Details

sample67.0ms

Algorithm

intervals

Results

24.0ms	56×	body	10240	exit
14.0ms	306×	body	80	nan
14.0ms	256×	body	80	valid

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	110	9
5	268	9
6	748	9
7	2674	9
done	5000	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`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 → 63

Calls

3 calls:

6.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series93.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
20.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(sqrt (atan2 b b))

simplify3.0s

Counts

72 → 72

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	117	962
1	256	840
2	554	757
3	1309	728
4	4013	699
done	5000	699

prune155.0ms

Pruning

2 alts after pruning (2 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))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
93×	`sqrt-prod`
87×	`unpow-prod-down`
59×	`unpow-prod-up`
58×	`*-un-lft-identity`
56×	`add-cube-cbrt`
45×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
17×	`add-exp-log`
15×	`sqr-pow`
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×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `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 → 206

Calls

4 calls:

6.0ms	(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)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series89.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(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)))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify1.5s

Counts

218 → 218

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	210	5420
1	462	3909
2	1644	3574
done	5001	3547

prune487.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
36×	`prod-diff`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
22×	`distribute-rgt-in` `distribute-lft-in` `exp-sum`
11×	`pow1`
7×	`add-exp-log`
6×	`log-prod` `associate-l` `sqrt-prod` `log-pow` `add-cbrt-cube`
5×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
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 → 117

Calls

4 calls:

5.0ms	(exp (* (log (sqrt (atan2 b b))) (- b a)))
13.0ms	(* (log (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(log (sqrt (atan2 b b)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (* (log (sqrt (atan2 b b))) (- b a)))
70.0ms	(* (log (sqrt (atan2 b b))) (- b a))
10.0ms	(sqrt (atan2 b b))
66.0ms	(log (sqrt (atan2 b b)))

simplify1.6s

Counts

129 → 129

Iterations

Useful iterations: 3 (709.0ms)

Iter	Nodes	Cost
0	172	2253
1	316	1766
2	814	1513
3	2786	1411
done	5000	1411

prune227.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

101×	`unpow-prod-down`
88×	`add-sqr-sqrt`
69×	`sqrt-prod`
35×	`unswap-sqr`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
24×	`add-exp-log` `associate-l`
22×	`unpow-prod-up`
21×	`sqr-pow`
18×	`prod-diff` `pow-exp`
17×	`associate-r`
15×	`prod-exp`
12×	`pow-to-exp`
9×	`pow1`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `rem-sqrt-square` `pow-sub`
1×	`associate-l/` `-commutative` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 177

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
47.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series636.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
588.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify857.0ms

Counts

189 → 189

Iterations

Useful iterations: done (851.0ms)

Iter	Nodes	Cost
0	239	5195
1	564	4897
2	1777	4550
done	5001	4524

prune522.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	10	11
done	10	11

end0.0ms

sample1.9s

Algorithm

intervals

Results

722.0ms	1811×	body	10240	exit
425.0ms	9846×	body	80	nan
425.0ms	7989×	body	80	valid
10.0ms	2×	body	5120	valid
1.0ms	2×	body	1280	valid
1.0ms	1×	body	2560	valid
1.0ms	2×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid