Details

sample122.0ms

Algorithm

intervals

Results

36.0ms	62×	body	10240	exit
27.0ms	306×	body	80	nan
25.0ms	255×	body	80	valid
3.0ms	1×	body	5120	valid

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

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:

18.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))

series126.0ms

Counts

2 → 6

Calls

2 calls:

113.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
13.0ms	(sqrt (atan2 b b))

simplify4.2s

Counts

26 → 26

Iterations

Useful iterations: 3 (59.0ms)

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

prune95.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

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))

rewrite27.0ms

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:

14.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series211.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
91.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms	(sqrt (atan2 b b))
16.0ms	(sqrt (atan2 b b))

simplify4.1s

Counts

52 → 52

Iterations

Useful iterations: 3 (57.0ms)

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

prune278.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

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)))

rewrite72.0ms

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:

52.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0ms	(sqrt (atan2 b b))
14.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
2.0ms	(log (sqrt (atan2 b b)))

series654.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
16.0ms	(sqrt (atan2 b b))
251.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
106.0ms	(log (sqrt (atan2 b b)))

simplify2.7s

Counts

101 → 101

Iterations

Useful iterations: 2 (142.0ms)

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

prune325.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
2.0b	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

66×	`sqrt-pow1`
56×	`pow1`
44×	`log-pow`
34×	`pow1/2`
25×	`associate-r`
18×	`pow-prod-up`
12×	`add-sqr-sqrt`
11×	`pow-prod-down`
10×	`pow-sqr`
9×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod` `add-cbrt-cube`
4×	`add-log-exp`
3×	`log-prod` `associate-l`
2×	`pow2` `rem-sqrt-square` `pow-plus` `rem-log-exp` `prod-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

92.0ms	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
24.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
12.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))
94.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

simplify2.7s

Counts

112 → 112

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	93	1083
1	173	699
2	481	647
3	2510	647
done	5002	647

prune393.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes109.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	21
done	9	21

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.9s	1890×	body	10240	exit
1.5s	9694×	body	80	nan
1.5s	7992×	body	80	valid
6.0ms	2×	body	5120	valid
5.0ms	2×	body	2560	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid