Details

sample135.0ms

Algorithm

intervals

Results

39.0ms	54×	body	10240	exit
38.0ms	308×	body	80	nan
23.0ms	254×	body	80	valid
5.0ms	1×	body	5120	valid
0.0ms	1×	body	160	valid

simplify592.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.5b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite19.0ms

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:

7.0ms	(pow (sqrt (atan2 b b)) (- b a))
10.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series161.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(pow (sqrt (atan2 b b)) (- b a))
108.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
12.0ms	(sqrt (atan2 b b))

simplify674.0ms

Counts: 57 → 57

prune179.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))
1.0b	(sqrt (atan2 b b))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity`
8×	`add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3--` `pow1/3` `sqrt-prod` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

7.0ms	(cbrt (- b a))
8.0ms	(cbrt (- b a))
8.0ms	(cbrt (- b a))
2.0ms	(sqrt (atan2 b b))

series630.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt (- b a))
235.0ms	(cbrt (- b a))
184.0ms	(cbrt (- b a))
14.0ms	(sqrt (atan2 b b))

simplify1.4s

Counts: 70 → 70

prune463.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- b a))
0.7b	(pow (pow (sqrt (atan2 b b)) (* (cbrt (- b a)) (cbrt (- b a)))) (pow b 1/3))
1.0b	(sqrt (atan2 b b))
5.1b	(pow b 1/3)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-down`
16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
10×	`pow-unpow`
7×	`add-exp-log`
6×	`pow1` `sqrt-prod`
5×	`cbrt-prod` `pow-exp`
4×	`add-cbrt-cube` `add-log-exp` `sqr-pow`
3×	`pow-to-exp`
2×	`cbrt-div` `pow-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `unpow1/3` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

8.0ms	(cbrt (- b a))
19.0ms	(pow (pow (sqrt (atan2 b b)) (* (cbrt (- b a)) (cbrt (- b a)))) (pow b 1/3))
2.0ms	(sqrt (atan2 b b))
5.0ms	(pow b 1/3)

series1.8s

Counts

4 → 12

Calls

4 calls:

210.0ms	(cbrt (- b a))
1.3s	(pow (pow (sqrt (atan2 b b)) (* (cbrt (- b a)) (cbrt (- b a)))) (pow b 1/3))
27.0ms	(sqrt (atan2 b b))
287.0ms	(pow b 1/3)

simplify669.0ms

Counts: 88 → 88

prune464.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(* (cos 1) (log (sqrt (atan2 b b))))
2.0b	(log (sqrt (atan2 b b)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

46.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0ms	(sqrt (atan2 b b))
21.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
2.0ms	(log (sqrt (atan2 b b)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
12.0ms	(sqrt (atan2 b b))
215.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
92.0ms	(log (sqrt (atan2 b b)))

simplify658.0ms

Counts: 101 → 101

prune295.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes122.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify927.0ms

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.8s	1800×	body	10240	exit
1.6s	9851×	body	80	nan
1.3s	7987×	body	80	valid
9.0ms	2×	body	5120	valid
3.0ms	2×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	320	valid