Details

sample203.0ms

Algorithm

intervals

Results

56.0ms	256×	body	80	valid
47.0ms	58×	body	10240	exit
28.0ms	327×	body	80	nan

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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))

rewrite26.0ms

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)))
7.0ms	(pow (sqrt (atan2 b b)) (- b a))
5.0ms	(sqrt (atan2 b b))

series161.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
43.0ms	(pow (sqrt (atan2 b b)) (- b a))
24.0ms	(sqrt (atan2 b b))

simplify2.5s

Counts

57 → 57

Iterations

Useful iterations: 3 (252.0ms)

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

prune193.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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))

rewrite108.0ms

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:

9.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
79.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series160.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
71.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
20.0ms	(sqrt (atan2 b b))
22.0ms	(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

prune493.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (* (pow (sqrt (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))

rewrite64.0ms

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:

53.0ms	(sin (* (pow (sqrt (sqrt 1)) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
7.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0ms	(sqrt (atan2 b b))

series8.7m

Counts

3 → 9

Calls

3 calls:

8.7m	(sin (* (pow (sqrt (sqrt 1)) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
54.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
20.0ms	(sqrt (atan2 b b))

simplify1.2s

Counts

59 → 59

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	101	935
1	223	835
2	504	716
3	1566	668
done	5001	610

prune161.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

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)))

rewrite40.0ms

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)))
28.0ms	(* (log (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
2.0ms	(log (sqrt (atan2 b b)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(exp (* (log (sqrt (atan2 b b))) (- b a)))
72.0ms	(* (log (sqrt (atan2 b b))) (- b a))
11.0ms	(sqrt (atan2 b b))
72.0ms	(log (sqrt (atan2 b b)))

simplify995.0ms

Counts

85 → 85

Iterations

Useful iterations: 2 (65.0ms)

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

prune238.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	15	20
1	19	18
done	19	18

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1777×	body	10240	exit
734.0ms	9788×	body	80	nan
653.0ms	7988×	body	80	valid
12.0ms	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

sample203.0ms

simplify3.8s

prune7.0ms

localize25.0ms

rewrite26.0ms

series161.0ms

simplify2.5s

prune193.0ms

localize15.0ms

rewrite108.0ms

series160.0ms

simplify3.6s

prune493.0ms

localize36.0ms

rewrite64.0ms

series8.7m

simplify1.2s

prune161.0ms

localize17.0ms

rewrite40.0ms

series178.0ms

simplify995.0ms

prune238.0ms

regimes40.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample3.0s

end1.0m