Details

sample315.0ms

Algorithm

intervals

Results

23.0ms	56×	body	10240	exit
15.0ms	256×	body	80	valid
15.0ms	325×	body	80	nan

simplify2.7s

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	110	9
5	248	9
6	724	9
7	2612	9
done	5000	9

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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))

rewrite13.0ms

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:

4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series103.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
23.0ms	(pow (sqrt (atan2 b b)) (- b a))
17.0ms	(sqrt (atan2 b b))

simplify1.6s

Counts

57 → 57

Iterations

Useful iterations: 3 (154.0ms)

Iter	Nodes	Cost
0	75	614
1	148	571
2	343	536
3	806	527
4	2373	527
done	5001	527

prune131.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

rewrite39.0ms

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:

5.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
26.0ms	(* (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))

series88.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
37.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
14.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify2.2s

Counts

174 → 174

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	144	3870
1	293	2885
2	984	2741
3	4113	2692
done	5000	2692

prune352.0ms

Pruning

3 alts after pruning (3 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)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)))
0.0b	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

169×	`unpow-prod-down`
133×	`add-sqr-sqrt`
120×	`sqrt-prod`
96×	`cbrt-prod`
65×	`unswap-sqr`
55×	`cube-prod`
39×	`associate-r`
35×	`sqr-pow`
29×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-l`
11×	`add-exp-log`
10×	`unpow-prod-up`
6×	`pow1` `add-cbrt-cube`
5×	`sub-neg` `pow-exp` `pow-sub`
4×	`add-log-exp`
3×	`cube-div` `pow-to-exp` `pow-unpow` `prod-exp`
2×	`cube-mult` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `unpow3`
1×	`frac-times` `pow-pow` `associate-r/` `associate-l/` `*-commutative` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 210

Calls

4 calls:

55.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)))
6.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series107.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)))
51.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify819.0ms

Counts

222 → 222

Iterations

Useful iterations: 2 (245.0ms)

Iter	Nodes	Cost
0	190	6132
1	446	5013
2	1687	4518
done	5000	4518

prune431.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (* (- b a) 3))
0.0b	(* (- b a) 3)
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`sqrt-prod`
13×	`*-un-lft-identity`
11×	`pow1` `add-cube-cbrt`
9×	`unpow-prod-down`
7×	`add-exp-log`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-pow` `associate-l`
4×	`pow1/2` `add-log-exp`
3×	`associate-r`
2×	`rem-sqrt-square` `associate-*l/`
1×	`pow-to-exp` `pow-unpow` `flip3--` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

5.0ms	(pow (sqrt (sqrt (atan2 b b))) (* (- b a) 3))
10.0ms	(* (- b a) 3)
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series77.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (sqrt (sqrt (atan2 b b))) (* (- b a) 3))
27.0ms	(* (- b a) 3)
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify1.4s

Counts

86 → 86

Iterations

Useful iterations: 3 (615.0ms)

Iter	Nodes	Cost
0	114	880
1	254	775
2	754	733
3	2349	726
done	5000	726

prune242.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes112.0ms

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: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	15	23
done	15	23

end0.0ms

sample2.0s

Algorithm

intervals

Results

720.0ms	1753×	body	10240	exit
447.0ms	9664×	body	80	nan
438.0ms	7986×	body	80	valid
6.0ms	2×	body	5120	valid
1.0ms	3×	body	640	valid
1.0ms	6×	body	160	valid
1.0ms	1×	body	1280	valid
0.0ms	2×	body	320	valid