Details

sample386.0ms

Algorithm

intervals

Results

110.0ms	48×	body	10240	exit
99.0ms	320×	body	80	nan
33.0ms	256×	body	80	valid

simplify118.0ms

Counts: 1 → 1

prune4.0ms

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))

rewrite25.0ms

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:

8.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

series134.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(pow (sqrt (atan2 b b)) (- b a))
75.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
34.0ms	(sqrt (atan2 b b))

simplify84.0ms

Counts: 57 → 57

prune163.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

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))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

4×	`unpow-prod-up`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 26

Calls

2 calls:

9.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
31.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

series103.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
78.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify168.0ms

Counts: 32 → 32

prune124.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`cbrt-prod`
29×	`sqrt-prod`
19×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
11×	`swap-sqr`
9×	`associate-r` `associate-l` `unswap-sqr`
6×	`add-exp-log` `pow1/3`
4×	`add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
20.0ms	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))
22.0ms	(sqrt (atan2 b b))
179.0ms	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

simplify67.0ms

Counts: 107 → 107

prune531.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

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)))

rewrite81.0ms

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:

59.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
2.0ms	(sqrt (atan2 b b))
15.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
2.0ms	(log (sqrt (atan2 b b)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
13.0ms	(sqrt (atan2 b b))
273.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
100.0ms	(log (sqrt (atan2 b b)))

simplify120.0ms

Counts: 101 → 101

prune347.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify53.0ms

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.7s	9977×	body	80	nan
1.7s	1840×	body	10240	exit
1.5s	7987×	body	80	valid
5.0ms	2×	body	2560	valid
2.0ms	6×	body	160	valid
1.0ms	2×	body	640	valid
1.0ms	2×	body	320	valid
1.0ms	1×	body	1280	valid