Details

sample362.0ms

Algorithm

intervals

Results

171.0ms	52×	body	10240	exit
36.0ms	316×	body	80	nan
32.0ms	255×	body	80	valid
3.0ms	1×	body	5120	valid

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	115	9
5	268	9
6	834	9
7	3197	9
done	5001	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 48

Calls

3 calls:

15.0ms	(pow (sqrt (atan2 b b)) (- b a))
20.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(sqrt (atan2 b b))

series156.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(pow (sqrt (atan2 b b)) (- b a))
93.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(sqrt (atan2 b b))

simplify3.1s

Counts

57 → 57

Iterations

Useful iterations: 3 (284.0ms)

Iter	Nodes	Cost
0	75	614
1	147	571
2	337	536
3	843	527
4	2738	527
done	5000	527

prune210.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (* (- b a) 1/2))
0.2b	(sin (pow (atan2 b b) (* (- b a) 1/2)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
2×	`add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 22

Calls

2 calls:

8.0ms	(pow (atan2 b b) (* (- b a) 1/2))
21.0ms	(sin (pow (atan2 b b) (* (- b a) 1/2)))

series133.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(pow (atan2 b b) (* (- b a) 1/2))
98.0ms	(sin (pow (atan2 b b) (* (- b a) 1/2)))

simplify3.7s

Counts

28 → 28

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	56	418
1	123	398
2	313	360
3	877	318
4	3082	317
done	5000	315

prune110.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(* (cos 1) (log (sqrt (atan2 b b))))
2.0b	(log (sqrt (atan2 b b)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`log-prod`
16×	`pow1` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`add-exp-log` `sqrt-prod`
11×	`associate-r` `add-cbrt-cube`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`log-pow`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`sub-neg` `associate-r/` `-commutative`
1×	`rem-sqrt-square` `flip3--` `rem-log-exp` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

65.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0ms	(sqrt (atan2 b b))
13.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
2.0ms	(log (sqrt (atan2 b b)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
12.0ms	(sqrt (atan2 b b))
210.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
128.0ms	(log (sqrt (atan2 b b)))

simplify2.6s

Counts

101 → 101

Iterations

Useful iterations: 2 (195.0ms)

Iter	Nodes	Cost
0	119	1237
1	240	1183
2	842	1012
3	3049	1012
done	5000	1012

prune294.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
2.0b	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

66×	`sqrt-pow1`
56×	`pow1`
44×	`log-pow`
34×	`pow1/2`
25×	`associate-r`
18×	`pow-prod-up`
12×	`add-sqr-sqrt`
11×	`pow-prod-down`
10×	`pow-sqr`
9×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod` `add-cbrt-cube`
4×	`add-log-exp`
3×	`log-prod` `associate-l`
2×	`pow2` `rem-sqrt-square` `pow-plus` `rem-log-exp` `prod-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

82.0ms	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
2.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))
36.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
15.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))
83.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

simplify2.6s

Counts

112 → 112

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	93	1083
1	173	699
2	481	647
3	2510	647
done	5002	647

prune422.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes47.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10
done	9	10

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.6s	1799×	body	10240	exit
1.2s	9789×	body	80	nan
1.1s	7992×	body	80	valid
7.0ms	2×	body	5120	valid
4.0ms	2×	body	2560	valid
1.0ms	4×	body	160	valid