Details

sample153.0ms

Algorithm

intervals

Results

47.0ms	46×	body	10240	exit
45.0ms	256×	body	80	valid
42.0ms	312×	body	80	nan

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
7	2433
6	740
5	248
4	110
3	45
2	22
1	13
0	7

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

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))

rewrite28.0ms

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` `insert-posit16` `add-log-exp`
2×	`unpow-prod-up` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 51

Calls

3 calls:

15.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
9.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series173.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
37.0ms	(pow (sqrt (atan2 b b)) (- b a))
25.0ms	(sqrt (atan2 b b))

simplify975.0ms

Counts

60 → 60

Iterations

Iter	Nodes
4	2133
3	900
2	409
1	182
0	78

prune556.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

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))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite16.0ms

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×	`pow1/2` `add-exp-log`
4×	`unpow-prod-up` `add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

5.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series92.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
40.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify1.7s

Counts

108 → 108

Iterations

Iter	Nodes
4	3383
3	1233
2	517
1	212
0	84

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (- b a) (/ (log (atan2 b b)) 4)))
0.2b	(* (- b a) (/ (log (atan2 b b)) 4))
1.0b	(sqrt (atan2 b b))
1.6b	(log (atan2 b b))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`associate-r`
15×	`add-cube-cbrt`
13×	`times-frac`
11×	`pow1`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
5×	`associate-l`
4×	`log-pow` `insert-posit16`
3×	`log-prod` `sqrt-prod`
2×	`frac-times` `flip3--` `exp-to-pow` `associate-*l/` `prod-exp` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `exp-prod` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

4 → 81

Calls

4 calls:

15.0ms	(exp (* (- b a) (/ (log (atan2 b b)) 4)))
44.0ms	(* (- b a) (/ (log (atan2 b b)) 4))
2.0ms	(sqrt (atan2 b b))
2.0ms	(log (atan2 b b))

series201.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(exp (* (- b a) (/ (log (atan2 b b)) 4)))
82.0ms	(* (- b a) (/ (log (atan2 b b)) 4))
23.0ms	(sqrt (atan2 b b))
72.0ms	(log (atan2 b b))

simplify1.4s

Counts

93 → 93

Iterations

Iter	Nodes
3	3494
2	949
1	310
0	133

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

1.6b	(log (atan2 b b))
1.6b	(cbrt (log (atan2 b b)))
1.6b	(cbrt (log (atan2 b b)))
1.6b	(cbrt (log (atan2 b b)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
5×	`add-exp-log`
4×	`add-cbrt-cube` `log-pow` `insert-posit16` `add-log-exp`
3×	`log-prod` `pow1/3`
1×	`rem-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(log (atan2 b b))
1.0ms	(cbrt (log (atan2 b b)))
1.0ms	(cbrt (log (atan2 b b)))
1.0ms	(cbrt (log (atan2 b b)))

series762.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(log (atan2 b b))
221.0ms	(cbrt (log (atan2 b b)))
212.0ms	(cbrt (log (atan2 b b)))
241.0ms	(cbrt (log (atan2 b b)))

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
5	2406
4	445
3	134
2	74
1	43
0	31

prune948.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes88.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	21
1	21
0	17

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.7s	1808×	body	10240	exit
2.2s	9757×	body	80	nan
1.5s	7990×	body	80	valid
12.0ms	3×	body	5120	valid
4.0ms	4×	body	640	valid
2.0ms	1×	body	2560	valid
1.0ms	2×	body	320	valid