Details

sample1.4s

Algorithm

intervals

Results

558.0ms	96×	body	10240	exit
283.0ms	74×	body	1280	valid
267.0ms	47×	body	640	valid
109.0ms	97×	body	80	valid
38.0ms	1×	body	5120	valid
24.0ms	22×	body	320	valid
9.0ms	15×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize51.0ms

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)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 43

Calls

4 calls:

1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
7.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series288.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
145.0ms	(expm1 (sin (expm1 a)))
124.0ms	(sin (expm1 a))
16.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.2s

Counts

55 → 55

Iterations

Iter	Nodes
done	2001
5	2001
4	983
3	411
2	204
1	118
0	74

prune446.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 30.6b

localize35.0ms

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)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`log-prod`
1×	`rem-log-exp` `sin-diff` `expm1-udef` `rem-exp-log`

Counts

4 → 53

Calls

4 calls:

2.0ms	(sin (expm1 a))
3.0ms	(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)

series168.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(sin (expm1 a))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
56.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.3s

Counts

65 → 65

Iterations

Iter	Nodes
done	2010
6	2010
5	1105
4	544
3	290
2	171
1	119
0	81

prune486.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 30.3b

localize61.0ms

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)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`sin-diff` `expm1-udef`

Counts

4 → 41

Calls

4 calls:

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

series103.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.3s

Counts

53 → 53

Iterations

Iter	Nodes
done	2001
6	2001
5	1016
4	465
3	217
2	108
1	73
0	46

prune602.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 30.1b

localize71.0ms

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)

rewrite14.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `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 → 73

Calls

4 calls:

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

series261.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (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)

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
4	2000
3	808
2	378
1	174
0	93

prune723.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 29.9b

regimes860.0ms

Accuracy

0% (2.1b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	22
1	22
0	20

end0.0ms

sample25.9s

Algorithm

intervals

Results

12.7s	2581×	body	10240	exit
7.3s	2336×	body	1280	valid
2.5s	1596×	body	640	valid
2.2s	2848×	body	80	valid
616.0ms	801×	body	320	valid
208.0ms	412×	body	160	valid
37.0ms	4×	body	5120	valid
14.0ms	3×	body	2560	valid