Details

sample82.0ms

Algorithm

intervals

Results

31.0ms	58×	body	10240	exit
16.0ms	321×	body	80	nan
15.0ms	255×	body	80	valid
3.0ms	1×	body	5120	valid

simplify5.8s

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	270	9
6	1202	9
7	4218	9
done	5000	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.3b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite15.0ms

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:

5.0ms	(pow (sqrt (atan2 b b)) (- b a))
7.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series106.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(pow (sqrt (atan2 b b)) (- b a))
68.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(sqrt (atan2 b b))

simplify2.2s

Counts

72 → 72

Iterations

Useful iterations: 3 (428.0ms)

Iter	Nodes	Cost
0	117	962
1	260	840
2	702	748
3	2398	710
done	5001	710

prune166.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.3b	(sin (* (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))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
84×	`sqrt-prod`
78×	`unpow-prod-down`
48×	`unpow-prod-up`
46×	`add-cube-cbrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
16×	`add-exp-log`
14×	`sqr-pow`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 171

Calls

4 calls:

45.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
9.0ms	(sin (* (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))

series201.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
124.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
15.0ms	(sqrt (atan2 b b))
17.0ms	(sqrt (atan2 b b))

simplify2.0s

Counts

183 → 183

Iterations

Useful iterations: 2 (177.0ms)

Iter	Nodes	Cost
0	209	4894
1	462	3407
2	1797	3064
done	5000	3064

prune461.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3))
0.0b	(pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3)
0.3b	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
1.0b	(sqrt (atan2 b b))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `unpow-prod-down` `cube-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 72

Calls

4 calls:

14.0ms	(cbrt (pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3))
16.0ms	(pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3)
13.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
1.0ms	(sqrt (atan2 b b))

series390.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cbrt (pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3))
173.0ms	(pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3)
122.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
13.0ms	(sqrt (atan2 b b))

simplify2.9s

Counts

84 → 84

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	107	1571
1	232	1363
2	764	1216
3	4423	1168
done	5000	1164

prune240.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3))
0.0b	(pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3)
0.3b	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
1.0b	(sqrt (atan2 b b))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `unpow-prod-down` `cube-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 72

Calls

4 calls:

13.0ms	(cbrt (pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3))
14.0ms	(pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3)
13.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
1.0ms	(sqrt (atan2 b b))

series313.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(cbrt (pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3))
147.0ms	(pow (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) 3)
78.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
11.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

84 → 84

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	107	1571
1	232	1363
2	764	1216
3	4423	1168
done	5000	1164

prune246.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes48.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
done	9	20

end0.0ms

sample2.2s

Algorithm

intervals

Results

849.0ms	1866×	body	10240	exit
502.0ms	10105×	body	80	nan
477.0ms	7995×	body	80	valid
7.0ms	2×	body	5120	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid