Details

sample121.0ms

Algorithm

intervals

Results

37.0ms	256×	body	80	valid
36.0ms	58×	body	10240	exit
22.0ms	327×	body	80	nan

simplify3.8s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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))

rewrite39.0ms

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:

20.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
15.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series149.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
42.0ms	(pow (sqrt (atan2 b b)) (- b a))
21.0ms	(sqrt (atan2 b b))

simplify2.4s

Counts

57 → 57

Iterations

Useful iterations: 3 (323.0ms)

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

prune247.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite89.0ms

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:

20.0ms	(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)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series129.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
43.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
20.0ms	(sqrt (atan2 b b))
14.0ms	(sqrt (atan2 b b))

simplify3.6s

Counts

174 → 174

Iterations

Useful iterations: done (3.6s)

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

prune521.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))

rewrite68.0ms

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)))))
13.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
2.0ms	(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)))))
48.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
22.0ms	(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

prune144.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (log (sqrt (atan2 b b))) (- b a)))
0.2b	(* (log (sqrt (atan2 b b))) (- b a))
1.0b	(sqrt (atan2 b b))
2.0b	(log (sqrt (atan2 b b)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

7.0ms	(exp (* (log (sqrt (atan2 b b))) (- b a)))
23.0ms	(* (log (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
2.0ms	(log (sqrt (atan2 b b)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (* (log (sqrt (atan2 b b))) (- b a)))
69.0ms	(* (log (sqrt (atan2 b b))) (- b a))
11.0ms	(sqrt (atan2 b b))
70.0ms	(log (sqrt (atan2 b b)))

simplify921.0ms

Counts

85 → 85

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	92	881
1	174	794
2	509	720
3	1836	720
done	5002	720

prune208.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

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

sample3.8s

Algorithm

intervals

Results

1.5s	9788×	body	80	nan
1.0s	1777×	body	10240	exit
719.0ms	7988×	body	80	valid
42.0ms	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

sample121.0ms

simplify3.8s

prune5.0ms

localize20.0ms

rewrite39.0ms

series149.0ms

simplify2.4s

prune247.0ms

localize13.0ms

rewrite89.0ms

series129.0ms

simplify3.6s

prune521.0ms

localize31.0ms

rewrite68.0ms

series8.5m

simplify1.1s

prune144.0ms

localize15.0ms

rewrite35.0ms

series172.0ms

simplify921.0ms

prune208.0ms

regimes38.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.8s

end1.2m