Details

sample168.0ms

Algorithm

intervals

Results

57.0ms	380×	body	80	nan
51.0ms	64×	body	10240	exit
32.0ms	256×	body	80	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	492
1	13	492
2	22	492
3	45	492
4	110	492
5	256	492
6	1114	492
done	5001	492

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

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` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 63

Calls

3 calls:

12.0ms	(pow (sqrt (atan2 b b)) (- b a))
13.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series126.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(pow (sqrt (atan2 b b)) (- b a))
87.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
15.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

72 → 72

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	117	39662
1	307	37381
2	677	35659
3	1701	35629
done	5001	35099

prune400.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (* 1/2 (- b a)))
0.0b	(sin (pow (atan2 b b) (* 1/2 (- b a))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-up`
18×	`prod-diff`
15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
3×	`pow1` `unpow-prod-down` `add-exp-log`
2×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 48

Calls

2 calls:

6.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
14.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

series117.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
78.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify3.8s

Counts

54 → 54

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	144	42527
1	354	40203
2	794	35577
3	2730	35472
done	5025	34217

prune216.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- b a) (log (atan2 b b)))
1.6b	(log (atan2 b b))
1.6b	(log (atan2 b b))
1.6b	(log (atan2 b b))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `log-prod`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`pow1`
9×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `rem-log-exp`
2×	`associate-*l/`
1×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

18.0ms	(* (- b a) (log (atan2 b b)))
1.0ms	(log (atan2 b b))
1.0ms	(log (atan2 b b))
1.0ms	(log (atan2 b b))

series325.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (- b a) (log (atan2 b b)))
63.0ms	(log (atan2 b b))
78.0ms	(log (atan2 b b))
89.0ms	(log (atan2 b b))

simplify2.5s

Counts

85 → 85

Iterations

Useful iterations: 3 (557.0ms)

Iter	Nodes	Cost
0	70	28072
1	143	26889
2	386	26605
3	1507	26525
done	5000	26525

prune621.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes77.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	493
1	9	493
done	9	493

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.0s	1909×	body	10240	exit
1.4s	7992×	body	80	valid
1.1s	9995×	body	80	nan
2.0ms	4×	body	640	valid
1.0ms	4×	body	160	valid