Details

sample155.0ms

Algorithm

intervals

Results

57.0ms	58×	body	10240	exit
33.0ms	327×	body	80	nan
30.0ms	256×	body	80	valid

simplify571.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

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:

38.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
14.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series145.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
33.0ms	(pow (sqrt (atan2 b b)) (- b a))
21.0ms	(sqrt (atan2 b b))

simplify2.1s

Counts: 57 → 57

prune186.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
87×	`unpow-prod-down`
82×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`unswap-sqr`
23×	`swap-sqr`
17×	`add-exp-log`
15×	`associate-r` `associate-l` `sqr-pow`
14×	`unpow-prod-up`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`pow1/2` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 162

Calls

4 calls:

16.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
79.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series132.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
56.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
16.0ms	(sqrt (atan2 b b))
23.0ms	(sqrt (atan2 b b))

simplify689.0ms

Counts: 174 → 174

prune569.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (* (pow 1 (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
9×	`unpow-prod-down`
8×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow-pow` `sqrt-pow1`
4×	`unpow-prod-up` `add-exp-log`
3×	`pow1/2` `add-cbrt-cube` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

3 → 50

Calls

3 calls:

50.0ms	(sin (* (pow 1 (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
7.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0ms	(sqrt (atan2 b b))

series8.6m

Counts

3 → 9

Calls

3 calls:

8.6m	(sin (* (pow 1 (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
53.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
12.0ms	(sqrt (atan2 b b))

simplify989.0ms

Counts: 59 → 59

prune169.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (- b a) (log (sqrt (atan2 b b)))))
0.2b	(* (- b a) (log (sqrt (atan2 b b))))
1.0b	(sqrt (atan2 b b))
2.0b	(log (sqrt (atan2 b b)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`sqrt-prod`
17×	`add-cube-cbrt`
12×	`distribute-rgt-in` `distribute-lft-in` `exp-sum`
11×	`pow1`
8×	`add-log-exp`
7×	`add-exp-log`
6×	`associate-r` `log-pow` `add-cbrt-cube`
5×	`associate-l`
3×	`sqrt-pow1` `pow1/2`
2×	`exp-to-pow` `associate-*l/`
1×	`rem-sqrt-square` `exp-prod` `flip3--` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

11.0ms	(exp (* (- b a) (log (sqrt (atan2 b b)))))
30.0ms	(* (- b a) (log (sqrt (atan2 b b))))
1.0ms	(sqrt (atan2 b b))
2.0ms	(log (sqrt (atan2 b b)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(exp (* (- b a) (log (sqrt (atan2 b b)))))
72.0ms	(* (- b a) (log (sqrt (atan2 b b))))
11.0ms	(sqrt (atan2 b b))
73.0ms	(log (sqrt (atan2 b b)))

simplify818.0ms

Counts: 102 → 102

prune244.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify776.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.0s	1777×	body	10240	exit
759.0ms	7988×	body	80	valid
754.0ms	9788×	body	80	nan
11.0ms	4×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	5×	body	160	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid

Details

sample155.0ms

simplify571.0ms

prune3.0ms

localize10.0ms

rewrite55.0ms

series145.0ms

simplify2.1s

prune186.0ms

localize35.0ms

rewrite119.0ms

series132.0ms

simplify689.0ms

prune569.0ms

localize19.0ms

rewrite60.0ms

series8.6m

simplify989.0ms

prune169.0ms

localize15.0ms

rewrite47.0ms

series179.0ms

simplify818.0ms

prune244.0ms

regimes35.0ms

bsearch0.0ms

simplify776.0ms

end0.0ms

sample3.1s

end1.2m