Details

sample984.0ms

Algorithm

intervals

Results

649.0ms	86×	body	10240	exit
175.0ms	79×	body	1280	valid
51.0ms	48×	body	640	valid
12.0ms	90×	body	80	valid
12.0ms	25×	body	320	valid
3.0ms	13×	body	160	valid
2.0ms	1×	body	2560	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: 33.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
38.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
4.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series158.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(expm1 (sin (expm1 a)))
105.0ms	(sin (expm1 a))
51.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.0s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
8	3071
7	934
6	395
5	166
4	66
3	44
2	35
1	31
0	28

prune243.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.5b

localize87.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
38.0b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite25.0ms

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 (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
19.0ms	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series486.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (expm1 (sin (expm1 a))))
152.0ms	(cbrt (expm1 (sin (expm1 a))))
199.0ms	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
7.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify2.0s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	501
1	119
0	62

prune643.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 31.6b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
3.3b	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
38.1b	(fmod (atan2 (* (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`cbrt-prod` `pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1/3`
12×	`exp-prod`
9×	`log-pow`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `pow-prod-down` `pow-sqr` `pow-prod-up` `add-log-exp` `unswap-sqr`
2×	`pow2` `pow-plus`
1×	`log-prod` `exp-sum` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log`

Counts

4 → 79

Calls

4 calls:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
23.0ms	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
23.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
0.0ms	(fmod (atan2 (* (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series515.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (expm1 (sin (expm1 a))))
182.0ms	(* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))
185.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
5.0ms	(fmod (atan2 (* (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify1.5s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	639
1	155
0	84

prune915.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 31.3b

localize155.0ms

Local error

Found 4 expressions with local error:

3.3b	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
3.3b	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
3.3b	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
38.1b	(fmod (atan2 (* (* (* (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

36×	`exp-prod`
28×	`pow1`
27×	`log-pow`
18×	`pow1/3`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-prod-down` `pow-sqr` `pow-prod-up`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow2` `log-prod` `pow-plus` `exp-sum` `rem-exp-log`

Counts

4 → 70

Calls

4 calls:

27.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
31.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
30.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
1.0ms	(fmod (atan2 (* (* (* (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series564.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
205.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
166.0ms	(exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
6.0ms	(fmod (atan2 (* (* (* (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (exp (log (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify10.4s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
4	2370
3	604
2	197
1	85
0	52

prune635.0ms

Pruning

41 alts after pruning (40 fresh and 1 done)

Merged error: 31.0b

regimes1.5s

Accuracy

0% (2.4b remaining)

Error of 34.1b against oracle of 31.8b and baseline of 34.1b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample21.6s

Algorithm

intervals

Results

10.5s	2633×	body	10240	exit
7.4s	2305×	body	1280	valid
2.2s	1690×	body	640	valid
516.0ms	2708×	body	80	valid
507.0ms	855×	body	320	valid
157.0ms	439×	body	160	valid
7.0ms	3×	body	2560	valid