Details

sample236.0ms

Algorithm

intervals

Results

86.0ms	328×	body	80	nan
57.0ms	80×	body	10240	exit
24.0ms	256×	body	80	valid

simplify3.8s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite47.0ms

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:

21.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
15.0ms	(pow (sqrt (atan2 b b)) (- b a))
7.0ms	(sqrt (atan2 b b))

series178.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
63.0ms	(pow (sqrt (atan2 b b)) (- b a))
33.0ms	(sqrt (atan2 b b))

simplify2.8s

Counts

57 → 57

Iterations

Useful iterations: 3 (259.0ms)

Iter	Nodes	Cost
0	75	614
1	147	571
2	337	536
3	836	527
4	2732	527
done	5001	527

prune237.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
20×	`add-sqr-sqrt`
18×	`unpow-prod-down` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`add-exp-log` `pow1/2`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

17.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
11.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series170.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
60.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
22.0ms	(sqrt (atan2 b b))
30.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

104 → 104

Iterations

Useful iterations: 3 (283.0ms)

Iter	Nodes	Cost
0	80	1180
1	160	1056
2	351	1032
3	896	1018
4	2657	1018
done	5000	1018

prune465.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))
0.2b	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

15.0ms	(exp (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))
45.0ms	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
7.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series224.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(exp (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))
161.0ms	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
12.0ms	(sqrt (atan2 b b))
15.0ms	(sqrt (atan2 b b))

simplify1.6s

Counts

83 → 83

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	90	898
1	182	825
2	506	735
3	1465	735
done	5000	735

prune369.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- b a))
0.5b	(cbrt (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`cbrt-prod`
8×	`add-cube-cbrt`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

5.0ms	(cbrt (- b a))
4.0ms	(cbrt (- b a))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series475.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(cbrt (- b a))
240.0ms	(cbrt (- b a))
13.0ms	(sqrt (atan2 b b))
14.0ms	(sqrt (atan2 b b))

simplify4.5s

Counts

68 → 68

Iterations

Useful iterations: 5 (2.2s)

Iter	Nodes	Cost
0	85	564
1	164	528
2	306	508
3	619	484
4	1467	458
5	4549	450
done	5001	450

prune803.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes106.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	33
1	16	33
done	16	33

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.9s	9847×	body	80	nan
1.7s	1870×	body	10240	exit
988.0ms	7993×	body	80	valid
3.0ms	1×	body	5120	valid
2.0ms	1×	body	2560	valid
2.0ms	2×	body	1280	valid
1.0ms	1×	body	640	valid
1.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid