Details

sample275.0ms

Algorithm

intervals

Results

92.0ms	306×	body	80	nan
46.0ms	62×	body	10240	exit
28.0ms	255×	body	80	valid
7.0ms	1×	body	5120	valid

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	115	9
5	268	9
6	834	9
7	3197	9
done	5001	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

2 → 20

Calls

2 calls:

12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

series152.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
34.0ms	(sqrt (atan2 b b))

simplify4.3s

Counts

26 → 26

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	37	238
1	61	224
2	102	204
3	172	195
4	273	195
5	478	195
6	1126	195
7	3829	195
done	5000	195

prune106.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 40

Calls

4 calls:

10.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
13.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series231.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
104.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify4.6s

Counts

52 → 52

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	37	476
1	61	448
2	102	408
3	172	390
4	273	390
5	478	390
6	1126	390
7	3829	390
done	5000	390

prune269.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

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)))

rewrite82.0ms

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:

38.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
2.0ms	(sqrt (atan2 b b))
28.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
8.0ms	(log (sqrt (atan2 b b)))

series740.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
15.0ms	(sqrt (atan2 b b))
289.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
114.0ms	(log (sqrt (atan2 b b)))

simplify3.2s

Counts

101 → 101

Iterations

Useful iterations: 2 (211.0ms)

Iter	Nodes	Cost
0	119	1237
1	240	1183
2	842	1012
3	3049	1012
done	5000	1012

prune358.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

42.0ms	(* (* (cos 1) (log (log (exp (sqrt (atan2 b b)))))) (- b a))
36.0ms	(* (cos 1) (log (log (exp (sqrt (atan2 b b))))))
1.0ms	(sqrt (atan2 b b))
4.0ms	(log (log (exp (sqrt (atan2 b b)))))

series629.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(* (* (cos 1) (log (log (exp (sqrt (atan2 b b)))))) (- b a))
240.0ms	(* (cos 1) (log (log (exp (sqrt (atan2 b b))))))
20.0ms	(sqrt (atan2 b b))
107.0ms	(log (log (exp (sqrt (atan2 b b)))))

simplify2.6s

Counts

109 → 109

Iterations

Useful iterations: 2 (166.0ms)

Iter	Nodes	Cost
0	147	1617
1	269	1341
2	868	1146
3	3035	1146
done	5000	1146

prune401.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes107.0ms

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	21
done	9	21

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.0s	1890×	body	10240	exit
1.5s	9694×	body	80	nan
1.1s	7992×	body	80	valid
8.0ms	2×	body	5120	valid
3.0ms	2×	body	2560	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid