Details

sample184.0ms

Algorithm

intervals

Results

80.0ms	80×	body	10240	exit
22.0ms	328×	body	80	nan
18.0ms	256×	body	80	valid

simplify43.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b	(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:

11.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
7.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series130.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
27.0ms	(pow (sqrt (atan2 b b)) (- b a))
32.0ms	(sqrt (atan2 b b))

simplify41.0ms

Counts: 57 → 57

prune136.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b	(pow (sqrt (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

24×	`sqrt-prod`
20×	`add-sqr-sqrt`
18×	`unpow-prod-down` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`add-exp-log` `pow1/2`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

13.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
9.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series89.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
33.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
12.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify45.0ms

Counts: 104 → 104

prune293.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
2.9b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
24×	`sqrt-prod`
18×	`unpow-prod-down`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity` `exp-sum`
6×	`pow1` `add-exp-log`
4×	`unpow-prod-up` `exp-prod` `add-cbrt-cube` `add-log-exp`
3×	`rem-log-exp`
2×	`sub-neg` `rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `log-pow` `pow-sub` `sqr-pow`
1×	`pow-to-exp` `exp-diff` `pow-exp` `rem-exp-log`

Counts

4 → 81

Calls

4 calls:

8.0ms	(exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
7.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
94.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify41.0ms

Counts: 93 → 93

prune303.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- b a))
0.5b	(cbrt (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`cbrt-prod`
8×	`add-cube-cbrt`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

4.0ms	(cbrt (- b a))
4.0ms	(cbrt (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series351.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (- b a))
159.0ms	(cbrt (- b a))
12.0ms	(sqrt (atan2 b b))
17.0ms	(sqrt (atan2 b b))

simplify105.0ms

Counts: 68 → 68

prune286.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.8s	1870×	body	10240	exit
866.0ms	9847×	body	80	nan
756.0ms	7993×	body	80	valid
3.0ms	1×	body	5120	valid
1.0ms	2×	body	1280	valid
1.0ms	1×	body	2560	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid