Details

sample78.0ms

Algorithm

intervals

Results

26.0ms	51×	body	10240	exit
19.0ms	256×	body	80	valid
18.0ms	300×	body	80	nan

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5019
6	1161
5	250
4	110
3	45
2	22
1	13
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))

rewrite15.0ms

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:

9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series112.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
33.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sqrt (atan2 b b))

simplify2.4s

Counts

60 → 60

Iterations

Iter	Nodes
done	5032
4	3465
3	1051
2	391
1	184
0	78

prune278.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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))

rewrite21.0ms

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:

8.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
5.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series98.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
43.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
11.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify3.7s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
4	3943
3	1208
2	490
1	214
0	84

prune582.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `pow1` `unpow-prod-down` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
2×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 24

Calls

2 calls:

19.0ms	(sin (pow (atan2 b b) (* (- b a) 1/2)))
7.0ms	(pow (atan2 b b) (* (- b a) 1/2))

series142.0ms

Counts

2 → 6

Calls

2 calls:

107.0ms	(sin (pow (atan2 b b) (* (- b a) 1/2)))
35.0ms	(pow (atan2 b b) (* (- b a) 1/2))

simplify3.4s

Counts

30 → 30

Iterations

Iter	Nodes
done	5010
4	4092
3	1071
2	325
1	136
0	59

prune193.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (pow (atan2 b b) (* (- b a) 1/2))) (cbrt (pow (atan2 b b) (* (- b a) 1/2))))
0.3b	(cbrt (pow (atan2 b b) (* (- b a) 1/2)))
0.3b	(cbrt (pow (atan2 b b) (* (- b a) 1/2)))
0.3b	(cbrt (pow (atan2 b b) (* (- b a) 1/2)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`*-un-lft-identity` `add-cube-cbrt`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 113

Calls

4 calls:

30.0ms	(* (cbrt (pow (atan2 b b) (* (- b a) 1/2))) (cbrt (pow (atan2 b b) (* (- b a) 1/2))))
3.0ms	(cbrt (pow (atan2 b b) (* (- b a) 1/2)))
3.0ms	(cbrt (pow (atan2 b b) (* (- b a) 1/2)))
4.0ms	(cbrt (pow (atan2 b b) (* (- b a) 1/2)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (cbrt (pow (atan2 b b) (* (- b a) 1/2))) (cbrt (pow (atan2 b b) (* (- b a) 1/2))))
53.0ms	(cbrt (pow (atan2 b b) (* (- b a) 1/2)))
60.0ms	(cbrt (pow (atan2 b b) (* (- b a) 1/2)))
48.0ms	(cbrt (pow (atan2 b b) (* (- b a) 1/2)))

simplify3.3s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
4	4893
3	1471
2	532
1	219
0	107

prune665.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes74.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
0	9

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.8s	1881×	body	10240	exit
1.6s	9841×	body	80	nan
1.4s	7992×	body	80	valid
3.0ms	1×	body	5120	valid
2.0ms	2×	body	1280	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid
0.0ms	1×	body	640	valid