Details

sample1.0s

Algorithm

intervals

Results

457.0ms	88×	body	10240	exit
272.0ms	86×	body	1280	valid
66.0ms	54×	body	640	valid
23.0ms	37×	body	320	valid
12.0ms	64×	body	80	valid
6.0ms	15×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize122.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
44.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite18.0ms

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:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
9.0ms	(sin (expm1 a))
2.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series234.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
162.0ms	(sin (expm1 a))
13.0ms	(expm1 (sin (expm1 a)))
49.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.7s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
8	1725
7	669
6	306
5	162
4	88
3	59
2	48
1	43
0	39

prune725.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 36.5b

localize100.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
1.0b	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-plus` `pow-prod-up`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow2` `swap-sqr` `pow-sqr`
2×	`pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 74

Calls

4 calls:

19.0ms	(* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))
25.0ms	(cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
27.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series360.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))
33.0ms	(cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
210.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
35.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify7.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5002
4	2634
3	1342
2	544
1	164
0	70

prune866.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 36.1b

localize475.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `pow-sqr`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

42.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series198.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
17.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
26.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
18.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify6.2s

Counts

65 → 65

Iterations

Iter	Nodes
done	5004
5	2261
4	971
3	618
2	276
1	104
0	50

prune1.1s

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 35.8b

localize648.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
44.1b	(fmod (cbrt (* (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) a)
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
44.1b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `pow-sqr`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

43.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(fmod (cbrt (* (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) a)
1.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
1.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series328.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
48.0ms	(fmod (cbrt (* (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) a)
35.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify10.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	5002
5	3473
4	1168
3	675
2	297
1	115
0	61

prune872.0ms

Pruning

29 alts after pruning (26 fresh and 3 done)

Merged error: 35.7b

regimes1.3s

Accuracy

0% (2.2b remaining)

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

bsearch0.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample21.8s

Algorithm

intervals

Results

11.0s	2682×	body	10240	exit
7.2s	2304×	body	1280	valid
1.8s	1648×	body	640	valid
656.0ms	2802×	body	80	valid
499.0ms	826×	body	320	valid
238.0ms	416×	body	160	valid
10.0ms	1×	body	5120	valid
9.0ms	3×	body	2560	valid