid