Details

sample139.0ms

Algorithm

intervals

Results

46.0ms	58×	body	10240	exit
39.0ms	327×	body	80	nan
24.0ms	256×	body	80	valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

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:

10.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
14.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series147.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
38.0ms	(pow (sqrt (atan2 b b)) (- b a))
13.0ms	(sqrt (atan2 b b))

simplify2.5s

Counts

57 → 57

Iterations

Useful iterations: 3 (255.0ms)

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

prune182.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
87×	`unpow-prod-down`
82×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`unswap-sqr`
23×	`swap-sqr`
17×	`add-exp-log`
15×	`associate-r` `associate-l` `sqr-pow`
14×	`unpow-prod-up`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`pow1/2` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 162

Calls

4 calls:

17.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
91.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series118.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
59.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
11.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify3.4s

Counts

174 → 174

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	144	3870
1	292	2885
2	996	2741
3	3713	2692
done	5001	2683

prune563.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (* (pow (sqrt 1) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
9×	`unpow-prod-down`
8×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow-pow` `sqrt-pow1`
4×	`unpow-prod-up` `add-exp-log`
3×	`pow1/2` `add-cbrt-cube` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

3 → 50

Calls

3 calls:

50.0ms	(sin (* (pow (sqrt 1) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
8.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0ms	(sqrt (atan2 b b))

series8.5m

Counts

3 → 9

Calls

3 calls:

8.5m	(sin (* (pow (sqrt 1) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
57.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
13.0ms	(sqrt (atan2 b b))

simplify1.1s

Counts

59 → 59

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	101	925
1	223	835
2	504	716
3	1566	668
done	5001	610

prune149.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (sin (pow (sqrt (atan2 b b)) (- b a)))))
0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.5b	(log (sin (pow (sqrt (atan2 b b)) (- b a))))
1.0b	(sqrt (atan2 b b))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

14.0ms	(exp (log (sin (pow (sqrt (atan2 b b)) (- b a)))))
7.0ms	(pow (sqrt (atan2 b b)) (- b a))
7.0ms	(log (sin (pow (sqrt (atan2 b b)) (- b a))))
1.0ms	(sqrt (atan2 b b))

series190.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(exp (log (sin (pow (sqrt (atan2 b b)) (- b a)))))
22.0ms	(pow (sqrt (atan2 b b)) (- b a))
91.0ms	(log (sin (pow (sqrt (atan2 b b)) (- b a))))
11.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

80 → 80

Iterations

Useful iterations: 4 (943.0ms)

Iter	Nodes	Cost
0	102	985
1	190	905
2	417	827
3	1017	818
4	3191	808
done	5000	808

prune189.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes90.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	14	19
1	18	18
done	18	18

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1777×	body	10240	exit
749.0ms	9788×	body	80	nan
607.0ms	7988×	body	80	valid
14.0ms	4×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	5×	body	160	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid

Details

sample139.0ms

simplify3.4s

prune3.0ms

localize14.0ms

rewrite28.0ms

series147.0ms

simplify2.5s

prune182.0ms

localize14.0ms

rewrite121.0ms

series118.0ms

simplify3.4s

prune563.0ms

localize18.0ms

rewrite61.0ms

series8.5m

simplify1.1s

prune149.0ms

localize13.0ms

rewrite31.0ms

series190.0ms

simplify1.9s

prune189.0ms

regimes90.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.0s

end1.2m